From 3701531fb1f805bfb83b5942d3d6862dbf68293b Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 21 Nov 2025 15:35:54 +0100 Subject: [PATCH 01/63] move old examples to separate folder --- examples/{ => old_examples}/maxwell_2d_multi_patch.py | 0 examples/{ => old_examples}/poisson_1d.py | 0 .../poisson_2d_jacobi_iteration/plot_cart_poisson.py | 0 .../poisson_2d_jacobi_iteration/test_cart_poisson.py | 0 examples/{ => old_examples}/poisson_2d_mapping.py | 0 examples/{ => old_examples}/poisson_2d_multi_patch.py | 0 examples/{ => old_examples}/poisson_3d_multi_patch.py | 0 examples/{ => old_examples}/poisson_3d_target_torus.py | 0 examples/{ => old_examples}/sample_multi_patch_parallel.py | 0 examples/{ => old_examples}/test_cg_perf.py | 0 examples/{ => old_examples}/test_mass_matrix.py | 0 examples/{ => old_examples}/visualize_matrices.py | 0 12 files changed, 0 insertions(+), 0 deletions(-) rename examples/{ => old_examples}/maxwell_2d_multi_patch.py (100%) rename examples/{ => old_examples}/poisson_1d.py (100%) rename examples/{ => old_examples}/poisson_2d_jacobi_iteration/plot_cart_poisson.py (100%) rename examples/{ => old_examples}/poisson_2d_jacobi_iteration/test_cart_poisson.py (100%) rename examples/{ => old_examples}/poisson_2d_mapping.py (100%) rename examples/{ => old_examples}/poisson_2d_multi_patch.py (100%) rename examples/{ => old_examples}/poisson_3d_multi_patch.py (100%) rename examples/{ => old_examples}/poisson_3d_target_torus.py (100%) rename examples/{ => old_examples}/sample_multi_patch_parallel.py (100%) rename examples/{ => old_examples}/test_cg_perf.py (100%) rename examples/{ => old_examples}/test_mass_matrix.py (100%) rename examples/{ => old_examples}/visualize_matrices.py (100%) diff --git a/examples/maxwell_2d_multi_patch.py b/examples/old_examples/maxwell_2d_multi_patch.py similarity index 100% rename from examples/maxwell_2d_multi_patch.py rename to examples/old_examples/maxwell_2d_multi_patch.py diff --git a/examples/poisson_1d.py b/examples/old_examples/poisson_1d.py similarity index 100% rename from examples/poisson_1d.py rename to examples/old_examples/poisson_1d.py diff --git a/examples/poisson_2d_jacobi_iteration/plot_cart_poisson.py b/examples/old_examples/poisson_2d_jacobi_iteration/plot_cart_poisson.py similarity index 100% rename from examples/poisson_2d_jacobi_iteration/plot_cart_poisson.py rename to examples/old_examples/poisson_2d_jacobi_iteration/plot_cart_poisson.py diff --git a/examples/poisson_2d_jacobi_iteration/test_cart_poisson.py b/examples/old_examples/poisson_2d_jacobi_iteration/test_cart_poisson.py similarity index 100% rename from examples/poisson_2d_jacobi_iteration/test_cart_poisson.py rename to examples/old_examples/poisson_2d_jacobi_iteration/test_cart_poisson.py diff --git a/examples/poisson_2d_mapping.py b/examples/old_examples/poisson_2d_mapping.py similarity index 100% rename from examples/poisson_2d_mapping.py rename to examples/old_examples/poisson_2d_mapping.py diff --git a/examples/poisson_2d_multi_patch.py b/examples/old_examples/poisson_2d_multi_patch.py similarity index 100% rename from examples/poisson_2d_multi_patch.py rename to examples/old_examples/poisson_2d_multi_patch.py diff --git a/examples/poisson_3d_multi_patch.py b/examples/old_examples/poisson_3d_multi_patch.py similarity index 100% rename from examples/poisson_3d_multi_patch.py rename to examples/old_examples/poisson_3d_multi_patch.py diff --git a/examples/poisson_3d_target_torus.py b/examples/old_examples/poisson_3d_target_torus.py similarity index 100% rename from examples/poisson_3d_target_torus.py rename to examples/old_examples/poisson_3d_target_torus.py diff --git a/examples/sample_multi_patch_parallel.py b/examples/old_examples/sample_multi_patch_parallel.py similarity index 100% rename from examples/sample_multi_patch_parallel.py rename to examples/old_examples/sample_multi_patch_parallel.py diff --git a/examples/test_cg_perf.py b/examples/old_examples/test_cg_perf.py similarity index 100% rename from examples/test_cg_perf.py rename to examples/old_examples/test_cg_perf.py diff --git a/examples/test_mass_matrix.py b/examples/old_examples/test_mass_matrix.py similarity index 100% rename from examples/test_mass_matrix.py rename to examples/old_examples/test_mass_matrix.py diff --git a/examples/visualize_matrices.py b/examples/old_examples/visualize_matrices.py similarity index 100% rename from examples/visualize_matrices.py rename to examples/old_examples/visualize_matrices.py From 0096b01f95484b1f1da8f111cde545c6faeec9d1 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 21 Nov 2025 15:37:32 +0100 Subject: [PATCH 02/63] move performance scripts to examples folder --- .../performance}/compare_3d_matrix_assembly_speed.py | 0 .../performance}/matrix_assembly_speed_log.md | 0 {performance => examples/performance}/test_perf_1d.py | 0 {performance => examples/performance}/test_perf_2d.py | 0 {performance => examples/performance}/test_perf_2d_parallel.py | 0 {performance => examples/performance}/test_perf_3d.py | 0 6 files changed, 0 insertions(+), 0 deletions(-) rename {performance => examples/performance}/compare_3d_matrix_assembly_speed.py (100%) rename {performance => examples/performance}/matrix_assembly_speed_log.md (100%) rename {performance => examples/performance}/test_perf_1d.py (100%) rename {performance => examples/performance}/test_perf_2d.py (100%) rename {performance => examples/performance}/test_perf_2d_parallel.py (100%) rename {performance => examples/performance}/test_perf_3d.py (100%) diff --git a/performance/compare_3d_matrix_assembly_speed.py b/examples/performance/compare_3d_matrix_assembly_speed.py similarity index 100% rename from performance/compare_3d_matrix_assembly_speed.py rename to examples/performance/compare_3d_matrix_assembly_speed.py diff --git a/performance/matrix_assembly_speed_log.md b/examples/performance/matrix_assembly_speed_log.md similarity index 100% rename from performance/matrix_assembly_speed_log.md rename to examples/performance/matrix_assembly_speed_log.md diff --git a/performance/test_perf_1d.py b/examples/performance/test_perf_1d.py similarity index 100% rename from performance/test_perf_1d.py rename to examples/performance/test_perf_1d.py diff --git a/performance/test_perf_2d.py b/examples/performance/test_perf_2d.py similarity index 100% rename from performance/test_perf_2d.py rename to examples/performance/test_perf_2d.py diff --git a/performance/test_perf_2d_parallel.py b/examples/performance/test_perf_2d_parallel.py similarity index 100% rename from performance/test_perf_2d_parallel.py rename to examples/performance/test_perf_2d_parallel.py diff --git a/performance/test_perf_3d.py b/examples/performance/test_perf_3d.py similarity index 100% rename from performance/test_perf_3d.py rename to examples/performance/test_perf_3d.py From 7c75c0eb279d0c909dbae01be1b4f306a168c2d5 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 10:03:57 +0100 Subject: [PATCH 03/63] try nbsphinx --- docs/requirements.txt | 2 ++ docs/source/conf.py | 1 + docs/source/examples.rst | 6 ++++++ 3 files changed, 9 insertions(+) diff --git a/docs/requirements.txt b/docs/requirements.txt index 2cfa37e55..b8a28b763 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -3,3 +3,5 @@ pydata_sphinx_theme numpydoc tomli sphinx-math-dollar +nbsphinx +ipykernel \ No newline at end of file diff --git a/docs/source/conf.py b/docs/source/conf.py index ca5f7955d..02ab5a0a0 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -52,6 +52,7 @@ def fixed_init(self, app): 'sphinx.ext.githubpages', 'sphinx_math_dollar', 'sphinx.ext.mathjax', +'nbsphinx', ] from docutils.nodes import FixedTextElement, literal,math diff --git a/docs/source/examples.rst b/docs/source/examples.rst index d05be7e0f..a09375165 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -4,3 +4,9 @@ Examples +------------------------------------------------------------------------------------------------------------------------+ | Here you will find examples of how to use PSYDAC and explanations thereof as well as links to notebooks in the future. | +------------------------------------------------------------------------------------------------------------------------+ + +.. toctree:: + :maxdepth: 1 + :caption: Notebooks: + + ../examples/notebooks/Poisson_non_periodic.ipynb From f5dc200e830e8b529dd8647dd98d9fc34f90888b Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 10:21:01 +0100 Subject: [PATCH 04/63] copy notebooks into docs by CI --- .github/workflows/documentation.yml | 3 +++ docs/source/examples.rst | 6 ++++-- 2 files changed, 7 insertions(+), 2 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index 41896bbb9..71c1417c8 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -39,6 +39,9 @@ jobs: - name: Install Python dependencies run: | python -m pip install -r docs/requirements.txt + - name: Copy Notebooks + run: | + cp -r examples/notebooks/* docs/source/ - name: Make the sphinx doc run: | rm -rf docs/source/modules/STUBDIR diff --git a/docs/source/examples.rst b/docs/source/examples.rst index a09375165..451ec90f8 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -3,10 +3,12 @@ Examples +------------------------------------------------------------------------------------------------------------------------+ | Here you will find examples of how to use PSYDAC and explanations thereof as well as links to notebooks in the future. | -+------------------------------------------------------------------------------------------------------------------------+ ++------------------------------------------------------------------------------------------------------------------------+ +.. The notebooks get copied into the source directory by the continuous integration pipeline. .. toctree:: :maxdepth: 1 :caption: Notebooks: - ../examples/notebooks/Poisson_non_periodic.ipynb + Poisson_non_periodic + Helmholtz_non_periodic From a6dbd86b57f134492fddd7ff1f876b2b1808a8d5 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 10:22:57 +0100 Subject: [PATCH 05/63] also install pandoc --- docs/requirements.txt | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/requirements.txt b/docs/requirements.txt index b8a28b763..073a2a0bb 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -4,4 +4,5 @@ numpydoc tomli sphinx-math-dollar nbsphinx -ipykernel \ No newline at end of file +ipykernel +pandoc \ No newline at end of file From 06559fe616854a51ae4f0e5dde938d2c334551b4 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 10:26:03 +0100 Subject: [PATCH 06/63] install pandoc globally --- .github/workflows/documentation.yml | 2 +- docs/requirements.txt | 3 +-- 2 files changed, 2 insertions(+), 3 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index 71c1417c8..66c0e37c4 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -35,7 +35,7 @@ jobs: - name: Install non-Python dependencies on Ubuntu run: | sudo apt update - sudo apt install graphviz + sudo apt install graphviz pandoc - name: Install Python dependencies run: | python -m pip install -r docs/requirements.txt diff --git a/docs/requirements.txt b/docs/requirements.txt index 073a2a0bb..b8a28b763 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -4,5 +4,4 @@ numpydoc tomli sphinx-math-dollar nbsphinx -ipykernel -pandoc \ No newline at end of file +ipykernel \ No newline at end of file From 6bb798d326c19415232da4005f5d32c9c794a9d1 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 10:34:13 +0100 Subject: [PATCH 07/63] clear notebook output --- docs/source/examples.rst | 1 + .../notebooks/Helmholtz_non_periodic.ipynb | 42 +++++++------------ examples/notebooks/Poisson_non_periodic.ipynb | 41 ++++-------------- 3 files changed, 24 insertions(+), 60 deletions(-) diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 451ec90f8..9a68a1869 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -6,6 +6,7 @@ Examples +------------------------------------------------------------------------------------------------------------------------+ .. The notebooks get copied into the source directory by the continuous integration pipeline. +.. The notebooks should have all output cleared before being committed to the repository. .. toctree:: :maxdepth: 1 :caption: Notebooks: diff --git a/examples/notebooks/Helmholtz_non_periodic.ipynb b/examples/notebooks/Helmholtz_non_periodic.ipynb index e680e0eb7..1a02f2e01 100644 --- a/examples/notebooks/Helmholtz_non_periodic.ipynb +++ b/examples/notebooks/Helmholtz_non_periodic.ipynb @@ -18,7 +18,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -37,7 +37,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -95,7 +95,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -145,21 +145,9 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "> CG info :: {'niter': 46, 'success': True, 'res_norm': 5.330478803717119e-15}\n", - "> L2 error :: 2.07e-07\n", - "> H1 error :: 3.80e-05\n", - "> Solution time :: 3.76e+00s\n", - "> Evaluat. time :: 4.00e-01s \n" - ] - } - ], + "outputs": [], "source": [ "# Set the solver parameters\n", "# 'cbig' -> Biconjugate gradient method\n", @@ -193,7 +181,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -228,7 +216,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -283,13 +271,18 @@ " \n", "

" ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [] } ], "metadata": { "kernelspec": { - "display_name": "v_psydac", + "display_name": "venv3.13", "language": "python", - "name": "v_psydac" + "name": "python3" }, "language_info": { "codemirror_mode": { @@ -301,12 +294,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.10.6" - }, - "vscode": { - "interpreter": { - "hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a" - } + "version": "3.13.7" } }, "nbformat": 4, diff --git a/examples/notebooks/Poisson_non_periodic.ipynb b/examples/notebooks/Poisson_non_periodic.ipynb index 873b73374..c042b68b8 100644 --- a/examples/notebooks/Poisson_non_periodic.ipynb +++ b/examples/notebooks/Poisson_non_periodic.ipynb @@ -18,22 +18,9 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], + "outputs": [], "source": [ "import numpy as np\n", "\n", @@ -78,7 +65,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -137,7 +124,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -187,21 +174,9 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": null, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "> CG info :: {'niter': 109, 'success': True, 'res_norm': 5.704506834276634e-15}\n", - "> L2 error :: 9.14e-02\n", - "> H1 error :: 1.62e+00\n", - "> Solution time :: 1.42e+01s\n", - "> Evaluat. time :: 4.73e-01s \n" - ] - } - ], + "outputs": [], "source": [ "# Set the solver parameters\n", "# 'cg' -> Conjugate gradient method\n", @@ -235,7 +210,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ @@ -270,7 +245,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": null, "metadata": {}, "outputs": [], "source": [ From 33a5a6597bba86b9b680aee36d6e756c144a840c Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 11:06:22 +0100 Subject: [PATCH 08/63] install psydac in doc ci --- .github/workflows/documentation.yml | 109 +++++++++++++++++++++++++++- 1 file changed, 106 insertions(+), 3 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index 66c0e37c4..36567688a 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -25,31 +25,134 @@ jobs: runs-on: ubuntu-latest env: GITHUB_PAT: ${{ secrets.GITHUB_TOKEN}} + PSYDAC_MESH_DIR: ${{ github.workspace }}/mesh + OMP_NUM_THREADS: 2 steps: - name: Checkout - uses: actions/checkout@v4 + uses: actions/checkout@v5 + - name: Set up Python uses: actions/setup-python@v5 with: python-version: 3.9 + cache: 'pip' + cache-dependency-path: | + pyproject.toml + requirements.txt + requirements_extra.txt + - name: Install non-Python dependencies on Ubuntu + uses: awalsh128/cache-apt-pkgs-action@latest + with: + packages: gfortran openmpi-bin libopenmpi-dev libhdf5-openmpi-dev + version: 1.0 + execute_install_scripts: true + + - name: Reconfigure non-Python dependencies on Ubuntu run: | - sudo apt update + sudo apt-get update + sudo apt-get install --reinstall openmpi-bin libhdf5-openmpi-dev liblapack-dev libblas-dev sudo apt install graphviz pandoc - - name: Install Python dependencies + + - name: Print information on MPI and HDF5 libraries + run: | + ompi_info + h5pcc -showconfig -echo || true + + - name: Upgrade pip, setuptools, and wheel + run: | + python -m pip install --upgrade pip setuptools wheel + + - name: Determine directory of parallel HDF5 library + run: | + if [[ "${{ matrix.os }}" == "ubuntu-24.04" ]]; then + HDF5_DIR=$(dpkg -L libhdf5-openmpi-dev | grep libhdf5.so | xargs dirname) + elif [[ "${{ matrix.os }}" == "macos-14" ]]; then + HDF5_DIR=$(brew list hdf5-mpi | grep "libhdf5.dylib" | xargs dirname | xargs dirname) + fi + echo $HDF5_DIR + echo "HDF5_DIR=$HDF5_DIR" >> $GITHUB_ENV + + - name: Cache PETSc + uses: actions/cache@v4 + id: cache-petsc + env: + cache-name: cache-PETSc + with: + path: "./petsc" + key: petsc-${{ matrix.os }}-${{ matrix.python-version }} + + - if: steps.cache-petsc.outputs.cache-hit != 'true' + name: Download a specific release of PETSc + run: | + git clone --depth 1 --branch v3.23.2 https://gitlab.com/petsc/petsc.git + + - if: steps.cache-petsc.outputs.cache-hit != 'true' + name: Install PETSc with complex support + working-directory: ./petsc + run: | + export PETSC_DIR=$(pwd) + export PETSC_ARCH=petsc-cmplx + ./configure --with-scalar-type=complex --with-fortran-bindings=0 --have-numpy=1 + make all + echo "PETSC_DIR=$PETSC_DIR" > petsc.env + echo "PETSC_ARCH=$PETSC_ARCH" >> petsc.env + + # This step is not really necessary and could be combined with PETSc install + # step; however it's good to verify if the cached PETSc installation really works! + - name: Test PETSc installation + working-directory: ./petsc + run: | + source petsc.env + make check + echo "PETSC_DIR=$PETSC_DIR" >> $GITHUB_ENV + echo "PETSC_ARCH=$PETSC_ARCH" >> $GITHUB_ENV + + - name: Install petsc4py + working-directory: ./petsc + run: | + python -m pip install wheel Cython numpy + python -m pip install src/binding/petsc4py + + - name: Install h5py in parallel mode + run: | + export CC="mpicc" + export HDF5_MPI="ON" + python -m pip install h5py --no-cache-dir --no-binary h5py + python -m pip list + + - name: Check parallel h5py installation + run: | + python -c " + from mpi4py import MPI + import h5py + # This particular instantiation of h5py.File will fail if parallel h5py isn't installed + f = h5py.File('parallel_test.hdf5', 'w', driver='mpio', comm=MPI.COMM_WORLD) + print(f)" + + - name: Install project + run: | + python -m pip install .[test] + python -m pip freeze + + - name: Install Python dependencies for Documentation run: | python -m pip install -r docs/requirements.txt + - name: Copy Notebooks run: | cp -r examples/notebooks/* docs/source/ + - name: Make the sphinx doc run: | rm -rf docs/source/modules/STUBDIR make -C docs clean make -C docs html python docs/update_links.py + - name: Setup Pages uses: actions/configure-pages@v5 + - name: Upload artifact uses: actions/upload-pages-artifact@v3 with: From cad20f813c8d4fb83f92dc6ba9c78f455e0731e6 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 11:28:45 +0100 Subject: [PATCH 09/63] remove metadata using nb-clean --- .../notebooks/Helmholtz_non_periodic.ipynb | 20 +-------------- examples/notebooks/Poisson_non_periodic.ipynb | 25 +------------------ 2 files changed, 2 insertions(+), 43 deletions(-) diff --git a/examples/notebooks/Helmholtz_non_periodic.ipynb b/examples/notebooks/Helmholtz_non_periodic.ipynb index 1a02f2e01..8ff504869 100644 --- a/examples/notebooks/Helmholtz_non_periodic.ipynb +++ b/examples/notebooks/Helmholtz_non_periodic.ipynb @@ -278,25 +278,7 @@ "source": [] } ], - "metadata": { - "kernelspec": { - "display_name": "venv3.13", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.13.7" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 4 } diff --git a/examples/notebooks/Poisson_non_periodic.ipynb b/examples/notebooks/Poisson_non_periodic.ipynb index c042b68b8..764830d91 100644 --- a/examples/notebooks/Poisson_non_periodic.ipynb +++ b/examples/notebooks/Poisson_non_periodic.ipynb @@ -286,30 +286,7 @@ ] } ], - "metadata": { - "kernelspec": { - "display_name": "v_psydac", - "language": "python", - "name": "v_psydac" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.6" - }, - "vscode": { - "interpreter": { - "hash": "e7370f93d1d0cde622a1f8e1c04877d8463912d04d973331ad4851f04de6915a" - } - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 4 } From 36d672af7d52dd276e870efed3ebf4851e7dd99d Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 11:32:24 +0100 Subject: [PATCH 10/63] change cp folder --- .github/workflows/documentation.yml | 5 +++-- docs/source/examples.rst | 4 ++-- 2 files changed, 5 insertions(+), 4 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index 36567688a..98e669c69 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -141,7 +141,8 @@ jobs: - name: Copy Notebooks run: | - cp -r examples/notebooks/* docs/source/ + mkdir docs/source/examples + cp -r examples/notebooks/* docs/source/examples/ - name: Make the sphinx doc run: | @@ -152,7 +153,7 @@ jobs: - name: Setup Pages uses: actions/configure-pages@v5 - + - name: Upload artifact uses: actions/upload-pages-artifact@v3 with: diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 9a68a1869..e9e417ebd 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -11,5 +11,5 @@ Examples :maxdepth: 1 :caption: Notebooks: - Poisson_non_periodic - Helmholtz_non_periodic + examples/Poisson_non_periodic + examples/Helmholtz_non_periodic From ebd11950ee321c5b9e42eae7e494ff84dc763efa Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 13:59:40 +0100 Subject: [PATCH 11/63] fix error in notebook and test ipytest --- docs/requirements.txt | 3 +- examples/notebooks/Poisson_non_periodic.ipynb | 50 +++++++++++++++++-- 2 files changed, 49 insertions(+), 4 deletions(-) diff --git a/docs/requirements.txt b/docs/requirements.txt index b8a28b763..e28506761 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -4,4 +4,5 @@ numpydoc tomli sphinx-math-dollar nbsphinx -ipykernel \ No newline at end of file +ipykernel +ipytest \ No newline at end of file diff --git a/examples/notebooks/Poisson_non_periodic.ipynb b/examples/notebooks/Poisson_non_periodic.ipynb index 764830d91..7837cfb12 100644 --- a/examples/notebooks/Poisson_non_periodic.ipynb +++ b/examples/notebooks/Poisson_non_periodic.ipynb @@ -39,14 +39,14 @@ "\n", "# Second quarter annulus\n", "domain_log_2 = Square('A_2', bounds1=(0., 1.), bounds2=(np.pi, 3/2 * np.pi))\n", - "F_2 = PolarMapping('F_1', dim=2, c1=rmin+rmax, c2=0., rmin=rmin, rmax=rmax)\n", + "F_2 = PolarMapping('F_2', dim=2, c1=rmin+rmax, c2=0., rmin=rmax, rmax=rmin)\n", "Omega_2 = F_2(domain_log_2)\n", "\n", "# Join the patches\n", "\n", "from sympde import Domain\n", - "connectivity = [((0,1,1),(1,1,-1))]\n", - "patches = [Omega_1,Omega_2]\n", + "connectivity = [((0,1,-1),(1,1,-1), 1)]\n", + "patches = [Omega_1, Omega_2]\n", "Omega = Domain.join(patches, connectivity, 'domain')\n", "\n", "# Example of a complex multi-patch domain\n", @@ -272,6 +272,50 @@ "Pm.close()" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "__file__ = \"Poisson_non_periodic.ipynb\"\n", + "\n", + "import ipytest\n", + "import pytest\n", + "\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_pass():\n", + " assert True\n", + "\n", + "def test_fail():\n", + " assert False" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_l2error():\n", + " assert l2_error < 3e-05\n", + "\n", + "def test_h1error():\n", + " assert h1_error < 2e-03" + ] + }, { "cell_type": "markdown", "metadata": {}, From 986607024c032426ea0b9e2ecf74148aa94f00ce Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 14:07:21 +0100 Subject: [PATCH 12/63] remove failing test from notebook --- examples/notebooks/Poisson_non_periodic.ipynb | 15 --------------- 1 file changed, 15 deletions(-) diff --git a/examples/notebooks/Poisson_non_periodic.ipynb b/examples/notebooks/Poisson_non_periodic.ipynb index 7837cfb12..3e269d221 100644 --- a/examples/notebooks/Poisson_non_periodic.ipynb +++ b/examples/notebooks/Poisson_non_periodic.ipynb @@ -286,21 +286,6 @@ "ipytest.autoconfig(raise_on_error=True)" ] }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [ - "%%ipytest\n", - "\n", - "def test_pass():\n", - " assert True\n", - "\n", - "def test_fail():\n", - " assert False" - ] - }, { "cell_type": "code", "execution_count": null, From c4b08e223ceddd758b88bdb4ff6095a6ee3959d2 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 25 Nov 2025 14:32:30 +0100 Subject: [PATCH 13/63] make the notebook tests a little nicer --- examples/notebooks/Poisson_non_periodic.ipynb | 37 ++++++++++--------- 1 file changed, 20 insertions(+), 17 deletions(-) diff --git a/examples/notebooks/Poisson_non_periodic.ipynb b/examples/notebooks/Poisson_non_periodic.ipynb index 3e269d221..2c6134d71 100644 --- a/examples/notebooks/Poisson_non_periodic.ipynb +++ b/examples/notebooks/Poisson_non_periodic.ipynb @@ -272,17 +272,33 @@ "Pm.close()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Example: Results on the pretzel domain\n", + "\n", + "

\n", + " \n", + " \n", + " \n", + "

" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Testing the notebook" + ] + }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ - "__file__ = \"Poisson_non_periodic.ipynb\"\n", - "\n", "import ipytest\n", - "import pytest\n", - "\n", "ipytest.autoconfig(raise_on_error=True)" ] }, @@ -300,19 +316,6 @@ "def test_h1error():\n", " assert h1_error < 2e-03" ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Example: Results on the pretzel domain\n", - "\n", - "

\n", - " \n", - " \n", - " \n", - "

" - ] } ], "metadata": {}, From 44e676002ddd52e39a9f233d9bc6c7ef83c21edd Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Thu, 27 Nov 2025 14:49:49 +0100 Subject: [PATCH 14/63] remove performance folder from header script --- scripts/add_header.py | 1 - 1 file changed, 1 deletion(-) diff --git a/scripts/add_header.py b/scripts/add_header.py index 8708a9709..18e49dd29 100644 --- a/scripts/add_header.py +++ b/scripts/add_header.py @@ -45,4 +45,3 @@ def add_header_to_python_files(directory, string_to_add, *, dry_run=True): add_header_to_python_files('../psydac' , header, dry_run=dry_run) add_header_to_python_files('../examples' , header, dry_run=dry_run) add_header_to_python_files('../mesh' , header, dry_run=dry_run) - add_header_to_python_files('../performance', header, dry_run=dry_run) From f00c89c8cf8c399fcd149da298ac41700c0813f7 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Thu, 27 Nov 2025 15:41:21 +0100 Subject: [PATCH 15/63] add test to Helmholtz notebook --- .../notebooks/Helmholtz_non_periodic.ipynb | 29 ++++++++++++++++++- 1 file changed, 28 insertions(+), 1 deletion(-) diff --git a/examples/notebooks/Helmholtz_non_periodic.ipynb b/examples/notebooks/Helmholtz_non_periodic.ipynb index 8ff504869..6a0c19d97 100644 --- a/examples/notebooks/Helmholtz_non_periodic.ipynb +++ b/examples/notebooks/Helmholtz_non_periodic.ipynb @@ -275,7 +275,34 @@ { "cell_type": "markdown", "metadata": {}, - "source": [] + "source": [ + "### Testing the notebook" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import ipytest\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_l2error():\n", + " assert l2_error < 3e-07\n", + "\n", + "def test_h1error():\n", + " assert h1_error < 4e-05" + ] } ], "metadata": {}, From 97fe8bc1b4aa6463547236059dcc8e86a4af3555 Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Fri, 28 Nov 2025 19:06:09 +0100 Subject: [PATCH 16/63] add notebook with example of L2 fem projection --- examples/notebooks/fem_L2_projection.ipynb | 195 +++++++++++++++++++++ 1 file changed, 195 insertions(+) create mode 100644 examples/notebooks/fem_L2_projection.ipynb diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb new file mode 100644 index 000000000..93076a47a --- /dev/null +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -0,0 +1,195 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2443e734", + "metadata": {}, + "source": [ + "# Projecting a function onto a finite element space\n", + "\n", + "In this notebook we show how to define a scalar FEM space over a given (discretized) domain, how to plot some basis functions, assemble a mass matrix and compute the L2 projection of a given function \n", + "\n", + "## Step 1 : define the domain and discretize it\n", + "\n", + "This is similar to what is done in other examples" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3f2bc988", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "from sympde.topology import Square, PolarMapping\n", + "from sympde.utilities.utils import plot_domain\n", + "\n", + "from psydac.api.tests.build_domain import build_pretzel\n", + "\n", + "# Define the topological geometry for each patch\n", + "rmin, rmax = 0.3, 1.\n", + "\n", + "# First quarter annulus\n", + "domain_log_1 = Square('A_1', bounds1=(0., 1.), bounds2=(0., np.pi/2))\n", + "F_1 = PolarMapping('F_1', dim=2, c1=0., c2=0., rmin=rmin, rmax=rmax)\n", + "Omega_1 = F_1(domain_log_1)\n", + "\n", + "# Second quarter annulus\n", + "domain_log_2 = Square('A_2', bounds1=(0., 1.), bounds2=(np.pi, 3/2 * np.pi))\n", + "F_2 = PolarMapping('F_2', dim=2, c1=rmin+rmax, c2=0., rmin=rmax, rmax=rmin)\n", + "Omega_2 = F_2(domain_log_2)\n", + "\n", + "# Join the patches\n", + "\n", + "# [remark] this could be an opportunity to describe how the interfaces of a domain are numbered\n", + "from sympde import Domain\n", + "connectivity = [((0,1,-1),(1,1,-1), 1)]\n", + "patches = [Omega_1, Omega_2]\n", + "Omega = Domain.join(patches, connectivity, 'domain')\n", + "\n", + "# Example of a complex multi-patch domain\n", + "# Omega = build_pretzel()\n", + "\n", + "# Simple visualization of the topological domain\n", + "plot_domain(Omega, draw=False, isolines=True)" + ] + }, + { + "cell_type": "markdown", + "id": "b1f65c13", + "metadata": {}, + "source": [ + "## Step 2 : define a FEM space and plot some basis functions\n", + "\n", + "[this could actually be a good opportunity to present how the indices work in psydac arrays]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "39c21151", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.topology import ScalarFunctionSpace\n", + "\n", + "from psydac.linalg.utilities import array_to_psydac\n", + "from psydac.api.discretization import discretize\n", + "from psydac.fem.basic import FemField\n", + "from psydac.fem.plotting_utilities import plot_field_2d as plot_field\n", + "\n", + "# the kind argument also specifies the pushforward defining the FEM space on the physical domain\n", + "# kind=None results in a (scalar, vector?) space defined by a simple change of variable (0-form pushforward)\n", + "V = ScalarFunctionSpace('V', Omega, kind=None)\n", + "\n", + "ncells = [10, 10]\n", + "degree = [2, 2]\n", + "\n", + "# [remark] for multipatch domains the periodic flag is a priori unrelevant, should raise an error / warning \n", + "# periodic = [ False, True]\n", + "periodic = [False, False] \n", + "\n", + "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic)\n", + "Vh = discretize(V, Omega_h, degree=degree)\n", + "\n", + "npatches = len(Vh.patch_spaces)\n", + "for k in range(npatches):\n", + " knots = Vh.patch_spaces[k].knots[0]\n", + " print(f'Spline knots (logical coords) along axis 0 in patch {k}: \\n {knots}')\n", + "\n", + "# plot some basis function from the space \n", + "# [remark] here I'm using numpy arrays, but one could illustrate the psydac indexing\n", + "bf_c = np.zeros(Vh.nbasis)\n", + "bf_c[Vh.nbasis//4] = 1\n", + "bf_c[Vh.nbasis//4+6] = 1\n", + "bf = FemField(Vh, coeffs=array_to_psydac(bf_c, Vh.coeff_space))\n", + "\n", + "plot_field(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, title='two basis functions', hide_plot=False)\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "id": "36a9632b", + "metadata": {}, + "source": [ + "## Step 3 : compute the mass matrix\n", + "\n", + "we assemble the mass matrix and visualize it" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "091d4560", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "from matplotlib import cm, colors\n", + "\n", + "from sympde.topology import elements_of\n", + "from sympde.expr.expr import BilinearForm\n", + "from sympde.expr.expr import integral \n", + "\n", + "from psydac.api.settings import PSYDAC_BACKENDS\n", + "\n", + "backend_language = 'python'\n", + "backend = PSYDAC_BACKENDS[backend_language]\n", + "\n", + "# domain = V.domain # = Omega\n", + "u, v = elements_of(V, names='u, v')\n", + "a = BilinearForm((u, v), integral(Omega, u * v))\n", + "ah = discretize(a, Omega_h, [Vh, Vh], backend=backend)\n", + "\n", + "M = ah.assemble() # Mass matrix in stencil format (linear operator)\n", + "\n", + "# visualize the mass matrix by plotting its numpy conversion\n", + "mat = M.toarray()\n", + "\n", + "#----------------\n", + "fig,ax = plt.subplots(1,1)\n", + "ax.set_title(f\"Mass matrix M on the domain with {npatches} patch(es)\")\n", + "im = ax.matshow(mat, norm=colors.LogNorm(), cmap='hot_r')\n", + "cb = fig.colorbar(im, ax=ax)\n", + "fig.show()" + ] + }, + { + "cell_type": "markdown", + "id": "dae32f1c", + "metadata": {}, + "source": [ + "## Step 4 : compute the moments of a given target function and its L2 projection\n", + "\n", + "we invert the mass matrix on the moments of a given function f" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "db7f74ca", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.linalg.solvers import inverse\n", + "from psydac.fem.projectors import get_dual_dofs\n", + "\n", + "x,y = Omega.coordinates\n", + "ref_f = (x-1/2)**2 + y**2\n", + "tilde_f = get_dual_dofs(Vh=Vh, f=ref_f, domain_h=Omega_h, backend_language=backend_language)\n", + "\n", + "inv_M = inverse(M, solver='cg')\n", + "\n", + "f_h = inv_M @ tilde_f\n", + "\n", + "plot_field(stencil_coeffs=f_h, Vh=Vh, space_kind='h1', domain=Omega, title='f_h: L2 projection of f', hide_plot=False)" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} From e4fc59df1ae15ca2dd55a751ee57c8fbe7d7bc83 Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Fri, 28 Nov 2025 21:18:30 +0100 Subject: [PATCH 17/63] added the case of a vector-valued space --- examples/notebooks/fem_L2_projection.ipynb | 135 ++++++++++++++++++++- 1 file changed, 129 insertions(+), 6 deletions(-) diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb index 93076a47a..27d3d1d19 100644 --- a/examples/notebooks/fem_L2_projection.ipynb +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -66,6 +66,14 @@ "[this could actually be a good opportunity to present how the indices work in psydac arrays]" ] }, + { + "cell_type": "markdown", + "id": "a8ea7ee6", + "metadata": {}, + "source": [ + "We first define a scalar-valued FEM space V" + ] + }, { "cell_type": "code", "execution_count": null, @@ -73,7 +81,7 @@ "metadata": {}, "outputs": [], "source": [ - "from sympde.topology import ScalarFunctionSpace\n", + "from sympde.topology import ScalarFunctionSpace, VectorFunctionSpace\n", "\n", "from psydac.linalg.utilities import array_to_psydac\n", "from psydac.api.discretization import discretize\n", @@ -106,8 +114,39 @@ "bf_c[Vh.nbasis//4+6] = 1\n", "bf = FemField(Vh, coeffs=array_to_psydac(bf_c, Vh.coeff_space))\n", "\n", - "plot_field(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, title='two basis functions', hide_plot=False)\n", - "\n" + "plot_field(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, title='two basis functions', hide_plot=False)" + ] + }, + { + "cell_type": "markdown", + "id": "1de55bc2", + "metadata": {}, + "source": [ + "Then we define a vector-valued FEM space W" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d4b778e1", + "metadata": {}, + "outputs": [], + "source": [ + "\n", + "W = VectorFunctionSpace('W', Omega, kind=None) # a priori 2d vectors\n", + "Wh = discretize(W, Omega_h, degree=degree)\n", + "\n", + "# plot some basis function from the space \n", + "# [remark] here I'm using numpy arrays, but one could illustrate the psydac indexing\n", + "dim_Wh = Wh.nbasis\n", + "bf2_c = np.zeros(dim_Wh)\n", + "bf2_c[dim_Wh//4+5] = 1\n", + "bf2_c[dim_Wh//4+42] = 1\n", + "bf2_c[dim_Wh//4+102] = 1\n", + "bf2 = FemField(Wh, coeffs=array_to_psydac(bf2_c, Wh.coeff_space))\n", + "\n", + "plot_field(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", + " plot_type='components', title='three basis vector functions', hide_plot=False)\n" ] }, { @@ -117,7 +156,7 @@ "source": [ "## Step 3 : compute the mass matrix\n", "\n", - "we assemble the mass matrix and visualize it" + "We assemble the mass matrix and visualize it. Again we start with the scalar-valued FEM space" ] }, { @@ -139,7 +178,6 @@ "backend_language = 'python'\n", "backend = PSYDAC_BACKENDS[backend_language]\n", "\n", - "# domain = V.domain # = Omega\n", "u, v = elements_of(V, names='u, v')\n", "a = BilinearForm((u, v), integral(Omega, u * v))\n", "ah = discretize(a, Omega_h, [Vh, Vh], backend=backend)\n", @@ -154,6 +192,42 @@ "ax.set_title(f\"Mass matrix M on the domain with {npatches} patch(es)\")\n", "im = ax.matshow(mat, norm=colors.LogNorm(), cmap='hot_r')\n", "cb = fig.colorbar(im, ax=ax)\n", + "fig.show()\n" + ] + }, + { + "cell_type": "markdown", + "id": "57f85041", + "metadata": {}, + "source": [ + "We next assemble the mass matrix of the vector-valued FEM space" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "aa017e79", + "metadata": {}, + "outputs": [], + "source": [ + "## and we do the same for the vector-valued space W\n", + "\n", + "from sympde.calculus import dot\n", + "\n", + "u, v = elements_of(W, names='u, v')\n", + "a = BilinearForm((u, v), integral(Omega, dot(u,v)))\n", + "ah_W = discretize(a, Omega_h, [Wh, Wh], backend=backend)\n", + "\n", + "M_W = ah_W.assemble() # Mass matrix in stencil format (linear operator)\n", + "\n", + "# visualize the mass matrix by plotting its numpy conversion\n", + "mat_W = M_W.toarray()\n", + "\n", + "#----------------\n", + "fig,ax = plt.subplots(1,1)\n", + "ax.set_title(f\"Mass matrix M on the domain with {npatches} patch(es)\")\n", + "im = ax.matshow(mat_W, norm=colors.LogNorm(), cmap='hot_r')\n", + "cb = fig.colorbar(im, ax=ax)\n", "fig.show()" ] }, @@ -164,7 +238,7 @@ "source": [ "## Step 4 : compute the moments of a given target function and its L2 projection\n", "\n", - "we invert the mass matrix on the moments of a given function f" + "we invert the mass matrix on the moments of a given function f: first for the scalar-valued space" ] }, { @@ -187,6 +261,55 @@ "\n", "plot_field(stencil_coeffs=f_h, Vh=Vh, space_kind='h1', domain=Omega, title='f_h: L2 projection of f', hide_plot=False)" ] + }, + { + "cell_type": "markdown", + "id": "8258971a", + "metadata": {}, + "source": [ + "next for the vector-valued space" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f0f103d", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import pi, cos, sin, Tuple, exp, atan\n", + "\n", + "envelope = exp(-(x-.6)**2 / (2 * 0.15**2))\n", + "ref_gx = envelope * cos(2*pi*y)\n", + "ref_gy = envelope * 1\n", + "\n", + "ref_g = Tuple(ref_gx, ref_gy)\n", + "\n", + "tilde_g = get_dual_dofs(Vh=Wh, f=ref_g, domain_h=Omega_h, backend_language=backend_language)\n", + "\n", + "inv_M_W = inverse(M_W, solver='cg')\n", + "\n", + "g_h = inv_M_W @ tilde_g\n", + "\n", + "# plot_field(fem_field=, Vh=Wh, space_kind=None, domain=Omega, \n", + "# plot_type='components', title='two basis vector functions', hide_plot=False)\n", + "\n", + "plot_field(stencil_coeffs=g_h, Vh=Wh, space_kind='h1', domain=Omega, \n", + " plot_type='vector_field', title='g_h: L2 projection of g', hide_plot=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c77d25a", + "metadata": {}, + "outputs": [], + "source": [ + "# note: specifying a different space_kind is possible but will a priori result in inconsistent pushforward\n", + "\n", + "plot_field(stencil_coeffs=g_h, Vh=Wh, space_kind='hcurl', domain=Omega, \n", + " plot_type='vector_field', title='g_h: L2 projection of g with inconsistent pushforward', hide_plot=False)" + ] } ], "metadata": {}, From cbc527a6e1a09d79b701f448fca730f6b7a9cb3c Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 11:20:17 +0100 Subject: [PATCH 18/63] test transparency in docs logo --- README.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/README.md b/README.md index 8c891942f..1c634b6c6 100644 --- a/README.md +++ b/README.md @@ -1,5 +1,5 @@

-Shows the psydac logo. +Shows the psydac logo.


[![devel_tests](https://github.com/pyccel/psydac/actions/workflows/testing.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/testing.yml) [![docs](https://github.com/pyccel/psydac/actions/workflows/documentation.yml/badge.svg)](https://github.com/pyccel/psydac/actions/workflows/documentation.yml) From ce6ce7b22e888169c83a8cc3659b25b73bb0ba3c Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 11:37:16 +0100 Subject: [PATCH 19/63] enable github annotations in doc --- docs/requirements.txt | 1 + docs/source/conf.py | 2 ++ 2 files changed, 3 insertions(+) diff --git a/docs/requirements.txt b/docs/requirements.txt index a0ea40da1..ff96a8e57 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -7,3 +7,4 @@ nbsphinx ipykernel ipytest myst-parser +click-extra[sphinx] diff --git a/docs/source/conf.py b/docs/source/conf.py index c3c0c9272..a537bf79e 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -54,6 +54,7 @@ def fixed_init(self, app): 'sphinx.ext.mathjax', 'nbsphinx', 'myst_parser', +"click_extra.sphinx", ] from docutils.nodes import FixedTextElement, literal,math @@ -99,6 +100,7 @@ def fixed_init(self, app): # -- Options for myst_parser ------------------------------------------------- myst_heading_anchors = 3 +myst_enable_extensions = ["colon_fence"] # -- Options for autodoc extension ------------------------------------------- autodoc_member_order = 'bysource' From 43160456c294e60ec2407b1302e88b458da8c33a Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 11:56:31 +0100 Subject: [PATCH 20/63] don't specify parser --- docs/source/index.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/index.rst b/docs/source/index.rst index d3a66c26f..e4007bfa5 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -14,7 +14,7 @@ Welcome to PSYDAC's documentation! For the time being, its purpose is to assist the developers. .. include:: ../../README.md - :parser: myst_parser.sphinx_ + .. :parser: myst_parser.sphinx_ .. toctree:: From c7839760a2ef6415aa1fc9ca39c547c8c136e8bc Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 13:14:30 +0100 Subject: [PATCH 21/63] add new notebook; change md to rst files --- docs/requirements.txt | 1 - docs/source/conf.py | 2 - docs/source/examples.rst | 8 +- docs/source/index.rst | 7 +- docs/source/installation.rst | 245 +++++++++++++++++++++++++++++++++++ docs/source/output.rst | 184 ++++++++++++++++++++++++++ docs/source/psydac-mesh.rst | 11 ++ 7 files changed, 450 insertions(+), 8 deletions(-) create mode 100644 docs/source/installation.rst create mode 100644 docs/source/output.rst create mode 100644 docs/source/psydac-mesh.rst diff --git a/docs/requirements.txt b/docs/requirements.txt index ff96a8e57..a0ea40da1 100644 --- a/docs/requirements.txt +++ b/docs/requirements.txt @@ -7,4 +7,3 @@ nbsphinx ipykernel ipytest myst-parser -click-extra[sphinx] diff --git a/docs/source/conf.py b/docs/source/conf.py index a537bf79e..c3c0c9272 100644 --- a/docs/source/conf.py +++ b/docs/source/conf.py @@ -54,7 +54,6 @@ def fixed_init(self, app): 'sphinx.ext.mathjax', 'nbsphinx', 'myst_parser', -"click_extra.sphinx", ] from docutils.nodes import FixedTextElement, literal,math @@ -100,7 +99,6 @@ def fixed_init(self, app): # -- Options for myst_parser ------------------------------------------------- myst_heading_anchors = 3 -myst_enable_extensions = ["colon_fence"] # -- Options for autodoc extension ------------------------------------------- autodoc_member_order = 'bysource' diff --git a/docs/source/examples.rst b/docs/source/examples.rst index e9e417ebd..1db3d852a 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -1,9 +1,9 @@ Examples ======== -+------------------------------------------------------------------------------------------------------------------------+ -| Here you will find examples of how to use PSYDAC and explanations thereof as well as links to notebooks in the future. | -+------------------------------------------------------------------------------------------------------------------------+ +.. +------------------------------------------------------------------------------------------------------------------------+ +.. | Here you will find examples of how to use PSYDAC and explanations thereof as well as links to notebooks in the future. | +.. +------------------------------------------------------------------------------------------------------------------------+ .. The notebooks get copied into the source directory by the continuous integration pipeline. .. The notebooks should have all output cleared before being committed to the repository. @@ -13,3 +13,5 @@ Examples examples/Poisson_non_periodic examples/Helmholtz_non_periodic + examples/fem_l2_projection + \ No newline at end of file diff --git a/docs/source/index.rst b/docs/source/index.rst index e4007bfa5..d34b1e063 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -14,13 +14,16 @@ Welcome to PSYDAC's documentation! For the time being, its purpose is to assist the developers. .. include:: ../../README.md - .. :parser: myst_parser.sphinx_ + :parser: myst_parser.sphinx_ .. toctree:: :maxdepth: 1 :hidden: - modules + installation + output examples + modules + psydac-mesh maintenance diff --git a/docs/source/installation.rst b/docs/source/installation.rst new file mode 100644 index 000000000..de9c01e31 --- /dev/null +++ b/docs/source/installation.rst @@ -0,0 +1,245 @@ + +Installation +============ + + +* `Requirements <#requirements>`_ +* `Python setup and project download <#python-setup-and-project-download>`_ +* `Installing the library <#installing-the-library>`_ +* `Optional PETSc installation <#optional-petsc-installation>`_ +* `Uninstall <#uninstall>`_ + +Requirements +------------ + +Psydac requires a certain number of components to be installed on the machine: + + +* Fortran and C compilers with OpenMP support +* OpenMP library +* BLAS and LAPACK libraries +* MPI library +* HDF5 library with MPI support + +The installation instructions depend on the operating system and on the packaging manager used. + +Linux Debian-Ubuntu-Mint +^^^^^^^^^^^^^^^^^^^^^^^^ + +To install all requirements on a Linux Ubuntu operating system, just use APT, the Advanced Packaging Tool: + +.. code-block:: sh + + sudo apt update + sudo apt install python3 python3-dev python3-pip + sudo apt install gcc gfortran + sudo apt install libblas-dev liblapack-dev + sudo apt install libopenmpi-dev openmpi-bin + sudo apt install libomp-dev libomp5 + sudo apt install libhdf5-openmpi-dev + +macOS +^^^^^ + +To install all the requirements on a macOS operating system we recommend using `Homebrew `_\ : + +.. code-block:: eh + + brew update + brew install gcc + brew install openblas + brew install lapack + brew install open-mpi + brew install libomp + brew install hdf5-mpi + +Other operating systems +^^^^^^^^^^^^^^^^^^^^^^^ + +Please see the `instructions for the pyccel library `_ for further details. + +High-performance computers using Environment Modules +^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ + +Many high-performance computers use `Environment Modules `_. +On those systems one typically needs to load the correct versions (i.e. compatible with each other) of the modules ``gcc``\ , ``openmpi``\ , and ``hdf5-mpi``\ , e.g. + +.. code-block:: sh + + module load gcc/15 + module load openmpi/5.0 + module load hdf5-mpi/1.14.1 + +OpenMP instructions should work out of the box. +For access to BLAS and LAPACK routines there are usually different options, we refer therefore to any documentation provided by the supercomputer's maintainers. + +Python setup and project download +--------------------------------- + +We recommend creating a clean Python virtual environment using `venv `_\ : + +.. code-block:: sh + + python3 -m venv + +where ```` is the location to create the virtual environment. +(A new directory will be created at the required location.) +In order to activate the environment just run the command + +.. code-block:: sh + + source /bin/activate + +At this point the commands ``python`` and `\ ``pip`` `_ will refer to the Python 3 interpreter and package manager of the virtual environment, respectively. +Additionally, the command ``deactivate`` closes the environment. +It is good practice to keep ``pip`` up to date with + +.. code-block:: sh + + pip install --upgrade pip + +One can clone the Psydac repository at any location ```` in the filesystem which does not require administrator privileges, using either + +.. code-block:: sh + + git clone https://github.com/pyccel/psydac.git + +or + +.. code-block:: sh + + git clone git@github.com:pyccel/psydac.git + +The latter command requires a GitHub account. + +Installing the library +---------------------- + +Psydac depends on several Python packages, which should be installed in the newly created virtual environment. +Almost all of these dependencies will be automatically installed by ``pip`` at the time of installing the ``psydac`` package later on. + +The single exception is the ``h5py`` package, which needs to be installed in parallel mode. +This means that a wheel will be built from sources and linked to the local parallel HDF5 library. + +To this end, we first set the environment variable ``HDF5_DIR`` s.t. the path ``$HDF5_DIR/lib/`` will correspond to the folder containing the dynamic library ``libhdf5.so`` (on Ubuntu/Debian) or ``libhdf5.dylib`` (on macOS). +This path can be obtained with a command which depends on your system. + + +* + **Ubuntu/Debian**\ : + + .. code-block:: sh + + export HDF5_DIR=$(dpkg -L libhdf5-openmpi-dev | grep "libhdf5.so" | xargs dirname) + +* + **macOS**\ : + + .. code-block:: sh + + export HDF5_DIR=$(brew list hdf5-mpi | grep "libhdf5.dylib" | xargs dirname | xargs dirname) + +* + **High-performance computers using `Environment Modules `_\ **\ : + + The correct location of the HDF5 library can be found using the ``module show`` command, which reveals any environment variables after the ``setenv`` keyword. + For example, on this system both ``HDF5_HOME`` and ``HDF5_ROOT`` contain the information we need: + + .. code-block:: sh + + > module show hdf5-mpi/1.14.1 + + ------------------------------------------------------------------- + /mpcdf/soft/SLE_15/sub/gcc_15/sub/openmpi_5_0/modules/libs/hdf5-mpi/1.14.1: + + module-whatis {HDF5 library 1.14.1 with MPI support, built for openmpi_5_0_7_gcc_15_1} + conflict hdf5-serial + conflict hdf5-mpi + setenv HDF5_HOME /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 + setenv HDF5_ROOT /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 + prepend-path PATH /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1/bin + ------------------------------------------------------------------- + + Therefore it is sufficient to set + + .. code-block:: sh + + export HDF5_DIR=$HDF5_HOME + +Next, install ``h5py`` in parallel mode using ``pip``\ : + +.. code-block:: sh + + export CC="mpicc" + export HDF5_MPI="ON" + + pip install h5py --no-cache-dir --no-binary h5py + +At this point the Psydac library may be installed from the cloned directory ``/psydac`` in **standard mode**\ , which copies the relevant files to the correct locations of the virtual environment, or in **development mode**\ , which only installs symbolic links to the Psydac directory. The latter mode allows one to affect the behavior of Psydac by modifying the source files. + + +* + **Standard mode**\ : + + .. code-block:: bash + + pip install . + +* + **Development mode**\ : + + .. code-block:: bash + + pip install --editable . + +Optional PETSc installation +--------------------------- + +Although Psydac provides several iterative linear solvers which work with our native matrices and vectors, it is often useful to access a dedicated library like `PETSc `_. To this end, our matrices and vectors have the method ``topetsc()``\ , which converts them to the corresponding ``petsc4py`` objects. +(\ ``petsc4py`` is a Python package which provides Python bindings to PETSc.) After solving the linear system with a PETSc solver, the function ``petsc_to_psydac`` allows converting the solution vector back to the Psydac format. + +In order to use these additional feature, PETSc and petsc4py must be installed as follows. +First, we download the latest release of PETSc from its `official Git repository `_\ : + +.. code-block:: sh + + git clone --depth 1 --branch v3.21.4 https://gitlab.com/petsc/petsc.git + +Next, we specify a configuration for complex numbers, and install PETSc in a local directory: + +.. code-block:: sh + + cd petsc + + export PETSC_DIR=$(pwd) + export PETSC_ARCH=petsc-cmplx + + ./configure --with-scalar-type=complex --with-fortran-bindings=0 --have-numpy=1 + + make all check + + cd - + +Finally, we install the Python package ``petsc4py`` which is included in the ``PETSc`` source distribution: + +.. code-block:: sh + + pip install wheel Cython numpy + pip install petsc/src/binding/petsc4py + +Uninstall +--------- + + +* **Whichever the install mode**\ : + .. code-block:: bash + + pip uninstall psydac + +* **If PETSc was installed**\ : + .. code-block:: bash + + pip uninstall petsc4py + +The non-Python dependencies can be uninstalled manually using the package manager. +In the case of PETSc, it is sufficient to remove the cloned source directory given that the installation has been performed locally. diff --git a/docs/source/output.rst b/docs/source/output.rst new file mode 100644 index 000000000..20ccc54e0 --- /dev/null +++ b/docs/source/output.rst @@ -0,0 +1,184 @@ + +Psydac's outputs +================ + +Structure +--------- + +Psydac has a class meant to take care of outputing simulation results. This class, named ``OuputManager`` is located in ``psydac/api/postprocessing.py``. +It writes ``FemSpace`` related information in the Yaml syntax. The file looks like this: + +.. code-block:: yaml + + ndim: 2 + fields: file.h5 # Name of the fields file + patches: + - name: patch_0 + breakpoints: + - [0.0, 0.25, 0.5, 0.75, 1.0] + - [0.0, 0.25, 0.5, 0.75, 1.0] + scalar_spaces: + - name: Scalar_space + ldim: 2 + kind: l2 + dtype: + rational: false + periodic: [false, false] + degree: [1, 1] + multiplicity: [1, 1] + basis: [B, B] + knots: + - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] + - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] + - &id001 + name: Vector_space[0] + ldim: 2 + kind: undefined + dtype: + rational: false + periodic: [false, false] + degree: [1, 2] + multiplicity: [1, 1] + basis: [B, B] + knots: + - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] + - [0.0, 0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0] + - &id002 + name: Vector_space[1] + ldim: 2 + kind: undefined + dtype: + rational: false + periodic: [false, false] + degree: [2, 1] + multiplicity: [1, 1] + basis: [B, B] + knots: + - [0.0, 0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0] + - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] + vector_spaces: + - name: Vector_space + kind: hcurl + components: + - *id001 + - *id002 + - name: patch_1 + breakpoints: + - [1.0, 1.25, 1.5, 1.75, 2.0] + - [0.0, 0.25, 0.5, 0.75, 1.0] + scalar_spaces: + - name: Scalar_space + ldim: 2 + kind: l2 + dtype: + rational: false + periodic: [false, false] + degree: [1, 1] + multiplicity: [1, 1] + basis: [B, B] + knots: + - [1.0, 1.0, 1.25, 1.5, 1.75, 2.0, 2.0] + - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] + +The field coefficients are saved to the ``HDF5`` format in the following manner : + +.. code-block:: bash + + file.h5 + attribute: spaces # name of the aforementioned Yaml file + static/ + scalar_space_1/ + field_s1_1 + field_s1_2 + .... + field_s1_n + vector_space_1_[0]/ + attribute: parent_space # 'vector_space_1' + field_v1_1_[0] + attribute: parent_field # 'field_v1_1' + vector_space_1_[1]/ + attribute: parent_space # 'vector_space_1' + field_v1_1_[1] + attribute: parent_field # 'field_v1_1' + ... + snapshot_1/ + attribute: t + attribute: ts + space_1/ + ... + space_n/ + ... + snapshot_n/ + +In addition to that, Psydac also features the ``PostProcessManager`` class to read those files, recreate all the ``FemSpace`` and ``FemField`` objects and export them to ``VTK``. + +Usage of class ``OutputManager`` +------------------------------------ + +An instance of the ``OutputManager`` class is created at the beginning of the simulation, by specifying the following: + + +#. The name of the YAML file (e.g. ``spaces.yaml``\ ) where the information about all FEM spaces will be written, and +#. The name of the HDF5 file (e.g. ``fields.h5``\ ) where the coefficients of all FEM fields will be written. + +References to the available FEM spaces are given to the OutputManager object through the ``add_spaces(**kwargs)`` method, and the corresponding YAML file is created upon calling the method ``export_space_info()``. In order to inform the OutputManager object that the next fields to be exported are time-independent, the user should call the ``set_static()`` method. In the case of time-dependent fields, the user should prepare a time snapshot (which is defined for a specific integer time step ``ts`` and time value ``t``\ ) by calling the method ``add_snapshot(t, ts)``. In both cases the fields are exported to the HDF5 file through a call to the method ``export_fields(**kwargs)``. Here is a usage example: + +.. code-block:: python + + # SymPDE Layer + # Discretization + # V0h and V1h are discretized SymPDE Space + # u0 and u1 are FemFields belonging to either of those spaces + output_m = OutputManager('spaces.yml', 'fields.h5') + + output_m.add_spaces(V0=V0h, V1=V1h) + output_m.export_space_info() # Writes the space information to Yaml + + output_m.set_static() # Tells the object to save in /static/ + output_m.export_fields(u0_static=u0, u1_static=u1) # Actually does the saving + + output_m.add_snapshot(t=0., ts=0) + # The line above tells the object to: + # 1. create the group snapshot_x with attribute t and ts + # 2. save in this snapshot + output_m.export_fields(u0=u0, u1=u1) + +Usage of class ``PostProcessManager`` +----------------------------------------- + +Typically the ``PostProcessManager`` class is used in a separate post-processing script, which is run after the simulation has finished. In essence it evaluates the FEM fields over a uniform grid (applying the appropriate push-forward operations) and exports the values to a VTK file (or a sequence of files in the case of a time series). An instance of the ``PostProcessManager`` class is created by specifying the following: + + +#. The name of the geometry file (in HDF5 format) which defines the geometry or the topological domain from which the geometry is derived. +#. The name of the YAML file that contains the information about the FEM spaces +#. The name of the HDF5 file that contains the coefficients of all the FEM fields + +In order to export the fields to a VTK file, the user needs to call the method ``export_to_vtk(base_name, grid, npts_per_cell, snapshots, fields)``\ , where: + + +#. ``base_name`` is the base name for the VTK output files. +#. ``grid`` is either a user specified evaluation grid or ``None``. +#. ``npts_per_cell`` specifies the refinement in the case of a uniform grid. +#. ``snapshots`` specifies which time snapshots should be extracted from the HDF5 file (\ ``none`` in the case of static fields) +#. ``fields`` is a tuple of ``h5_field_name``. + +Here is a usage example: + +.. code-block:: python + + # geometry.h5 is where the domain comes from. See PostProcessManager's docstring for more information + post = PostProcessManager(geometry_file='geometry.h5', space_file='spaces.yml', fields_file='fields.h5') + + # See PostProcessManager.export_to_vtk's and TensorFemSpace.eval_fields' docstrings for more information + post.export_to_vtk('filename_vtk', grid=grid, npts_per_cell=npts_per_cell, snapshots='all', fields = ('u0', 'u1')) + +Further Examples +---------------- + +Further examples are present in the following files: + + +* ``examples/poisson_3d_target_torus.py`` +* ``examples/sample_multipatch_parallel.py`` +* ``examples/notebooks/Poisson_non_periodic.ipynb`` +* ``psydac/api/tests/test_postprocessing.py`` diff --git a/docs/source/psydac-mesh.rst b/docs/source/psydac-mesh.rst new file mode 100644 index 000000000..1987994ef --- /dev/null +++ b/docs/source/psydac-mesh.rst @@ -0,0 +1,11 @@ +Psydac mesh +=============== + +After installation, the command ``psydac-mesh`` will be available. + +Example of usage +---------------- + +.. code-block:: bash + + psydac-mesh -n='16,16' -d='3,3' square mesh.h5 From b835af66bcf98df7486420c6aa5951700c8a0337 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 15:24:35 +0100 Subject: [PATCH 22/63] rm md files --- docs/installation.md | 202 ------------------------------------------- docs/output.md | 167 ----------------------------------- docs/psydac-mesh.md | 9 -- 3 files changed, 378 deletions(-) delete mode 100644 docs/installation.md delete mode 100644 docs/output.md delete mode 100644 docs/psydac-mesh.md diff --git a/docs/installation.md b/docs/installation.md deleted file mode 100644 index e71e4ddef..000000000 --- a/docs/installation.md +++ /dev/null @@ -1,202 +0,0 @@ -# Installation - -- [Requirements](#requirements) -- [Python setup and project download](#python-setup-and-project-download) -- [Installing the library](#installing-the-library) -- [Optional PETSc installation](#optional-petsc-installation) -- [Uninstall](#uninstall) - -## Requirements - -Psydac requires a certain number of components to be installed on the machine: - -- Fortran and C compilers with OpenMP support -- OpenMP library -- BLAS and LAPACK libraries -- MPI library -- HDF5 library with MPI support - -The installation instructions depend on the operating system and on the packaging manager used. - -### Linux Debian-Ubuntu-Mint - -To install all requirements on a Linux Ubuntu operating system, just use APT, the Advanced Packaging Tool: -```sh -sudo apt update -sudo apt install python3 python3-dev python3-pip -sudo apt install gcc gfortran -sudo apt install libblas-dev liblapack-dev -sudo apt install libopenmpi-dev openmpi-bin -sudo apt install libomp-dev libomp5 -sudo apt install libhdf5-openmpi-dev -``` - -### macOS - -To install all the requirements on a macOS operating system we recommend using [Homebrew](https://brew.sh/): - -```eh -brew update -brew install gcc -brew install openblas -brew install lapack -brew install open-mpi -brew install libomp -brew install hdf5-mpi -``` - -### Other operating systems - -Please see the [instructions for the pyccel library](https://github.com/pyccel/pyccel#Requirements) for further details. - -### High-performance computers using Environment Modules - -Many high-performance computers use [Environment Modules](https://modules.sourceforge.net/). -On those systems one typically needs to load the correct versions (i.e. compatible with each other) of the modules `gcc`, `openmpi`, and `hdf5-mpi`, e.g. - -```sh -module load gcc/15 -module load openmpi/5.0 -module load hdf5-mpi/1.14.1 -``` -OpenMP instructions should work out of the box. -For access to BLAS and LAPACK routines there are usually different options, we refer therefore to any documentation provided by the supercomputer's maintainers. - -## Python setup and project download - -We recommend creating a clean Python virtual environment using [venv](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment): -```sh -python3 -m venv -``` -where `` is the location to create the virtual environment. -(A new directory will be created at the required location.) -In order to activate the environment just run the command -```sh -source /bin/activate -``` -At this point the commands `python` and [`pip`](https://pip.pypa.io/en/stable/) will refer to the Python 3 interpreter and package manager of the virtual environment, respectively. -Additionally, the command `deactivate` closes the environment. -It is good practice to keep `pip` up to date with -```sh -pip install --upgrade pip -``` - -One can clone the Psydac repository at any location `` in the filesystem which does not require administrator privileges, using either -```sh -git clone https://github.com/pyccel/psydac.git -``` -or -```sh -git clone git@github.com:pyccel/psydac.git -``` -The latter command requires a GitHub account. - -## Installing the library - -Psydac depends on several Python packages, which should be installed in the newly created virtual environment. -Almost all of these dependencies will be automatically installed by `pip` at the time of installing the `psydac` package later on. - -The single exception is the `h5py` package, which needs to be installed in parallel mode. -This means that a wheel will be built from sources and linked to the local parallel HDF5 library. - -To this end, we first set the environment variable `HDF5_DIR` s.t. the path `$HDF5_DIR/lib/` will correspond to the folder containing the dynamic library `libhdf5.so` (on Ubuntu/Debian) or `libhdf5.dylib` (on macOS). -This path can be obtained with a command which depends on your system. - -- **Ubuntu/Debian**: - ```sh - export HDF5_DIR=$(dpkg -L libhdf5-openmpi-dev | grep "libhdf5.so" | xargs dirname) - ``` - -- **macOS**: - ```sh - export HDF5_DIR=$(brew list hdf5-mpi | grep "libhdf5.dylib" | xargs dirname | xargs dirname) - ``` - -- **High-performance computers using [Environment Modules](https://modules.sourceforge.net/)**: - - The correct location of the HDF5 library can be found using the `module show` command, which reveals any environment variables after the `setenv` keyword. - For example, on this system both `HDF5_HOME` and `HDF5_ROOT` contain the information we need: - - ```sh - > module show hdf5-mpi/1.14.1 - - ------------------------------------------------------------------- - /mpcdf/soft/SLE_15/sub/gcc_15/sub/openmpi_5_0/modules/libs/hdf5-mpi/1.14.1: - - module-whatis {HDF5 library 1.14.1 with MPI support, built for openmpi_5_0_7_gcc_15_1} - conflict hdf5-serial - conflict hdf5-mpi - setenv HDF5_HOME /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 - setenv HDF5_ROOT /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1 - prepend-path PATH /mpcdf/soft/SLE_15/packages/skylake/hdf5/gcc_15-15.1.0-openmpi_5.0-5.0.7/1.14.1/bin - ------------------------------------------------------------------- - ``` - - Therefore it is sufficient to set - - ```sh - export HDF5_DIR=$HDF5_HOME - ``` - -Next, install `h5py` in parallel mode using `pip`: -```sh -export CC="mpicc" -export HDF5_MPI="ON" - -pip install h5py --no-cache-dir --no-binary h5py -``` - -At this point the Psydac library may be installed from the cloned directory `/psydac` in **standard mode**, which copies the relevant files to the correct locations of the virtual environment, or in **development mode**, which only installs symbolic links to the Psydac directory. The latter mode allows one to affect the behavior of Psydac by modifying the source files. - -- **Standard mode**: - ```bash - pip install . - ``` - -- **Development mode**: - ```bash - pip install --editable . - ``` - -## Optional PETSc installation - -Although Psydac provides several iterative linear solvers which work with our native matrices and vectors, it is often useful to access a dedicated library like [PETSc](https://petsc.org). To this end, our matrices and vectors have the method `topetsc()`, which converts them to the corresponding `petsc4py` objects. -(`petsc4py` is a Python package which provides Python bindings to PETSc.) After solving the linear system with a PETSc solver, the function `petsc_to_psydac` allows converting the solution vector back to the Psydac format. - -In order to use these additional feature, PETSc and petsc4py must be installed as follows. -First, we download the latest release of PETSc from its [official Git repository](https://gitlab.com/petsc/petsc): -```sh -git clone --depth 1 --branch v3.21.4 https://gitlab.com/petsc/petsc.git -``` -Next, we specify a configuration for complex numbers, and install PETSc in a local directory: -```sh -cd petsc - -export PETSC_DIR=$(pwd) -export PETSC_ARCH=petsc-cmplx - -./configure --with-scalar-type=complex --with-fortran-bindings=0 --have-numpy=1 - -make all check - -cd - -``` -Finally, we install the Python package `petsc4py` which is included in the `PETSc` source distribution: -```sh -pip install wheel Cython numpy -pip install petsc/src/binding/petsc4py -``` - -## Uninstall - -- **Whichever the install mode**: - ```bash - pip uninstall psydac - ``` -- **If PETSc was installed**: - ```bash - pip uninstall petsc4py - ``` - -The non-Python dependencies can be uninstalled manually using the package manager. -In the case of PETSc, it is sufficient to remove the cloned source directory given that the installation has been performed locally. diff --git a/docs/output.md b/docs/output.md deleted file mode 100644 index 3ce4bb540..000000000 --- a/docs/output.md +++ /dev/null @@ -1,167 +0,0 @@ -# Psydac's outputs -## Structure -Psydac has a class meant to take care of outputing simulation results. This class, named `OuputManager` is located in `psydac/api/postprocessing.py`. -It writes `FemSpace` related information in the Yaml syntax. The file looks like this: -```yaml -ndim: 2 -fields: file.h5 # Name of the fields file -patches: -- name: patch_0 - breakpoints: - - [0.0, 0.25, 0.5, 0.75, 1.0] - - [0.0, 0.25, 0.5, 0.75, 1.0] - scalar_spaces: - - name: Scalar_space - ldim: 2 - kind: l2 - dtype: - rational: false - periodic: [false, false] - degree: [1, 1] - multiplicity: [1, 1] - basis: [B, B] - knots: - - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] - - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] - - &id001 - name: Vector_space[0] - ldim: 2 - kind: undefined - dtype: - rational: false - periodic: [false, false] - degree: [1, 2] - multiplicity: [1, 1] - basis: [B, B] - knots: - - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] - - [0.0, 0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0] - - &id002 - name: Vector_space[1] - ldim: 2 - kind: undefined - dtype: - rational: false - periodic: [false, false] - degree: [2, 1] - multiplicity: [1, 1] - basis: [B, B] - knots: - - [0.0, 0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0] - - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] - vector_spaces: - - name: Vector_space - kind: hcurl - components: - - *id001 - - *id002 -- name: patch_1 - breakpoints: - - [1.0, 1.25, 1.5, 1.75, 2.0] - - [0.0, 0.25, 0.5, 0.75, 1.0] - scalar_spaces: - - name: Scalar_space - ldim: 2 - kind: l2 - dtype: - rational: false - periodic: [false, false] - degree: [1, 1] - multiplicity: [1, 1] - basis: [B, B] - knots: - - [1.0, 1.0, 1.25, 1.5, 1.75, 2.0, 2.0] - - [0.0, 0.0, 0.25, 0.5, 0.75, 1.0, 1.0] - -``` -The field coefficients are saved to the `HDF5` format in the following manner : -```bash -file.h5 - attribute: spaces # name of the aforementioned Yaml file - static/ - scalar_space_1/ - field_s1_1 - field_s1_2 - .... - field_s1_n - vector_space_1_[0]/ - attribute: parent_space # 'vector_space_1' - field_v1_1_[0] - attribute: parent_field # 'field_v1_1' - vector_space_1_[1]/ - attribute: parent_space # 'vector_space_1' - field_v1_1_[1] - attribute: parent_field # 'field_v1_1' - ... - snapshot_1/ - attribute: t - attribute: ts - space_1/ - ... - space_n/ - ... - snapshot_n/ -``` -In addition to that, Psydac also features the `PostProcessManager` class to read those files, recreate all the `FemSpace` and `FemField` objects and export them to `VTK`. - -## Usage of class `OutputManager` - -An instance of the `OutputManager` class is created at the beginning of the simulation, by specifying the following: - -1. The name of the YAML file (e.g. `spaces.yaml`) where the information about all FEM spaces will be written, and -2. The name of the HDF5 file (e.g. `fields.h5`) where the coefficients of all FEM fields will be written. - -References to the available FEM spaces are given to the OutputManager object through the `add_spaces(**kwargs)` method, and the corresponding YAML file is created upon calling the method `export_space_info()`. In order to inform the OutputManager object that the next fields to be exported are time-independent, the user should call the `set_static()` method. In the case of time-dependent fields, the user should prepare a time snapshot (which is defined for a specific integer time step `ts` and time value `t`) by calling the method `add_snapshot(t, ts)`. In both cases the fields are exported to the HDF5 file through a call to the method `export_fields(**kwargs)`. Here is a usage example: - -```python -# SymPDE Layer -# Discretization -# V0h and V1h are discretized SymPDE Space -# u0 and u1 are FemFields belonging to either of those spaces -output_m = OutputManager('spaces.yml', 'fields.h5') - -output_m.add_spaces(V0=V0h, V1=V1h) -output_m.export_space_info() # Writes the space information to Yaml - -output_m.set_static() # Tells the object to save in /static/ -output_m.export_fields(u0_static=u0, u1_static=u1) # Actually does the saving - -output_m.add_snapshot(t=0., ts=0) -# The line above tells the object to: -# 1. create the group snapshot_x with attribute t and ts -# 2. save in this snapshot -output_m.export_fields(u0=u0, u1=u1) -``` - -## Usage of class `PostProcessManager` - -Typically the `PostProcessManager` class is used in a separate post-processing script, which is run after the simulation has finished. In essence it evaluates the FEM fields over a uniform grid (applying the appropriate push-forward operations) and exports the values to a VTK file (or a sequence of files in the case of a time series). An instance of the `PostProcessManager` class is created by specifying the following: - -1. The name of the geometry file (in HDF5 format) which defines the geometry or the topological domain from which the geometry is derived. -2. The name of the YAML file that contains the information about the FEM spaces -3. The name of the HDF5 file that contains the coefficients of all the FEM fields - -In order to export the fields to a VTK file, the user needs to call the method `export_to_vtk(base_name, grid, npts_per_cell, snapshots, fields)`, where: -1. `base_name` is the base name for the VTK output files. -2. `grid` is either a user specified evaluation grid or `None`. -3. `npts_per_cell` specifies the refinement in the case of a uniform grid. -4. `snapshots` specifies which time snapshots should be extracted from the HDF5 file (`none` in the case of static fields) -5. `fields` is a tuple of `h5_field_name`. - -Here is a usage example: - -```python -# geometry.h5 is where the domain comes from. See PostProcessManager's docstring for more information -post = PostProcessManager(geometry_file='geometry.h5', space_file='spaces.yml', fields_file='fields.h5') - -# See PostProcessManager.export_to_vtk's and TensorFemSpace.eval_fields' docstrings for more information -post.export_to_vtk('filename_vtk', grid=grid, npts_per_cell=npts_per_cell, snapshots='all', fields = ('u0', 'u1')) -``` - -## Further Examples -Further examples are present in the following files: - -* `examples/poisson_3d_target_torus.py` -* `examples/sample_multipatch_parallel.py` -* `examples/notebooks/Poisson_non_periodic.ipynb` -* `psydac/api/tests/test_postprocessing.py` \ No newline at end of file diff --git a/docs/psydac-mesh.md b/docs/psydac-mesh.md deleted file mode 100644 index 20a543c34..000000000 --- a/docs/psydac-mesh.md +++ /dev/null @@ -1,9 +0,0 @@ -# Mesh Generation - -After installation, the command `psydac-mesh` will be available. - -## Example of usage - -```bash -psydac-mesh -n='16,16' -d='3,3' square mesh.h5 -``` From f4ab560bb4c0f5bd338da3b048aa357207202b16 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Mon, 1 Dec 2025 15:49:11 +0100 Subject: [PATCH 23/63] update links in README to documentation --- README.md | 15 ++++++++------- docs/source/examples.rst | 2 +- 2 files changed, 9 insertions(+), 8 deletions(-) diff --git a/README.md b/README.md index 1c634b6c6..09a6a07e7 100644 --- a/README.md +++ b/README.md @@ -38,7 +38,7 @@ PSYDAC requires a certain number of components to be installed on the machine: The installation instructions depend on the operating system and on the packaging manager used. It is particularly important to determine the **HDF5 root folder**, as this will be needed to install the [`h5py`](https://docs.h5py.org/en/latest/build.html#source-installation) package in parallel mode. -Detailed instructions can be found in the [documentation](https://github.com/pyccel/psydac/blob/devel/docs/installation.md). +Detailed instructions can be found in the [documentation](https://pyccel.github.io/psydac/installation.html). Once those components are installed, we recommend using [`venv`](https://packaging.python.org/en/latest/guides/installing-using-pip-and-virtual-environments/#creating-a-virtual-environment) to set up a fresh Python virtual environment at a location ``: ```bash @@ -61,12 +61,12 @@ pip install ./psydac Here `` is the path to the HDF5 root folder, such that `/lib/` contains the HDF5 dynamic libraries with MPI support. For an editable install, the `-e/--editable` flag should be provided to the last command above. -Again, for more details we refer to our [documentation](https://github.com/pyccel/psydac/blob/devel/docs/installation.md). +Again, for more details we refer to our [documentation](https://pyccel.github.io/psydac/installation.html). > [!TIP] > PSYDAC provides the functionality to convert its MPI-parallel matrices and vectors to their [PETSc](https://petsc.org) equivalent, and back. > This gives the user access to a wide variety of linear solvers and other algorithms. -> Instructions for installing [PETSc](https://petsc.org) and `petsc4py` can be found in our [documentation](https://github.com/pyccel/psydac/blob/devel/docs/installation.md#optional-petsc-installation). +> Instructions for installing [PETSc](https://petsc.org) and `petsc4py` can be found in our [documentation](https://pyccel.github.io/psydac/installation.html#id9). ## Running Tests @@ -103,14 +103,15 @@ The classical installation translates all kernel files to Fortran without user i ## Examples and Tutorials -A [tutorial](https://pyccel.github.io/IGA-Python/intro.html) on isogeometric analysis, with many example notebooks where various PDEs are solved with PSYDAC, is under construction in the [IGA-Python](https://github.com/pyccel/IGA-Python) repository. +Our [documentation](https://pyccel.github.io/psydac/examples.html) provides Jupyter notebooks that present many aspects of this library. +Additional [tutorials](https://pyccel.github.io/IGA-Python/intro.html) on isogeometric analysis, with many example notebooks where various PDEs are solved with PSYDAC, is under construction in the [IGA-Python](https://github.com/pyccel/IGA-Python) repository. Some other examples can be found [here](https://github.com/pyccel/psydac/blob/devel/examples). ## Library Documentation -- [Output formats](https://github.com/pyccel/psydac/blob/devel/docs/output.md) -- [Mesh generation](https://github.com/pyccel/psydac/blob/devel/docs/psydac-mesh.md) -- [Library reference](https://pyccel.github.io/psydac/) +- [Output formats](https://pyccel.github.io/psydac/output.html) +- [Mesh generation](https://pyccel.github.io/psydac/psydac-mesh.html) +- [Modules](https://pyccel.github.io/psydac/modules.html) ## Contributing diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 1db3d852a..02c23698f 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -13,5 +13,5 @@ Examples examples/Poisson_non_periodic examples/Helmholtz_non_periodic - examples/fem_l2_projection + examples/fem_L2_projection \ No newline at end of file From 89dd5d8d2cea892b1ba51431db4ac6bb6c3f1036 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 2 Dec 2025 14:36:05 +0100 Subject: [PATCH 24/63] move files out of psydac/feec/multipatch --- .../examples => examples/feec}/h1_source_pbms_conga_2d.py | 0 .../examples => examples/feec}/hcurl_eigen_pbms_conga_2d.py | 0 .../examples => examples/feec}/hcurl_eigen_pbms_dg_2d.py | 0 .../examples => examples/feec}/hcurl_eigen_testcases.py | 0 .../examples => examples/feec}/hcurl_source_pbms_conga_2d.py | 0 .../examples => examples/feec}/hcurl_source_testcase.py | 0 .../examples => examples/feec}/mixed_source_pbms_conga_2d.py | 0 .../multipatch/examples => examples/feec}/ppc_test_cases.py | 0 .../multipatch/examples => examples/feec/tests}/__init__.py | 0 .../feec}/tests/test_feec_maxwell_multipatch_2d.py | 0 .../feec}/tests/test_feec_poisson_multipatch_2d.py | 0 .../examples => examples/feec}/timedomain_maxwell.py | 0 .../feec}/timedomain_maxwell_testcase.py | 0 psydac/feec/multipatch/tests/__init__.py | 5 ----- psydac/feec/{multipatch => }/multipatch_domain_utilities.py | 0 15 files changed, 5 deletions(-) rename {psydac/feec/multipatch/examples => examples/feec}/h1_source_pbms_conga_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/hcurl_eigen_pbms_conga_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/hcurl_eigen_pbms_dg_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/hcurl_eigen_testcases.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/hcurl_source_pbms_conga_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/hcurl_source_testcase.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/mixed_source_pbms_conga_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/ppc_test_cases.py (100%) rename {psydac/feec/multipatch/examples => examples/feec/tests}/__init__.py (100%) rename {psydac/feec/multipatch => examples/feec}/tests/test_feec_maxwell_multipatch_2d.py (100%) rename {psydac/feec/multipatch => examples/feec}/tests/test_feec_poisson_multipatch_2d.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/timedomain_maxwell.py (100%) rename {psydac/feec/multipatch/examples => examples/feec}/timedomain_maxwell_testcase.py (100%) delete mode 100644 psydac/feec/multipatch/tests/__init__.py rename psydac/feec/{multipatch => }/multipatch_domain_utilities.py (100%) diff --git a/psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py b/examples/feec/h1_source_pbms_conga_2d.py similarity index 100% rename from psydac/feec/multipatch/examples/h1_source_pbms_conga_2d.py rename to examples/feec/h1_source_pbms_conga_2d.py diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py b/examples/feec/hcurl_eigen_pbms_conga_2d.py similarity index 100% rename from psydac/feec/multipatch/examples/hcurl_eigen_pbms_conga_2d.py rename to examples/feec/hcurl_eigen_pbms_conga_2d.py diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py b/examples/feec/hcurl_eigen_pbms_dg_2d.py similarity index 100% rename from psydac/feec/multipatch/examples/hcurl_eigen_pbms_dg_2d.py rename to examples/feec/hcurl_eigen_pbms_dg_2d.py diff --git a/psydac/feec/multipatch/examples/hcurl_eigen_testcases.py b/examples/feec/hcurl_eigen_testcases.py similarity index 100% rename from psydac/feec/multipatch/examples/hcurl_eigen_testcases.py rename to examples/feec/hcurl_eigen_testcases.py diff --git a/psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py b/examples/feec/hcurl_source_pbms_conga_2d.py similarity index 100% rename from psydac/feec/multipatch/examples/hcurl_source_pbms_conga_2d.py rename to examples/feec/hcurl_source_pbms_conga_2d.py diff --git a/psydac/feec/multipatch/examples/hcurl_source_testcase.py b/examples/feec/hcurl_source_testcase.py similarity index 100% rename from psydac/feec/multipatch/examples/hcurl_source_testcase.py rename to examples/feec/hcurl_source_testcase.py diff --git a/psydac/feec/multipatch/examples/mixed_source_pbms_conga_2d.py b/examples/feec/mixed_source_pbms_conga_2d.py similarity index 100% rename from psydac/feec/multipatch/examples/mixed_source_pbms_conga_2d.py rename to examples/feec/mixed_source_pbms_conga_2d.py diff --git a/psydac/feec/multipatch/examples/ppc_test_cases.py b/examples/feec/ppc_test_cases.py similarity index 100% rename from psydac/feec/multipatch/examples/ppc_test_cases.py rename to examples/feec/ppc_test_cases.py diff --git a/psydac/feec/multipatch/examples/__init__.py b/examples/feec/tests/__init__.py similarity index 100% rename from psydac/feec/multipatch/examples/__init__.py rename to examples/feec/tests/__init__.py diff --git a/psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py b/examples/feec/tests/test_feec_maxwell_multipatch_2d.py similarity index 100% rename from psydac/feec/multipatch/tests/test_feec_maxwell_multipatch_2d.py rename to examples/feec/tests/test_feec_maxwell_multipatch_2d.py diff --git a/psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py b/examples/feec/tests/test_feec_poisson_multipatch_2d.py similarity index 100% rename from psydac/feec/multipatch/tests/test_feec_poisson_multipatch_2d.py rename to examples/feec/tests/test_feec_poisson_multipatch_2d.py diff --git a/psydac/feec/multipatch/examples/timedomain_maxwell.py b/examples/feec/timedomain_maxwell.py similarity index 100% rename from psydac/feec/multipatch/examples/timedomain_maxwell.py rename to examples/feec/timedomain_maxwell.py diff --git a/psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py b/examples/feec/timedomain_maxwell_testcase.py similarity index 100% rename from psydac/feec/multipatch/examples/timedomain_maxwell_testcase.py rename to examples/feec/timedomain_maxwell_testcase.py diff --git a/psydac/feec/multipatch/tests/__init__.py b/psydac/feec/multipatch/tests/__init__.py deleted file mode 100644 index 419109b64..000000000 --- a/psydac/feec/multipatch/tests/__init__.py +++ /dev/null @@ -1,5 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# diff --git a/psydac/feec/multipatch/multipatch_domain_utilities.py b/psydac/feec/multipatch_domain_utilities.py similarity index 100% rename from psydac/feec/multipatch/multipatch_domain_utilities.py rename to psydac/feec/multipatch_domain_utilities.py From a053c7bf9d2aef7f5edfd56b9a65b1148df44836 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 2 Dec 2025 14:50:46 +0100 Subject: [PATCH 25/63] add Poisson and curl-curl EV example --- examples/feec/h1_source_pbms_conga_2d.py | 119 +++++++-- examples/feec/hcurl_eigen_pbms_conga_2d.py | 137 +++++++--- examples/feec/hcurl_eigen_pbms_dg_2d.py | 197 ++++++-------- examples/feec/hcurl_eigen_testcases.py | 295 --------------------- 4 files changed, 279 insertions(+), 469 deletions(-) delete mode 100644 examples/feec/hcurl_eigen_testcases.py diff --git a/examples/feec/h1_source_pbms_conga_2d.py b/examples/feec/h1_source_pbms_conga_2d.py index e7e0088f7..1a6e43996 100644 --- a/examples/feec/h1_source_pbms_conga_2d.py +++ b/examples/feec/h1_source_pbms_conga_2d.py @@ -23,18 +23,19 @@ from sympde.topology import Derham from psydac.api.discretization import discretize +from psydac.api.postprocessing import OutputManager, PostProcessManager + from psydac.linalg.basic import IdentityOperator from psydac.linalg.solvers import inverse -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_h1 - -from psydac.fem.projectors import get_dual_dofs - -from psydac.fem.basic import FemField -from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.feec.multipatch_domain_utilities import build_multipatch_domain +from psydac.fem.projectors import get_dual_dofs +from psydac.fem.basic import FemField +#============================================================================== +# Solver for H1 source problems +#============================================================================== def solve_h1_source_pbm( nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_type='manu_poisson_elliptic', eta=-10., mu=1., gamma_h=10., plot_dir=None, @@ -132,9 +133,10 @@ def solve_h1_source_pbm( # useful for the boundary condition (if present) pre_A = cP0.T @ (eta * H0 - mu * DG) + # System matrix A = pre_A @ cP0 + gamma_h * JP0 - + # source and exact solution f_scal, u_bc, u_ex = get_source_and_solution_h1(source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) df = get_dual_dofs(Vh=V0h, f=f_scal, domain_h=domain_h, backend_language=backend_language) @@ -234,19 +236,103 @@ def lift_u_bc(u_bc): if u_ex: err = u - u_ex rel_err = np.sqrt(H0.dot_inner(err, err) / H0.dot_inner(u_ex, u_ex)) + print('relative L2 error = {:.6e}'.format(rel_err)) return rel_err +#============================================================================== +# Test sources and exact solutions +#============================================================================== +def get_source_and_solution_h1(source_type=None, eta=0, mu=0, + domain=None, domain_name=None): + """ + provide source, and exact solutions when available, for: -if __name__ == '__main__': + Find u in H^1, such that - omega = np.sqrt(170) # source - eta = -omega**2 - mu=0 - gamma_h = 10 + A u = f on \\Omega + u = u_bc on \\partial \\Omega + + with + + A u := eta * u - mu * div grad u - source_type = 'manu_poisson_elliptic' + see solve_h1_source_pbm() + """ + from sympy import pi, cos, sin, Tuple, exp + + # exact solutions (if available) + u_ex = None + + # bc solution: describe the bc on boundary. Inside domain, values should + # not matter. Homogeneous bc will be used if None + u_bc = None + + # source terms + f_scal = None + + # auxiliary term (for more diagnostics) + grad_phi = None + phi = None + + x, y = domain.coordinates + + if source_type in ['manu_poisson_elliptic']: + x0 = 1.5 + y0 = 1.5 + s = (x - x0) - (y - y0) + t = (x - x0) + (y - y0) + a = (1 / 1.9)**2 + b = (1 / 1.2)**2 + sigma2 = 0.0121 + tau = a * s**2 + b * t**2 - 1 + phi = exp(-tau**2 / (2 * sigma2)) + dx_tau = 2 * (a * s + b * t) + dy_tau = 2 * (-a * s + b * t) + dxx_tau = 2 * (a + b) + dyy_tau = 2 * (a + b) + + dx_phi = (-tau * dx_tau / sigma2) * phi + dy_phi = (-tau * dy_tau / sigma2) * phi + grad_phi = Tuple(dx_phi, dy_phi) + + f_scal = -((tau * dx_tau / sigma2)**2 - (tau * dxx_tau + dx_tau**2) / sigma2 + + (tau * dy_tau / sigma2)**2 - (tau * dyy_tau + dy_tau**2) / sigma2) * phi + + # exact solution of -p'' = f with hom. bc's on pretzel domain + if mu == 1 and eta == 0: + u_ex = phi + else: + print('WARNING (54375385643): exact solution not available in this case!') + + if not domain_name in ['pretzel', 'pretzel_f']: + # we may have non-hom bc's + u_bc = u_ex + + elif source_type == 'manu_poisson_2': + f_scal = -4 + if mu == 1 and eta == 0: + u_ex = x**2 + y**2 + else: + raise NotImplementedError + u_bc = u_ex + + elif source_type == 'manu_poisson_sincos': + u_ex = sin(pi * x) * cos(pi * y) + f_scal = (eta + 2 * mu * pi**2) * u_ex + u_bc = u_ex + + else: + raise ValueError(source_type) + + return f_scal, u_bc, u_ex + +if __name__ == '__main__': + eta = 0 + mu=1 + gamma_h = 10 + source_type = 'manu_poisson_2' domain_name = 'pretzel_f' nc = 4 @@ -256,9 +342,8 @@ def lift_u_bc(u_bc): solve_h1_source_pbm( nc=nc, deg=deg, eta=eta, - mu=mu, # 1, + mu=mu, domain_name=domain_name, source_type=source_type, backend_language='pyccel-gcc', - plot_dir='./plots/h1_source_pbms_conga_2d/' + run_dir, - ) \ No newline at end of file + ) diff --git a/examples/feec/hcurl_eigen_pbms_conga_2d.py b/examples/feec/hcurl_eigen_pbms_conga_2d.py index 7de33cb9a..aa38f1737 100644 --- a/examples/feec/hcurl_eigen_pbms_conga_2d.py +++ b/examples/feec/hcurl_eigen_pbms_conga_2d.py @@ -11,25 +11,20 @@ from sympde.topology import Derham -from psydac.api.discretization import discretize -from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.utilities import time_count +from psydac.api.discretization import discretize +from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.linalg.basic import IdentityOperator +from psydac.linalg.utilities import array_to_psydac -from scipy.sparse.linalg import spilu, lgmres -from scipy.sparse.linalg import LinearOperator, eigsh, minres -from scipy.linalg import norm -from psydac.linalg.basic import IdentityOperator - -from psydac.linalg.utilities import array_to_psydac from psydac.fem.basic import FemField -from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain - -from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.feec.multipatch_domain_utilities import build_cartesian_multipatch_domain, build_multipatch_domain +#============================================================================== +# Solver for curl-curl eigenvalue problems +#============================================================================== def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), domain=([0, np.pi], [0, np.pi]), domain_name='refined_square', backend_language='pyccel-gcc', mu=1, nu=0, gamma_h=0, generalized_pbm=False, sigma=5, nb_eigs_solve=8, nb_eigs_plot=5, skip_eigs_threshold=1e-7, plot_dir=None): @@ -68,8 +63,6 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma Directory for the plots """ - diags = {} - if sigma is None: raise ValueError('please specify a value for sigma') @@ -80,9 +73,8 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print(' domain_name = {}'.format(domain_name)) print(' backend_language = {}'.format(backend_language)) print('---------------------------------------------------------------------------------------------------------') - t_stamp = time_count() - print('building symbolic and discrete domain...') + print('building symbolic and discrete domain...') int_x, int_y = domain if isinstance(ncells, int): domain = build_multipatch_domain(domain_name=domain_name) @@ -105,16 +97,13 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma ncells = {patch.name: [ncells[int(patch.name[2])][int(patch.name[4])], ncells[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior} - t_stamp = time_count(t_stamp) print(' .. discrete domain...') domain_h = discretize(domain, ncells=ncells) # Vh space print('building symbolic and discrete derham sequences...') - t_stamp = time_count() print(' .. derham sequence...') derham = Derham(domain, ["H1", "Hcurl", "L2"]) - t_stamp = time_count(t_stamp) print(' .. discrete derham sequence...') derham_h = discretize(derham, domain_h, degree=degree) @@ -122,30 +111,22 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print('dim(V0h) = {}'.format(V0h.nbasis)) print('dim(V1h) = {}'.format(V1h.nbasis)) print('dim(V2h) = {}'.format(V2h.nbasis)) - diags['ndofs_V0'] = V0h.nbasis - diags['ndofs_V1'] = V1h.nbasis - diags['ndofs_V2'] = V2h.nbasis - t_stamp = time_count(t_stamp) print('building the discrete operators:') print('commuting projection operators...') I1 = IdentityOperator(V1h.coeff_space) - t_stamp = time_count(t_stamp) print('Hodge operators...') # multi-patch (broken) linear operators / matrices H0, H1, H2 = derham_h.hodge_operators(kind='linop', backend_language=backend_language) dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True, backend_language=backend_language) - t_stamp = time_count(t_stamp) print('conforming projection operators...') # conforming Projections (should take into account the boundary conditions # of the continuous deRham sequence) cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True) - - t_stamp = time_count(t_stamp) print('broken differential operators...') bD0, bD1 = derham_h.derivatives(kind='linop') @@ -155,7 +136,6 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma # Conga (projection-based) stiffness matrices if mu != 0: # curl curl: - t_stamp = time_count(t_stamp) print('mu = {}'.format(mu)) print('curl-curl stiffness matrix...') @@ -168,7 +148,6 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma # jump stabilization in V1h: if gamma_h != 0 or generalized_pbm: - t_stamp = time_count(t_stamp) print('jump stabilization matrix...') JS = (I1 - cP1).T @ H1 @ (I1 - cP1) A += gamma_h * JS @@ -179,11 +158,9 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma else: B = H1 - t_stamp = time_count(t_stamp) print('solving matrix eigenproblem...') all_eigenvalues, all_eigenvectors_transp = get_eigenvalues(nb_eigs_solve, sigma, A.tosparse(), B.tosparse()) # Eigenvalue processing - t_stamp = time_count(t_stamp) print('sorting out eigenvalues...') zero_eigenvalues = [] if skip_eigs_threshold is not None: @@ -200,15 +177,7 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma eigenvalues = all_eigenvalues eigenvectors = all_eigenvectors_transp.T - for k, val in enumerate(eigenvalues): - diags['eigenvalue_{}'.format(k)] = val # eigenvalues[k] - - for k, val in enumerate(zero_eigenvalues): - diags['skipped eigenvalue_{}'.format(k)] = val - - t_stamp = time_count(t_stamp) print('plotting the eigenmodes...') - if plot_dir: if not os.path.exists(plot_dir): @@ -249,11 +218,11 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma fields='vh') PM.close() - t_stamp = time_count(t_stamp) - - return diags, eigenvalues - + return eigenvalues +#============================================================================== +# Eigenvalue solver +#============================================================================== def get_eigenvalues(nb_eigs, sigma, A_m, M_m): """ Compute the eigenvalues of the matrix A close to sigma and right-hand-side M @@ -270,6 +239,10 @@ def get_eigenvalues(nb_eigs, sigma, A_m, M_m): Matrix M """ + from scipy.sparse.linalg import spilu, lgmres + from scipy.sparse.linalg import LinearOperator, eigsh, minres + from scipy.linalg import norm + print('----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ') print( 'computing {0} eigenvalues (and eigenvectors) close to sigma={1} with scipy.sparse.eigsh...'.format( @@ -327,3 +300,79 @@ def get_eigenvalues(nb_eigs, sigma, A_m, M_m): print("done: eigenvalues found: " + repr(eigenvalues)) return eigenvalues, eigenvectors + +if __name__ == '__main__': + # Degree + degree = [3, 3] + + # Refined square domain + domain_name = 'refined_square' + domain = [[0, np.pi], [0, np.pi]] + ncells = np.array([[10, 5, 10], + [5, 10, 5], + [10, 5, 10]]) + + # Curved L-shape domain + # domain_name = 'curved_L_shape' + # domain = [[1, 3], [0, np.pi / 4]] # interval in x- and y-direction + # ncells = np.array([[None, 5], + # [5, 10]]) + + # Jump stabilization parameter + gamma_h = 0 + # solves generalized eigenvalue problem with: B(v,w) = + + # <(I-P)v,(I-P)w> in rhs + generalized_pbm = True + + # curl-curl operator + nu = 0 + mu = 1 + + # reference eigenvalues for validation + if domain_name == 'refined_square': + assert domain == [[0, np.pi], [0, np.pi]] + ref_sigmas = [ + 1, 1, + 2, + 4, 4, + 5, 5, + 8, + 9, 9, + ] + sigma = 5 + nb_eigs_solve = 10 + nb_eigs_plot = 10 + skip_eigs_threshold = 1e-7 + + elif domain_name == 'curved_L_shape': + # ref eigenvalues from Monique Dauge benchmark page + assert domain == [[1, 3], [0, np.pi / 4]] + ref_sigmas = [ + 0.181857115231E+01, + 0.349057623279E+01, + 0.100656015004E+02, + 0.101118862307E+02, + 0.124355372484E+02, + ] + sigma = 7 + nb_eigs_solve = 5 + nb_eigs_plot = 5 + skip_eigs_threshold = 1e-7 + + eigenvalues = hcurl_solve_eigen_pbm( + ncells=ncells, degree=degree, + gamma_h=gamma_h, + generalized_pbm=generalized_pbm, + nu=nu, + mu=mu, + sigma=sigma, + skip_eigs_threshold=skip_eigs_threshold, + nb_eigs_solve=nb_eigs_solve, + nb_eigs_plot=nb_eigs_plot, + domain_name=domain_name, domain=domain, + ) + + if ref_sigmas is not None: + n_errs = min(len(ref_sigmas), len(eigenvalues)) + for k in range(n_errs): + print('error_{}: '.format(k), abs(eigenvalues[k] - ref_sigmas[k])) diff --git a/examples/feec/hcurl_eigen_pbms_dg_2d.py b/examples/feec/hcurl_eigen_pbms_dg_2d.py index 00dd63d87..0566a5804 100644 --- a/examples/feec/hcurl_eigen_pbms_dg_2d.py +++ b/examples/feec/hcurl_eigen_pbms_dg_2d.py @@ -9,37 +9,30 @@ SIAM Journal on Numerical Analysis 44 (2006) """ import os -from mpi4py import MPI -from collections import OrderedDict - import numpy as np -import matplotlib.pyplot - -from scipy.sparse.linalg import LinearOperator, eigsh, minres -from sympde.calculus import grad, dot, curl, cross +from sympde.calculus import dot, curl, cross from sympde.calculus import minus, plus from sympde.topology import VectorFunctionSpace from sympde.topology import elements_of from sympde.topology import NormalVector -from sympde.topology import Square -from sympde.topology import IdentityMapping, PolarMapping from sympde.expr.expr import LinearForm, BilinearForm from sympde.expr.expr import integral -from sympde.expr.expr import Norm -from sympde.expr.equation import find, EssentialBC from psydac.linalg.utilities import array_to_psydac + from psydac.fem.basic import FemField -from psydac.feec.pull_push import pull_2d_hcurl -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.utilities import time_count +from psydac.feec.multipatch_domain_utilities import build_multipatch_domain, build_cartesian_multipatch_domain + from psydac.api.discretization import discretize -from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain from psydac.api.postprocessing import OutputManager, PostProcessManager +from hcurl_eigen_pbms_conga_2d import get_eigenvalues +#============================================================================== +# Solver for curl-curl eigenvalue problems +#============================================================================== def hcurl_solve_eigen_pbm_dg(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), domain=([0, np.pi], [0, np.pi]), domain_name='refined_square', backend_language='pyccel-gcc', mu=1, nu=0, sigma=5, nb_eigs_solve=8, nb_eigs_plot=5, skip_eigs_threshold=1e-7, plot_dir=None,): @@ -74,8 +67,6 @@ def hcurl_solve_eigen_pbm_dg(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), d Directory for the plots """ - diags = {} - if sigma is None: raise ValueError('please specify a value for sigma') @@ -86,7 +77,6 @@ def hcurl_solve_eigen_pbm_dg(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), d print(' domain_name = {}'.format(domain_name)) print(' backend_language = {}'.format(backend_language)) print('---------------------------------------------------------------------------------------------------------') - t_stamp = time_count() print('building symbolic and discrete domain...') int_x, int_y = domain @@ -111,13 +101,8 @@ def hcurl_solve_eigen_pbm_dg(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), d ncells = {patch.name: [ncells[int(patch.name[2])][int(patch.name[4])], ncells[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior} - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) - t_stamp = time_count(t_stamp) print(' .. discrete domain...') - V = VectorFunctionSpace('V', domain, kind='hcurl') u, v, F = elements_of(V, names='u, v, F') @@ -166,17 +151,16 @@ def avr(w): return 0.5 * plus(w) + 0.5 * minus(w) bh = discretize(b, domain_h, [Vh, Vh]) Bh_m = bh.assemble().tosparse() - all_eigenvalues_2, all_eigenvectors_transp_2 = get_eigenvalues( + all_eigenvalues, all_eigenvectors_transp = get_eigenvalues( nb_eigs_solve, sigma, Ah_m, Bh_m) # Eigenvalue processing - t_stamp = time_count(t_stamp) print('sorting out eigenvalues...') zero_eigenvalues = [] if skip_eigs_threshold is not None: eigenvalues = [] eigenvectors = [] - for val, vect in zip(all_eigenvalues_2, all_eigenvectors_transp_2.T): + for val, vect in zip(all_eigenvalues, all_eigenvectors_transp.T): if abs(val) < skip_eigs_threshold: zero_eigenvalues.append(val) # we skip the eigenvector @@ -184,18 +168,10 @@ def avr(w): return 0.5 * plus(w) + 0.5 * minus(w) eigenvalues.append(val) eigenvectors.append(vect) else: - eigenvalues = all_eigenvalues_2 - eigenvectors = all_eigenvectors_transp_2.T - diags['DG'] = True - for k, val in enumerate(eigenvalues): - diags['eigenvalue2_{}'.format(k)] = val # eigenvalues[k] - - for k, val in enumerate(zero_eigenvalues): - diags['skipped eigenvalue2_{}'.format(k)] = val + eigenvalues = all_eigenvalues + eigenvectors = all_eigenvectors_transp.T - t_stamp = time_count(t_stamp) print('plotting the eigenmodes...') - if plot_dir: if not os.path.exists(plot_dir): os.makedirs(plot_dir) @@ -232,81 +208,76 @@ def avr(w): return 0.5 * plus(w) + 0.5 * minus(w) fields='vh') PM.close() - t_stamp = time_count(t_stamp) - - return diags, eigenvalues - + return eigenvalues + +if __name__ == '__main__': + # Degree + degree = [3, 3] + + # Refined square domain + domain_name = 'refined_square' + domain = [[0, np.pi], [0, np.pi]] + ncells = np.array([[10, 5, 10], + [5, 10, 5], + [10, 5, 10]]) + + # Curved L-shape domain + # domain_name = 'curved_L_shape' + # domain = [[1, 3], [0, np.pi / 4]] # interval in x- and y-direction + # ncells = np.array([[None, 5], + # [5, 10]]) + + # solves generalized eigenvalue problem with: B(v,w) = + + # <(I-P)v,(I-P)w> in rhs + generalized_pbm = True + + # curl-curl operator + nu = 0 + mu = 1 + + # reference eigenvalues for validation + if domain_name == 'refined_square': + assert domain == [[0, np.pi], [0, np.pi]] + ref_sigmas = [ + 1, 1, + 2, + 4, 4, + 5, 5, + 8, + 9, 9, + ] + sigma = 5 + nb_eigs_solve = 10 + nb_eigs_plot = 10 + skip_eigs_threshold = 1e-7 -def get_eigenvalues(nb_eigs, sigma, A_m, M_m): - """ - Compute the eigenvalues of the matrix A close to sigma and right-hand-side M - - Parameters - ---------- - nb_eigs : int - Number of eigenvalues to compute - sigma : float - Value close to which the eigenvalues are computed - A_m : sparse matrix - Matrix A - M_m : sparse matrix - Matrix M - """ - - print('----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ') - print( - 'computing {0} eigenvalues (and eigenvectors) close to sigma={1} with scipy.sparse.eigsh...'.format( - nb_eigs, - sigma)) - mode = 'normal' - which = 'LM' - # from eigsh docstring: - # ncv = number of Lanczos vectors generated ncv must be greater than k and smaller than n; - # it is recommended that ncv > 2*k. Default: min(n, max(2*k + 1, 20)) - ncv = 4 * nb_eigs - print('A_m.shape = ', A_m.shape) - try_lgmres = True - max_shape_splu = 24000 # OK for nc=20, deg=6 on pretzel_f - if A_m.shape[0] < max_shape_splu: - print('(via sparse LU decomposition)') - OPinv = None - tol_eigsh = 0 - else: - - OP_m = A_m - sigma * M_m - tol_eigsh = 1e-7 - if try_lgmres: - print( - '(via SPILU-preconditioned LGMRES iterative solver for A_m - sigma*M1_m)') - OP_spilu = spilu(OP_m, fill_factor=15, drop_tol=5e-5) - preconditioner = LinearOperator( - OP_m.shape, lambda x: OP_spilu.solve(x)) - tol = tol_eigsh - OPinv = LinearOperator( - matvec=lambda v: lgmres(OP_m, v, x0=None, tol=tol, atol=tol, M=preconditioner, - callback=lambda x: print( - 'cg -- residual = ', norm(OP_m.dot(x) - v)) - )[0], - shape=M_m.shape, - dtype=M_m.dtype - ) - - else: - # from https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html: - # the user can supply the matrix or operator OPinv, which gives x = OPinv @ b = [A - sigma * M]^-1 @ b. - # > here, minres: MINimum RESidual iteration to solve Ax=b - # suggested in https://github.com/scipy/scipy/issues/4170 - print('(with minres iterative solver for A_m - sigma*M1_m)') - OPinv = LinearOperator( - matvec=lambda v: minres( - OP_m, - v, - tol=1e-10)[0], - shape=M_m.shape, - dtype=M_m.dtype) - - eigenvalues, eigenvectors = eigsh( - A_m, k=nb_eigs, M=M_m, sigma=sigma, mode=mode, which=which, ncv=ncv, tol=tol_eigsh, OPinv=OPinv) - - print("done: eigenvalues found: " + repr(eigenvalues)) - return eigenvalues, eigenvectors + elif domain_name == 'curved_L_shape': + # ref eigenvalues from Monique Dauge benchmark page + assert domain == [[1, 3], [0, np.pi / 4]] + ref_sigmas = [ + 0.181857115231E+01, + 0.349057623279E+01, + 0.100656015004E+02, + 0.101118862307E+02, + 0.124355372484E+02, + ] + sigma = 7 + nb_eigs_solve = 5 + nb_eigs_plot = 5 + skip_eigs_threshold = 1e-7 + + eigenvalues = hcurl_solve_eigen_pbm_dg( + ncells=ncells, degree=degree, + nu=nu, + mu=mu, + sigma=sigma, + skip_eigs_threshold=skip_eigs_threshold, + nb_eigs_solve=nb_eigs_solve, + nb_eigs_plot=nb_eigs_plot, + domain_name=domain_name, domain=domain, + ) + + if ref_sigmas is not None: + n_errs = min(len(ref_sigmas), len(eigenvalues)) + for k in range(n_errs): + print('error_{}: '.format(k), abs(eigenvalues[k] - ref_sigmas[k])) diff --git a/examples/feec/hcurl_eigen_testcases.py b/examples/feec/hcurl_eigen_testcases.py deleted file mode 100644 index 1cebbe9bc..000000000 --- a/examples/feec/hcurl_eigen_testcases.py +++ /dev/null @@ -1,295 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -""" - Runner script for solving the eigenvalue problem for the H(curl) operator for different discretizations. -""" - -import os -import numpy as np - -from psydac.feec.multipatch.examples.hcurl_eigen_pbms_conga_2d import hcurl_solve_eigen_pbm -from psydac.feec.multipatch.examples.hcurl_eigen_pbms_dg_2d import hcurl_solve_eigen_pbm_dg -from psydac.feec.multipatch.utilities import time_count, get_run_dir, get_plot_dir, get_mat_dir, get_sol_dir, diag_fn -from psydac.feec.multipatch.utils_conga_2d import write_diags_to_file -from psydac.api.postprocessing import OutputManager, PostProcessManager - -t_stamp_full = time_count() - -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- -# -# test-case and numerical parameters: -method = 'feec' -# method = 'dg' - -operator = 'curl-curl' -degree = [3, 3] # shared across all patches - -# pretzel_f (18 patches) -# domain_name = 'pretzel_f' -# ncells = np.array([8, 8, 16, 16, 8, 4, 4, 4, 4, 4, 2, 2, 4, 16, 16, 8, 2, 2, 2]) -# ncells = np.array([4 for _ in range(18)]) - -# domain onlyneeded for square like domains -# domain = [[0, np.pi], [0, np.pi]] # interval in x- and y-direction - -# refined square domain -# domain_name = 'refined_square' -# the shape of ncells gives the shape of the domain, -# while the entries describe the isometric number of cells in each patch -# 2x2 = 4 patches -# ncells = np.array([[8, 4], -# [4, 4]]) -# 3x3= 9 patches -# ncells = np.array([[4, 2, 4], -# [2, 4, 2], -# [4, 2, 4]]) - -# L-shaped domain -# domain_name = 'square_L_shape' -# domain=[[-1, 1],[-1, 1]] # interval in x- and y-direction - -# The None indicates the patches to leave out -# 2x2 = 4 patches -# ncells = np.array([[None, 2], -# [2, 2]]) -# 4x4 = 16 patches -# ncells = np.array([[None, None, 4, 2], -# [None, None, 8, 4], -# [4, 8, 8, 4], -# [2, 4, 4, 2]]) -# 8x8 = 64 patches -# ncells = np.array([[None, None, None, None, 2, 2, 2,1 2], -# [None, None, None, None, 2, 2, 2, 2], -# [None, None, None, None, 2, 2, 2, 2], -# [None, None, None, None, 4, 4, 2, 2], -# [2, 2, 2, 4, 8, 4, 2, 2], -# [2, 2, 2, 4, 4, 4, 2, 2], -# [2, 2, 2, 2, 2, 2, 2, 2], -# [2, 2, 2, 2, 2, 2, 2, 2]]) - -# Curved L-shape domain -domain_name = 'curved_L_shape' -domain = [[1, 3], [0, np.pi / 4]] # interval in x- and y-direction - - -ncells = np.array([[None, 5], - [5, 10]]) -# ncells = 5 - -# ncells = np.array([[None, None, 2, 2], -# [None, None, 4, 2], -# [ 2, 4, 8, 4], -# [ 2, 2, 4, 4]]) - -# ncells = np.array([[None, None, None, 2, 2, 2], -# [None, None, None, 4, 4, 2], -# [None, None, None, 8, 4, 2], -# [2, 4, 8, 8, 4, 2], -# [2, 4, 4, 4, 4, 2], -# [2, 2, 2, 2, 2, 2]]) - -# ncells = np.array([[None, None, None, None, 2, 2, 2, 2], -# [None, None, None, None, 4, 4, 4, 2], -# [None, None, None, None, 8, 8, 4, 2], -# [None, None, None, None, 16, 8, 4, 2], -# [2, 4, 8, 16, 16, 8, 4, 2], -# [2, 4, 8, 8, 8, 8, 4, 2], -# [2, 4, 4, 4, 4, 4, 4, 2], -# [2, 2, 2, 2, 2, 2, 2, 2]]) - -# all kinds of different square refinements and constructions are possible, eg -# doubly connected domains -# ncells = np.array([[4, 2, 2, 4], -# [2, None, None, 2], -# [2, None, None, 2], -# [4, 2, 2, 4]]) - -gamma_h = 0 -# solves generalized eigenvalue problem with: B(v,w) = + -# <(I-P)v,(I-P)w> in rhs -generalized_pbm = True - -if operator == 'curl-curl': - nu = 0 - mu = 1 -else: - raise ValueError(operator) - -case_dir = 'eigenpbm_' + operator + '_' + method -ref_case_dir = case_dir - -ref_sigmas = None -sigma = None -nb_eigs_solve = None -nb_eigs_plot = None -skip_eigs_threshold = None -diags = None -eigenvalues = None - -if domain_name == 'refined_square': - assert domain == [[0, np.pi], [0, np.pi]] - ref_sigmas = [ - 1, 1, - 2, - 4, 4, - 5, 5, - 8, - 9, 9, - ] - sigma = 5 - nb_eigs_solve = 10 - nb_eigs_plot = 10 - skip_eigs_threshold = 1e-7 - -elif domain_name == 'square_L_shape': - assert domain == [[-1, 1], [-1, 1]] - ref_sigmas = [ - 1.47562182408, - 3.53403136678, - 9.86960440109, - 9.86960440109, - 11.3894793979, - ] - sigma = 6 - nb_eigs_solve = 5 - nb_eigs_plot = 5 - skip_eigs_threshold = 1e-7 - -elif domain_name == 'curved_L_shape': - # ref eigenvalues from Monique Dauge benchmark page - assert domain == [[1, 3], [0, np.pi / 4]] - ref_sigmas = [ - 0.181857115231E+01, - 0.349057623279E+01, - 0.100656015004E+02, - 0.101118862307E+02, - 0.124355372484E+02, - ] - sigma = 7 - nb_eigs_solve = 7 - nb_eigs_plot = 7 - skip_eigs_threshold = 1e-7 - -elif domain_name in ['pretzel_f']: - if operator == 'curl-curl': - # ref sigmas computed with nc=20 and deg=6 and gamma = 0 (and - # generalized ev-pbm) - ref_sigmas = [ - 0.1795339843, - 0.1992261261, - 0.6992717244, - 0.8709410438, - 1.1945106937, - 1.2546992683, - ] - - sigma = .8 - nb_eigs_solve = 10 - nb_eigs_plot = 5 - skip_eigs_threshold = 1e-7 - -# -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -common_diag_filename = './' + case_dir + '_diags.txt' - - -params = { - 'domain_name': domain_name, - 'domain': domain, - 'operator': operator, - 'mu': mu, - 'nu': nu, - 'ncells': ncells, - 'degree': degree, - 'gamma_h': gamma_h, - 'generalized_pbm': generalized_pbm, - 'nb_eigs_solve': nb_eigs_solve, - 'skip_eigs_threshold': skip_eigs_threshold -} - -print(params) - -# backend_language = 'numba' -backend_language = 'pyccel-gcc' - -dims = 1 if isinstance(ncells, int) else ncells.shape -sz = 1 if isinstance(ncells, int) else ncells[ncells != None].sum() - -# get_run_dir(domain_name, nc, deg) -run_dir = domain_name + str(dims) + 'patches_' + 'size_{}'.format(sz) -plot_dir = get_plot_dir(case_dir, run_dir) -diag_filename = plot_dir + '/' + diag_fn() -common_diag_filename = './' + case_dir + '_diags.txt' - - -print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') -print(' Calling hcurl_solve_eigen_pbm() with params = {}'.format(params)) -print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') - -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- -# calling eigenpbm solver for: -# -# find lambda in R and u in H0(curl), such that -# A u = lambda * u on \Omega -# with -# -# A u := mu * curl curl u - nu * grad div u -# -# note: -# - we look for nb_eigs_solve eigenvalues close to sigma (skip zero eigenvalues if skip_zero_eigs==True) -# - we plot nb_eigs_plot eigenvectors -if method == 'feec': - diags, eigenvalues = hcurl_solve_eigen_pbm( - ncells=ncells, degree=degree, - gamma_h=gamma_h, - generalized_pbm=generalized_pbm, - nu=nu, - mu=mu, - sigma=sigma, - skip_eigs_threshold=skip_eigs_threshold, - nb_eigs_solve=nb_eigs_solve, - nb_eigs_plot=nb_eigs_plot, - domain_name=domain_name, domain=domain, - backend_language=backend_language, - plot_dir=plot_dir, - ) - -elif method == 'dg': - diags, eigenvalues = hcurl_solve_eigen_pbm_dg( - ncells=ncells, degree=degree, - nu=nu, - mu=mu, - sigma=sigma, - skip_eigs_threshold=skip_eigs_threshold, - nb_eigs_solve=nb_eigs_solve, - nb_eigs_plot=nb_eigs_plot, - domain_name=domain_name, domain=domain, - backend_language=backend_language, - plot_dir=plot_dir, - ) - -if ref_sigmas is not None: - errors = [] - n_errs = min(len(ref_sigmas), len(eigenvalues)) - for k in range(n_errs): - diags['error_{}'.format(k)] = abs(eigenvalues[k] - ref_sigmas[k]) -# -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=diag_filename, - params=params) -write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=common_diag_filename, - params=params) - -# PM = PostProcessManager(geometry_file=, ) -time_count(t_stamp_full, msg='full program') From 15fd15688fedb68bb319cdcb1388aaa7984bfb2d Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 2 Dec 2025 16:43:00 +0100 Subject: [PATCH 26/63] rename md so it shows up on github --- examples/performance/{matrix_assembly_speed_log.md => README.md} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename examples/performance/{matrix_assembly_speed_log.md => README.md} (100%) diff --git a/examples/performance/matrix_assembly_speed_log.md b/examples/performance/README.md similarity index 100% rename from examples/performance/matrix_assembly_speed_log.md rename to examples/performance/README.md From ae18af624cc668dff92194a0ab9d28f3f1ae59e0 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 2 Dec 2025 16:45:21 +0100 Subject: [PATCH 27/63] add time-harmonic Maxwell --- examples/feec/hcurl_eigen_pbms_conga_2d.py | 1 + examples/feec/hcurl_source_pbms_conga_2d.py | 184 +++++--- examples/feec/hcurl_source_testcase.py | 145 ------- examples/feec/mixed_source_pbms_conga_2d.py | 455 -------------------- 4 files changed, 120 insertions(+), 665 deletions(-) delete mode 100644 examples/feec/hcurl_source_testcase.py delete mode 100644 examples/feec/mixed_source_pbms_conga_2d.py diff --git a/examples/feec/hcurl_eigen_pbms_conga_2d.py b/examples/feec/hcurl_eigen_pbms_conga_2d.py index aa38f1737..e790ba852 100644 --- a/examples/feec/hcurl_eigen_pbms_conga_2d.py +++ b/examples/feec/hcurl_eigen_pbms_conga_2d.py @@ -160,6 +160,7 @@ def hcurl_solve_eigen_pbm(ncells=np.array([[8, 4], [4, 4]]), degree=(3, 3), doma print('solving matrix eigenproblem...') all_eigenvalues, all_eigenvectors_transp = get_eigenvalues(nb_eigs_solve, sigma, A.tosparse(), B.tosparse()) + # Eigenvalue processing print('sorting out eigenvalues...') zero_eigenvalues = [] diff --git a/examples/feec/hcurl_source_pbms_conga_2d.py b/examples/feec/hcurl_source_pbms_conga_2d.py index 41a4160a5..cfc31e331 100644 --- a/examples/feec/hcurl_source_pbms_conga_2d.py +++ b/examples/feec/hcurl_source_pbms_conga_2d.py @@ -23,24 +23,23 @@ from sympde.topology import Derham - from psydac.api.discretization import discretize -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_hcurl -from psydac.feec.multipatch.utils_conga_2d import P1_phys -from psydac.feec.multipatch.utilities import time_count -# from psydac.linalg.utilities import array_to_psydac -from psydac.fem.basic import FemField from psydac.api.postprocessing import OutputManager, PostProcessManager +from psydac.feec.multipatch_domain_utilities import build_multipatch_domain + +from psydac.fem.basic import FemField +from psydac.fem.projectors import get_dual_dofs + from psydac.linalg.basic import IdentityOperator -from psydac.fem.projectors import get_dual_dofs from psydac.linalg.solvers import inverse - +#============================================================================== +# Solver for H(curl) source problems +#============================================================================== def solve_hcurl_source_pbm( - nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_proj='tilde_Pi', source_type='manu_J', - eta=-10., mu=1., nu=1., gamma_h=10., + nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_type='manu_maxwell_inhom', + eta=-10., mu=1., nu=0., gamma_h=10., project_sol=True, plot_dir=None): """ solver for the problem: find u in H(curl), such that @@ -71,12 +70,8 @@ def solve_hcurl_source_pbm( :param nc: nb of cells per dimension, in each patch :param deg: coordinate degree in each patch :param gamma_h: jump penalization parameter - :param source_proj: approximation operator (in V1h) for the source, possible values are - - 'tilde_Pi': dual commuting projection, an L2 projection filtered by the adjoint conforming projection) :param source_type: must be implemented in get_source_and_solution() """ - diags = {} - degree = [deg, deg] @@ -85,45 +80,34 @@ def solve_hcurl_source_pbm( print(' ncells = {}'.format(nc)) print(' degree = {}'.format(degree)) print(' domain_name = {}'.format(domain_name)) - print(' source_proj = {}'.format(source_proj)) print(' backend_language = {}'.format(backend_language)) print('---------------------------------------------------------------------------------------------------------') print() print(' -- building discrete spaces and operators --') - t_stamp = time_count() print(' .. multi-patch domain...') domain = build_multipatch_domain(domain_name=domain_name) - # mappings = OrderedDict([(P.logical_domain, P.mapping) - # for P in domain.interior]) - # mappings_list = list(mappings.values()) - + if isinstance(nc, int): ncells = [nc, nc] else: ncells = {patch.name: [nc[i], nc[i]] for (i, patch) in enumerate(domain.interior)} - - t_stamp = time_count(t_stamp) print(' .. derham sequence...') derham = Derham(domain, ["H1", "Hcurl", "L2"]) - t_stamp = time_count(t_stamp) print(' .. discrete domain...') domain_h = discretize(domain, ncells=ncells) - t_stamp = time_count(t_stamp) print(' .. discrete derham sequence...') derham_h = discretize(derham, domain_h, degree=degree) - t_stamp = time_count(t_stamp) print(' .. commuting projection operators...') nquads = [10 * (d + 1) for d in degree] P0, P1, P2 = derham_h.projectors(nquads=nquads) - t_stamp = time_count(t_stamp) print(' .. multi-patch spaces...') V0h, V1h, V2h = derham_h.spaces mappings = derham_h.callable_mapping @@ -131,52 +115,39 @@ def solve_hcurl_source_pbm( print('dim(V0h) = {}'.format(V0h.nbasis)) print('dim(V1h) = {}'.format(V1h.nbasis)) print('dim(V2h) = {}'.format(V2h.nbasis)) - diags['ndofs_V0'] = V0h.nbasis - diags['ndofs_V1'] = V1h.nbasis - diags['ndofs_V2'] = V2h.nbasis - t_stamp = time_count(t_stamp) + print(' .. Id operator and matrix...') I1 = IdentityOperator(V1h.coeff_space) - t_stamp = time_count(t_stamp) print(' .. Hodge operators...') # multi-patch (broken) linear operators / matrices # other option: define as Hodge Operators: H0, H1, H2 = derham_h.hodge_operators(kind='linop', backend_language=backend_language) dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True, backend_language=backend_language) - - t_stamp = time_count(t_stamp) print(' .. conforming Projection operators...') # conforming Projections (should take into account the boundary conditions # of the continuous deRham sequence) cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True) - - t_stamp = time_count(t_stamp) print(' .. broken differential operators...') # broken (patch-wise) differential operators bD0, bD1 = derham_h.derivatives(kind='linop') # Conga (projection-based) stiffness matrices # curl curl: - t_stamp = time_count(t_stamp) print(' .. curl-curl stiffness matrix...') pre_CC = bD1.T @ H2 @ bD1 # grad div: - t_stamp = time_count(t_stamp) print(' .. grad-div stiffness matrix...') pre_GD = - H1 @ bD0 @ cP0 @ dH0 @ cP0.T @ bD0.T @ H1 # jump stabilization: - t_stamp = time_count(t_stamp) print(' .. jump stabilization matrix...') JS = (I1 - cP1).T @ H1 @ (I1 - cP1) - - t_stamp = time_count(t_stamp) print(' .. full operator matrix...') print('eta = {}'.format(eta)) print('mu = {}'.format(mu)) @@ -191,27 +162,21 @@ def solve_hcurl_source_pbm( A = pre_A @ cP1 + gamma_h * JS - t_stamp = time_count(t_stamp) print() print(' -- getting source --') - f_vect, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl(source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) + f_vect, u_bc, u_ex = get_source_and_solution_hcurl(source_type=source_type, eta=eta, mu=mu, domain=domain, domain_name=domain_name,) # compute approximate source f_h - t_stamp = time_count(t_stamp) - # f_h = L2 projection of f_vect, with filtering if tilde_Pi - print(' .. projecting the source with ' + source_proj +' projection...') - tilde_f = get_dual_dofs(Vh=V1h, f=f_vect, domain_h=domain_h, backend_language=backend_language) - if source_proj == 'tilde_Pi': - print(' .. filtering the discrete source with P1.T ...') - tilde_f = cP1.T @ tilde_f + print(' .. filtering the discrete source with P1.T ...') + tilde_f = cP1.T @ tilde_f def lift_u_bc(u_bc): if u_bc is not None: - ubc = P1_phys(u_bc, P1, domain).coeffs + ubc = P1(u_bc).coeffs ubc -= cP1.dot(ubc) else: @@ -219,40 +184,32 @@ def lift_u_bc(u_bc): return ubc - ubc = lift_u_bc(u_bc) if ubc is not None: # modified source for the homogeneous pbm - t_stamp = time_count(t_stamp) print(' .. modifying the source with lifted bc solution...') tilde_f -= pre_A.dot(ubc) # direct solve with scipy spsolve - t_stamp = time_count(t_stamp) print('solving source problem with conjugate gradient...') solver = inverse(A, solver='cg', tol=1e-8) u = solver.solve(tilde_f) # project the homogeneous solution on the conforming problem space - t_stamp = time_count(t_stamp) if project_sol: print(' .. projecting the homogeneous solution on the conforming problem space...') u = cP1.dot(u) if ubc is not None: # adding the lifted boundary condition - t_stamp = time_count(t_stamp) print(' .. adding the lifted boundary condition...') u += ubc uh = FemField(V1h, coeffs=u) - #need cp1 here? f = dH1.dot(tilde_f) jh = FemField(V1h, coeffs=f) - t_stamp = time_count(t_stamp) - print(' -- plots and diagnostics --') if plot_dir: if not os.path.exists(plot_dir): @@ -287,15 +244,112 @@ def lift_u_bc(u_bc): PM.close() - time_count(t_stamp) if u_ex: - u_ex_p = P1_phys(u_ex, P1, domain).coeffs + u_ex_p = P1(u_ex).coeffs err = u_ex_p - u - print(err.inner(H1.dot(err))) l2_error = np.sqrt( H1.dot_inner(err, err) / H1.dot_inner(u_ex_p, u_ex_p)) - print(l2_error) - diags['err'] = l2_error + print("L2 error: ", l2_error) + + return l2_error + +#============================================================================== +# Test sources and exact solutions +#============================================================================== +def get_source_and_solution_hcurl( + source_type=None, eta=0, mu=0, nu=0, + domain=None, domain_name=None): + """ + provide source, and exact solutions when available, for: + + Find u in H(curl) such that + + A u = f on \\Omega + n x u = n x u_bc on \\partial \\Omega + + with + + A u := eta * u + mu * curl curl u - nu * grad div u + + see solve_hcurl_source_pbm() + """ + from sympy import pi, cos, sin, Tuple, exp + + # exact solutions (if available) + u_ex = None + + # bc solution: describe the bc on boundary. Inside domain, values should + # not matter. Homogeneous bc will be used if None + u_bc = None + + # source terms + f_vect = None + + # auxiliary term (for more diagnostics) + grad_phi = None + phi = None + + x, y = domain.coordinates + + if source_type == 'manu_maxwell_inhom': + # used for Maxwell equation with manufactured solution + f_vect = Tuple(eta * sin(pi * y) - pi**2 * sin(pi * y) * cos(pi * x) + pi**2 * sin(pi * y), + eta * sin(pi * x) * cos(pi * y) + pi**2 * sin(pi * x) * cos(pi * y)) + if nu == 0: + u_ex = Tuple(sin(pi * y), sin(pi * x) * cos(pi * y)) + curl_u_ex = pi * (cos(pi * x) * cos(pi * y) - cos(pi * y)) + div_u_ex = -pi * sin(pi * x) * sin(pi * y) + else: + raise NotImplementedError + u_bc = u_ex + + elif source_type == 'elliptic_J': + # no manufactured solution for Maxwell pbm + x0 = 1.5 + y0 = 1.5 + s = (x - x0) - (y - y0) + t = (x - x0) + (y - y0) + a = (1 / 1.9)**2 + b = (1 / 1.2)**2 + sigma2 = 0.0121 + tau = a * s**2 + b * t**2 - 1 + phi = exp(-tau**2 / (2 * sigma2)) + dx_tau = 2 * (a * s + b * t) + dy_tau = 2 * (-a * s + b * t) + + f_x = dy_tau * phi + f_y = - dx_tau * phi + f_vect = Tuple(f_x, f_y) + + else: + raise ValueError(source_type) + + from sympy import lambdify + u_bc_x = lambdify(domain.coordinates, u_bc[0]) + u_bc_y = lambdify(domain.coordinates, u_bc[1]) + + u_ex_x = lambdify(domain.coordinates, u_ex[0]) + u_ex_y = lambdify(domain.coordinates, u_ex[1]) + + return f_vect, [u_bc_x, u_bc_y], [u_ex_x, u_ex_y] + +if __name__ == '__main__': + nc = 5 + deg = 3 + + source_type = 'manu_maxwell_inhom' + domain_name = 'pretzel_f' + + omega = np.pi + eta = -omega**2 # source - return diags + err = solve_hcurl_source_pbm( + nc=nc, deg=deg, + eta=eta, + nu=0, + mu=1, + domain_name=domain_name, + source_type=source_type, + backend_language='pyccel-gcc') + \ No newline at end of file diff --git a/examples/feec/hcurl_source_testcase.py b/examples/feec/hcurl_source_testcase.py deleted file mode 100644 index dc60f2102..000000000 --- a/examples/feec/hcurl_source_testcase.py +++ /dev/null @@ -1,145 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -""" - Runner script for solving the H(curl) source problem. -""" - -import os -import numpy as np -from psydac.feec.multipatch.examples.hcurl_source_pbms_conga_2d import solve_hcurl_source_pbm - -from psydac.feec.multipatch.utilities import time_count, FEM_sol_fn, get_run_dir, get_plot_dir, get_mat_dir, get_sol_dir, diag_fn -from psydac.feec.multipatch.utils_conga_2d import write_diags_to_file - -t_stamp_full = time_count() - -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- -# -# main test-cases used for the ppc paper: - -# test_case = 'maxwell_hom_eta=50' # used in paper -#test_case = 'maxwell_hom_eta=170' # used in paper -test_case = 'maxwell_inhom' # used in paper - -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -# numerical parameters: -domain_name = 'pretzel_f' -# domain_name = 'curved_L_shape' - -# currently only 'tilde_Pi' is implemented -source_proj = 'tilde_Pi' - -# nc_s = [np.array([16 for _ in range(18)])] - -# corners in pretzel [2, 2, 2*,2*, 2, 1, 1, 1, 1, 1, 0, 0, 1, 2*, 2*, 2, 0, 0 ] -nc_s = [np.array([16, 16, 16, 16, 16, 8, 8, 8, 8, - 8, 8, 8, 8, 16, 16, 16, 8, 8])] -# nc_s = [10] -# refine handles only -# nc_s = [np.array([16, 16, 16, 16, 16, 8, 8, 8, 8, 4, 2, 2, 4, 16, 16, 16, 2, 2])] - -# refine source -# nc_s = [np.array([32, 8, 8, 32, 32, 32, 32, 8, 8, 8, 8, 8, 8, 32, 8, 8, 8, 8])] - -deg_s = [3] - -if test_case == 'maxwell_hom_eta=50': - homogeneous = True - source_type = 'elliptic_J' - omega = np.sqrt(50) # source time pulsation - -elif test_case == 'maxwell_hom_eta=170': - homogeneous = True - source_type = 'elliptic_J' - omega = np.sqrt(170) # source time pulsation - -elif test_case == 'maxwell_inhom': - homogeneous = False - source_type = 'manu_maxwell_inhom' - omega = np.pi - -else: - raise ValueError(test_case) - -case_dir = test_case - -eta = int(-omega**2 * roundoff) / roundoff - -project_sol = True # True # (use conf proj of solution for visualization) -gamma_h = 10 - -# -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -common_diag_filename = './' + case_dir + '_diags.txt' - -for nc in nc_s: - for deg in deg_s: - - params = { - 'domain_name': domain_name, - 'nc': nc, - 'deg': deg, - 'homogeneous': homogeneous, - 'source_type': source_type, - 'source_proj': source_proj, - 'project_sol': project_sol, - 'omega': omega, - 'gamma_h': gamma_h, - } - # backend_language = 'numba' - backend_language = 'pyccel-gcc' - - run_dir = get_run_dir(domain_name, nc, deg, source_type=source_type) - plot_dir = get_plot_dir(case_dir, run_dir) - diag_filename = plot_dir + '/' + \ - diag_fn(source_type=source_type, source_proj=source_proj) - - - - print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') - print(' Calling solve_hcurl_source_pbm() with params = {}'.format(params)) - print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') - - # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - # calling solver for: - # - # find u in H(curl), s.t. - # A u = f on \Omega - # n x u = n x u_bc on \partial \Omega - # with - # A u := eta * u + mu * curl curl u - nu * grad div u - - diags = solve_hcurl_source_pbm( - nc=nc, deg=deg, - eta=eta, - nu=0, - mu=1, - domain_name=domain_name, - source_type=source_type, - source_proj=source_proj, - backend_language=backend_language, - project_sol=project_sol, - gamma_h=gamma_h, - plot_dir=plot_dir, - ) - - # - # ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - - write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=diag_filename, - params=params) - write_diags_to_file( - diags, - script_filename=__file__, - diag_filename=common_diag_filename, - params=params) - -time_count(t_stamp_full, msg='full program') diff --git a/examples/feec/mixed_source_pbms_conga_2d.py b/examples/feec/mixed_source_pbms_conga_2d.py deleted file mode 100644 index 7bc382bf4..000000000 --- a/examples/feec/mixed_source_pbms_conga_2d.py +++ /dev/null @@ -1,455 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -from mpi4py import MPI - -import os -import numpy as np -from collections import OrderedDict - -from sympy import lambdify - -from scipy.sparse import bmat -from scipy.sparse.linalg import spsolve - -from sympde.calculus import dot -from sympde.topology import element_of -from sympde.expr.expr import LinearForm -from sympde.expr.expr import integral -from sympde.topology import Derham - -from psydac.api.settings import PSYDAC_BACKENDS - -from psydac.feec.pull_push import pull_2d_h1, pull_2d_hcurl, pull_2d_l2 - -from psydac.feec.multipatch.api import discretize -from psydac.feec.multipatch.fem_linear_operators import IdLinearOperator -from psydac.feec.multipatch.operators import HodgeOperator -from psydac.fem.plotting_utilities import plot_field_2d as plot_field -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain -from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_sol_for_magnetostatic_pbm -from psydac.feec.multipatch.examples.hcurl_eigen_pbms_conga_2d import get_eigenvalues -from psydac.feec.multipatch.utilities import time_count - -from psydac.feec.multipatch.non_matching_operators import construct_h1_conforming_projection, construct_hcurl_conforming_projection - - -def solve_magnetostatic_pbm( - nc=4, deg=4, domain_name='pretzel_f', backend_language=None, source_proj='P_L2_wcurl_J', - source_type='dipole_J', bc_type='metallic', - gamma0_h=10., gamma1_h=10., - dim_harmonic_space=0, - project_solution=False, - plot_source=False, plot_dir=None, hide_plots=True, - m_load_dir="", -): - """ - solver for a magnetostatic problem - - div B = 0 - curl B = j - - written in the form of a mixed problem: find p in H1, u in H(curl), such that - - G^* u = f_scal on \\Omega - G p + A u = f_vect on \\Omega - - with operators - - G: p -> grad p - G^*: u -> -div u - A: u -> curl curl u - - and sources - - f_scal = 0 - f_vect = curl j - - -- then the solution u = (Bx, By) satisfies the original magnetostatic equation, see e.g. - Beirão da Veiga, Brezzi, Dassi, Marini and Russo, Virtual Element approx of 2D magnetostatic pbms, CMAME 327 (2017) - - Here the operators G and A are discretized with - - Gh: V0h -> V1h and Ah: V1h -> V1h - - in a broken-FEEC approach involving a discrete sequence on a 2D multipatch domain \\Omega, - - V0h --grad-> V1h -—curl-> V2h - - and boundary conditions to be specified (see the multi-patch paper for details). - - Harmonic constraint: if dim_harmonic_space > 0, a constraint is added, of the form - - u in H^\\perp - - where H = ker(L) is the kernel of the Hodge-Laplace operator L = curl curl u - grad div - - Note: if source_proj == 'P_L2_wcurl_J' then a scalar J is given and we define the V1h part of the discrete source as - l(v) := - - :param nc: nb of cells per dimension, in each patch - :param deg: coordinate degree in each patch - :param gamma0_h: jump penalization parameter in V0h - :param gamma1_h: jump penalization parameter in V1h - :param source_proj: approximation operator for the source, possible values are 'P_geom' or 'P_L2' - :param source_type: must be implemented as a test-case - :param bc_type: 'metallic' or 'pseudo-vacuum' -- see details in multi-patch paper - :param m_load_dir: directory for matrix storage - """ - - ncells = [nc, nc] - degree = [deg, deg] - - # if backend_language is None: - # backend_language='python' - # print('[note: using '+backend_language+ ' backends in discretize functions]') - assert bc_type in ['metallic', 'pseudo-vacuum'] - - print('---------------------------------------------------------------------------------------------------------') - print('Starting solve_mixed_source_pbm function with: ') - print(' ncells = {}'.format(ncells)) - print(' degree = {}'.format(degree)) - print(' domain_name = {}'.format(domain_name)) - print(' source_proj = {}'.format(source_proj)) - print(' bc_type = {}'.format(bc_type)) - print(' backend_language = {}'.format(backend_language)) - print('---------------------------------------------------------------------------------------------------------') - - print('building symbolic and discrete domain...') - domain = build_multipatch_domain(domain_name=domain_name) - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) - domain_h = discretize(domain, ncells=ncells) - - print('building symbolic and discrete derham sequences...') - derham = Derham(domain, ["H1", "Hcurl", "L2"]) - derham_h = discretize(derham, domain_h, degree=degree) - - V0h = derham_h.V0 - V1h = derham_h.V1 - V2h = derham_h.V2 - print('dim(V0h) = {}'.format(V0h.nbasis)) - print('dim(V1h) = {}'.format(V1h.nbasis)) - print('dim(V2h) = {}'.format(V2h.nbasis)) - - print('building the discrete operators:') - print('commuting projection operators...') - nquads = [4 * (d + 1) for d in degree] - P0, P1, P2 = derham_h.projectors(nquads=nquads) - - # these physical projection operators should probably be in the - # interface... - def P0_phys(f_phys): - f = lambdify(domain.coordinates, f_phys) - f_log = [pull_2d_h1(f, m.get_callable_mapping()) - for m in mappings_list] - return P0(f_log) - - def P1_phys(f_phys): - f_x = lambdify(domain.coordinates, f_phys[0]) - f_y = lambdify(domain.coordinates, f_phys[1]) - f_log = [pull_2d_hcurl([f_x, f_y], m.get_callable_mapping()) - for m in mappings_list] - return P1(f_log) - - def P2_phys(f_phys): - f = lambdify(domain.coordinates, f_phys) - f_log = [pull_2d_l2(f, m.get_callable_mapping()) - for m in mappings_list] - return P2(f_log) - - I0_m = IdLinearOperator(V0h).to_sparse_matrix() - I1_m = IdLinearOperator(V1h).to_sparse_matrix() - - print('Hodge operators...') - # multi-patch (broken) linear operators / matrices - H0 = HodgeOperator( - V0h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=0) - H1 = HodgeOperator( - V1h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=1) - H2 = HodgeOperator( - V2h, - domain_h, - backend_language=backend_language, - load_dir=m_load_dir, - load_space_index=2) - - H0_m = H0.to_sparse_matrix() # = mass matrix of V0 - dH0_m = H0.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V0 - H1_m = H1.to_sparse_matrix() # = mass matrix of V1 - dH1_m = H1.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V1 - H2_m = H2.to_sparse_matrix() # = mass matrix of V2 - dH2_m = H2.get_dual_Hodge_sparse_matrix() # = inverse mass matrix of V2 - - M0_m = H0_m - M1_m = H1_m # usual notation - - hom_bc = (bc_type == 'pseudo-vacuum') # /!\ here u = B is in H(curl), not E /!\ - print('with hom_bc = {}'.format(hom_bc)) - - print('conforming projection operators...') - # conforming Projections (should take into account the boundary conditions - # of the continuous deRham sequence) - cP0_m = construct_h1_conforming_projection(V0h, hom_bc=True) - cP1_m = construct_hcurl_conforming_projection(V1h, hom_bc=True) - - print('broken differential operators...') - bD0, bD1 = derham_h.broken_derivatives_as_operators - bD0_m = bD0.to_sparse_matrix() - bD1_m = bD1.to_sparse_matrix() - - if not os.path.exists(plot_dir): - os.makedirs(plot_dir) - - # Conga (projection-based) operator matrices - print('grad matrix...') - G_m = bD0_m @ cP0_m - tG_m = H1_m @ G_m # grad: V0h -> tV1h - - print('curl-curl stiffness matrix...') - C_m = bD1_m @ cP1_m - CC_m = C_m.transpose() @ H2_m @ C_m - - # jump penalization and stabilization operators: - JP0_m = I0_m - cP0_m - S0_m = JP0_m.transpose() @ H0_m @ JP0_m - - JP1_m = I1_m - cP1_m - S1_m = JP1_m.transpose() @ H1_m @ JP1_m - - if not hom_bc: - # very small regularization to avoid constant p=1 in the kernel - reg_S0_m = 1e-16 * M0_m + gamma0_h * S0_m - else: - reg_S0_m = gamma0_h * S0_m - - hf_cs = [] - if dim_harmonic_space > 0: - - print('computing the harmonic fields...') - gamma_Lh = 10 # penalization value should not change the kernel - - GD_m = - tG_m @ dH0_m @ G_m.transpose() @ H1_m # todo: check with paper - L_m = CC_m - GD_m + gamma_Lh * S1_m - eigenvalues, eigenvectors = get_eigenvalues( - dim_harmonic_space + 1, 1e-6, L_m, H1_m) - - for i in range(dim_harmonic_space): - lambda_i = eigenvalues[i] - print( - ".. storing eigenmode #{}, with eigenvalue = {}".format( - i, lambda_i)) - # check: - if abs(lambda_i) > 1e-8: - print(" ****** WARNING! this eigenvalue should be 0! ****** ") - hf_cs.append(eigenvectors[:, i]) - - # matrix of the coefs of the harmonic fields (Lambda^H_i) in the basis (Lambda_i), in the form: - # hf_m = (c^H_{i,j})_{i < dim_harmonic_space, j < dim_V1} such that - # Lambda^H_i = sum_j c^H_{i,j} Lambda^1_j - hf_m = np.array(hf_cs).transpose() - MH_m = M1_m @ hf_m - - # check: - # should be the first positive eigenvalue of L_h - lambda_i = eigenvalues[dim_harmonic_space] - if abs(lambda_i) < 1e-4: - print(" ****** Warning -- something is probably wrong: ") - print( - " ****** eigenmode #{} should have positive eigenvalue: {}".format( - dim_harmonic_space, lambda_i)) - - print('computing the full operator matrix with harmonic constraint...') - A_m = bmat([[reg_S0_m, tG_m.transpose(), None], - [tG_m, CC_m + gamma1_h * S1_m, MH_m], - [None, MH_m.transpose(), None]]) - - else: - print('computing the full operator matrix without harmonic constraint...') - - A_m = bmat([[reg_S0_m, tG_m.transpose()], - [tG_m, CC_m + gamma1_h * S1_m]]) - - # get exact source, bc's, ref solution... - # (not all the returned functions are useful here) - print('getting the source and ref solution...') - N_diag = 200 - method = 'conga' - f_scal, f_vect, j_scal, uh_ref = get_source_and_sol_for_magnetostatic_pbm( - source_type=source_type, domain=domain, domain_name=domain_name) - - # compute approximate source: - # ff_h = (f0_h, f1_h) = (P0_h f_scal, P1_h f_vect) with projection operators specified by source_proj - # and dual-basis coefficients in column array bb_c = (b0_c, b1_c) - # note: f1_h may also be defined through the special option 'P_L2_wcurl_J' - # for magnetostatic problems - f0_c = f1_c = j2_c = None - assert source_proj in ['P_geom', 'P_L2', 'P_L2_wcurl_J'] - - if f_scal is None: - tilde_f0_c = np.zeros(V0h.nbasis) - else: - print('approximating the V0 source with ' + source_proj) - if source_proj == 'P_geom': - f0_h = P0_phys(f_scal) - f0_c = f0_h.coeffs.toarray() - tilde_f0_c = H0_m.dot(f0_c) - else: - # L2 proj - tilde_f0_c = derham_h.get_dual_dofs( - space='V0', - f=f_scal, - backend_language=backend_language, - return_format='numpy_array') - - if source_proj == 'P_L2_wcurl_J': - if j_scal is None: - tilde_j2_c = np.zeros(V2h.nbasis) - tilde_f1_c = np.zeros(V1h.nbasis) - else: - print('approximating the V1 source as a weak curl of j_scal') - tilde_j2_c = derham_h.get_dual_dofs( - space='V2', - f=j_scal, - backend_language=backend_language, - return_format='numpy_array') - tilde_f1_c = C_m.transpose().dot(tilde_j2_c) - elif f_vect is None: - tilde_f1_c = np.zeros(V1h.nbasis) - else: - print('approximating the V1 source with ' + source_proj) - if source_proj == 'P_geom': - f1_h = P1_phys(f_vect) - f1_c = f1_h.coeffs.toarray() - tilde_f1_c = H1_m.dot(f1_c) - else: - assert source_proj == 'P_L2' - tilde_f1_c = derham_h.get_dual_dofs( - space='V1', - f=f_vect, - backend_language=backend_language, - return_format='numpy_array') - - if plot_source: - if f0_c is None: - f0_c = dH0_m.dot(tilde_f0_c) - plot_field(numpy_coeffs=f0_c, Vh=V0h, space_kind='h1', domain=domain, title='f0_h with P = ' + source_proj, - filename=plot_dir + 'f0h_' + source_proj + '.png', hide_plot=hide_plots) - if f1_c is None: - f1_c = dH1_m.dot(tilde_f1_c) - plot_field(numpy_coeffs=f1_c, Vh=V1h, space_kind='hcurl', domain=domain, title='f1_h with P = ' + source_proj, - filename=plot_dir + 'f1h_' + source_proj + '.png', hide_plot=hide_plots) - if source_proj == 'P_L2_wcurl_J': - if j2_c is None: - j2_c = dH2_m.dot(tilde_j2_c) - plot_field(numpy_coeffs=j2_c, Vh=V2h, space_kind='l2', domain=domain, title='P_L2 jh in V2h', - filename=plot_dir + 'j2h.png', hide_plot=hide_plots) - - print("building block RHS") - if dim_harmonic_space > 0: - tilde_h_c = np.zeros(dim_harmonic_space) # harmonic part of the rhs - b_c = np.block([tilde_f0_c, tilde_f1_c, tilde_h_c]) - else: - b_c = np.block([tilde_f0_c, tilde_f1_c]) - - # direct solve with scipy spsolve ------------------------------ - print('solving source problem with scipy.spsolve...') - sol_c = spsolve(A_m.asformat('csr'), b_c) - # ------------------------------------------------------------ - ph_c = sol_c[:V0h.nbasis] - uh_c = sol_c[V0h.nbasis:V0h.nbasis + V1h.nbasis] - hh_c = np.zeros(V1h.nbasis) - if dim_harmonic_space > 0: - # compute the harmonic part (h) of the solution - # coefs of the harmonic part, in the basis of the harmonic fields - hh_hbcoefs = sol_c[V0h.nbasis + V1h.nbasis:] - assert len(hh_hbcoefs) == dim_harmonic_space - for i in range(dim_harmonic_space): - # coefs the of the i-th harmonic field, in the B/M spline basis of - # V1h - hi_c = hf_cs[i] - hh_c += hh_hbcoefs[i] * hi_c - - if project_solution: - print('projecting the homogeneous solution on the conforming problem space...') - uh_c = cP1_m.dot(uh_c) - u_name = r'$P^1_h B_h$' - ph_c = cP0_m.dot(ph_c) - p_name = r'$P^0_h p_h$' - else: - u_name = r'$B_h$' - p_name = r'$p_h$' - - print('getting and plotting the FEM solution from numpy coefs array...') - params_str = 'gamma0_h={}_gamma1_h={}'.format(gamma0_h, gamma1_h) - title = r'solution {} (amplitude)'.format(p_name) - plot_field(numpy_coeffs=ph_c, Vh=V0h, space_kind='h1', - domain=domain, title=title, filename=plot_dir + params_str + '_ph.png', hide_plot=hide_plots) - title = r'solution $h_h$ (amplitude)' - plot_field(numpy_coeffs=hh_c, Vh=V1h, space_kind='hcurl', - domain=domain, title=title, filename=plot_dir + params_str + '_hh.png', hide_plot=hide_plots) - title = r'solution {} (amplitude)'.format(u_name) - plot_field(numpy_coeffs=uh_c, Vh=V1h, space_kind='hcurl', plot_type='amplitude', - domain=domain, title=title, filename=plot_dir + params_str + '_uh.png', hide_plot=hide_plots) - title = r'solution {} (vector field)'.format(u_name) - plot_field(numpy_coeffs=uh_c, Vh=V1h, space_kind='hcurl', plot_type='vector_field', - domain=domain, title=title, filename=plot_dir + params_str + '_uh_vf.png', hide_plot=hide_plots) - title = r'solution {} (components)'.format(u_name) - plot_field(numpy_coeffs=uh_c, Vh=V1h, space_kind='hcurl', plot_type='components', - domain=domain, title=title, filename=plot_dir + params_str + '_uh_xy.png', hide_plot=hide_plots) - - -if __name__ == '__main__': - - t_stamp_full = time_count() - - bc_type = 'metallic' - # bc_type = 'pseudo-vacuum' - source_type = 'dipole_J' - - # source_proj = 'P_L2_wcurl_J' - source_proj = 'P_geom' - - domain_name = 'pretzel_f' - dim_harmonic_space = 3 - - # nc = 20 - # deg = 4 - nc = 10 - deg = 2 - - # domain_name = 'curved_L_shape' - # dim_harmonic_space = 0 - - # nc = 2 - # deg = 2 - - run_dir = '{}_{}_bc={}_nc={}_deg={}/'.format( - domain_name, source_type, bc_type, nc, deg) - m_load_dir = 'matrices_{}_nc={}_deg={}/'.format(domain_name, nc, deg) - solve_magnetostatic_pbm( - nc=nc, deg=deg, - domain_name=domain_name, - source_type=source_type, - source_proj=source_proj, - bc_type=bc_type, - backend_language='pyccel-gcc', - dim_harmonic_space=dim_harmonic_space, - plot_source=True, - plot_dir='./plots/magnetostatic_runs/' + run_dir, - hide_plots=True, - m_load_dir=m_load_dir - ) - - time_count(t_stamp_full, msg='full program') From de759208c8cfaf02339a7cda69ba5cc5ec614653 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 13:35:41 +0100 Subject: [PATCH 28/63] fix td example --- examples/feec/ppc_test_cases.py | 412 ------------------------ examples/feec/timedomain_maxwell.py | 483 ++++++++++------------------ 2 files changed, 171 insertions(+), 724 deletions(-) delete mode 100644 examples/feec/ppc_test_cases.py diff --git a/examples/feec/ppc_test_cases.py b/examples/feec/ppc_test_cases.py deleted file mode 100644 index de3d487b2..000000000 --- a/examples/feec/ppc_test_cases.py +++ /dev/null @@ -1,412 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -import os -import numpy as np - -from sympy import pi, cos, sin, Tuple, exp, atan, atan2 -from sympy.functions.special.error_functions import erf -# todo [MCP, 12/02/2022]: add an 'equation' argument to be able to return -# 'exact solution' - -def get_phi_pulse(x_0, y_0, domain=None): - x, y = domain.coordinates - ds2_0 = (0.02)**2 - sigma_0 = (x - x_0)**2 + (y - y_0)**2 - phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) - - return phi_0 - - -def get_div_free_pulse(x_0, y_0, domain=None): - x, y = domain.coordinates - ds2_0 = (0.02)**2 - sigma_0 = (x - x_0)**2 + (y - y_0)**2 - phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) - dx_sig_0 = 2 * (x - x_0) - dy_sig_0 = 2 * (y - y_0) - dx_phi_0 = - dx_sig_0 * sigma_0 / ds2_0 * phi_0 - dy_phi_0 = - dy_sig_0 * sigma_0 / ds2_0 * phi_0 - f_x = dy_phi_0 - f_y = - dx_phi_0 - f_vect = Tuple(f_x, f_y) - - return f_vect - - -def get_curl_free_pulse(x_0, y_0, domain=None, pp=False): - # return -grad phi_0 - x, y = domain.coordinates - if pp: - # psi=phi - ds2_0 = (0.02)**2 - else: - ds2_0 = (0.1)**2 - sigma_0 = (x - x_0)**2 + (y - y_0)**2 - phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) - dx_sig_0 = 2 * (x - x_0) - dy_sig_0 = 2 * (y - y_0) - dx_phi_0 = - dx_sig_0 * sigma_0 / ds2_0 * phi_0 - dy_phi_0 = - dy_sig_0 * sigma_0 / ds2_0 * phi_0 - f_x = -dx_phi_0 - f_y = -dy_phi_0 - f_vect = Tuple(f_x, f_y) - - return f_vect - - -def get_Delta_phi_pulse(x_0, y_0, domain=None, pp=False): - # return -Delta phi_0, with same phi_0 as in get_curl_free_pulse() - x, y = domain.coordinates - if pp: - # psi=phi - ds2_0 = (0.02)**2 - else: - ds2_0 = (0.1)**2 - sigma_0 = (x - x_0)**2 + (y - y_0)**2 - phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) - dx_sig_0 = 2 * (x - x_0) - dy_sig_0 = 2 * (y - y_0) - dxx_sig_0 = 2 - dyy_sig_0 = 2 - dxx_phi_0 = ((dx_sig_0 * sigma_0 / ds2_0)**2 - - ((dx_sig_0)**2 + dxx_sig_0 * sigma_0) / ds2_0) * phi_0 - dyy_phi_0 = ((dy_sig_0 * sigma_0 / ds2_0)**2 - - ((dy_sig_0)**2 + dyy_sig_0 * sigma_0) / ds2_0) * phi_0 - f = - dxx_phi_0 - dyy_phi_0 - - return f - - -def get_Gaussian_beam_old(x_0, y_0, domain=None): - # return E = cos(k*x) exp( - x^2 + y^2 / 2 sigma^2) v - x, y = domain.coordinates - x = x - x_0 - y = y - y_0 - - k = (10, 0) - nk = np.sqrt(k[0]**2 + k[1]**2) - - v = (k[0] / nk, k[1] / nk) - - sigma = 0.05 - - xy = x**2 + y**2 - ef = exp(- xy / (2 * sigma**2)) - - E = cos(k[1] * x + k[0] * y) * ef - B = (-v[1] * x + v[0] * y) / (sigma**2) * E - - return Tuple(v[0] * E, v[1] * E), B - - -def get_Gaussian_beam(x_0, y_0, domain=None): - # return E = cos(k*x) exp( - x^2 + y^2 / 2 sigma^2) v - x, y = domain.coordinates - - x = x - x_0 - y = y - y_0 - - sigma = 0.1 - - xy = x**2 + y**2 - ef = 1 / (sigma**2) * exp(- xy / (2 * sigma**2)) - - # E = curl exp - E = Tuple(y * ef, -x * ef) - - # B = curl E - B = (xy / (sigma**2) - 2) * ef - - return E, B - - -def get_diag_Gaussian_beam(x_0, y_0, domain=None): - # return E = cos(k*x) exp( - x^2 + y^2 / 2 sigma^2) v - x, y = domain.coordinates - x = x - x_0 - y = y - y_0 - - k = (np.pi, np.pi) - nk = np.sqrt(k[0]**2 + k[1]**2) - - v = (k[0] / nk, k[1] / nk) - - sigma = 0.25 - - xy = x**2 + y**2 - ef = exp(- xy / (2 * sigma**2)) - - E = cos(k[1] * x + k[0] * y) * ef - B = (-v[1] * x + v[0] * y) / (sigma**2) * E - - return Tuple(v[0] * E, v[1] * E), B - - -def get_easy_Gaussian_beam(x_0, y_0, domain=None): - # return E = cos(k*x) exp( - x^2 + y^2 / 2 sigma^2) v - x, y = domain.coordinates - x = x - x_0 - y = y - y_0 - - k = pi - sigma = 0.5 - - xy = x**2 + y**2 - ef = exp(- xy / (2 * sigma**2)) - - E = cos(k * y) * ef - B = -y / (sigma**2) * E - - return Tuple(E, 0), B - - -def get_Gaussian_beam2(x_0, y_0, domain=None): - """ - Gaussian beam - Beam inciding from the left, centered and normal to wall: - x: axial normalized distance to the beam's focus - y: radial normalized distance to the center axis of the beam - """ - x, y = domain.coordinates - - x0 = x_0 - y0 = y_0 - theta = pi / 2 - w0 = 1 - - t = [(x - x0) * cos(theta) - (y - y0) * sin(theta), - (x - x0) * sin(theta) + (y - y0) * cos(theta)] - - EW0 = 1.0 # amplitude at the waist - k0 = 2 * pi # free-space wavenumber - - x_ray = pi * w0 ** 2 # Rayleigh range - - w = w0 * (1 + t[0]**2 / x_ray**2)**0.5 # width - curv = t[0] / (t[0]**2 + x_ray**2) # curvature - - # corresponds to atan(x / x_ray), which is the Gouy phase - gouy_psi = -0.5 * atan2(t[0] / x_ray, 1.) - - EW_mod = EW0 * (w0 / w)**0.5 * exp(-(t[1] ** 2) / (w ** 2)) # Amplitude - phase = k0 * t[0] + 0.5 * k0 * curv * t[1] ** 2 + gouy_psi # Phase - - EW_r = EW_mod * cos(phase) # Real part - EW_i = EW_mod * sin(phase) # Imaginary part - - B = 0 # t[1]/(w**2) * EW_r - - return Tuple(0, EW_r), B - - -def get_source_and_sol_for_magnetostatic_pbm( - source_type=None, - domain=None, domain_name=None, - refsol_params=None -): - """ - provide source, and exact solutions when available, for: - - Find u=B in H(curl) such that - - div B = 0 - curl B = j - - written as a mixed problem, see solve_magnetostatic_pbm() - """ - u_ex = None # exact solution - x, y = domain.coordinates - if source_type == 'dipole_J': - # we compute two possible source terms: - # . a dipole current j_scal = phi_0 - phi_1 (two blobs) - # . and f_vect = curl j_scal - x_0 = 1.0 - y_0 = 1.0 - ds2_0 = (0.02)**2 - sigma_0 = (x - x_0)**2 + (y - y_0)**2 - phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) - dx_sig_0 = 2 * (x - x_0) - dy_sig_0 = 2 * (y - y_0) - dx_phi_0 = - dx_sig_0 * sigma_0 / ds2_0 * phi_0 - dy_phi_0 = - dy_sig_0 * sigma_0 / ds2_0 * phi_0 - - x_1 = 2.0 - y_1 = 2.0 - ds2_1 = (0.02)**2 - sigma_1 = (x - x_1)**2 + (y - y_1)**2 - phi_1 = exp(-sigma_1**2 / (2 * ds2_1)) - dx_sig_1 = 2 * (x - x_1) - dy_sig_1 = 2 * (y - y_1) - dx_phi_1 = - dx_sig_1 * sigma_1 / ds2_1 * phi_1 - dy_phi_1 = - dy_sig_1 * sigma_1 / ds2_1 * phi_1 - - f_scal = None - j_scal = phi_0 - phi_1 - f_x = dy_phi_0 - dy_phi_1 - f_y = - dx_phi_0 + dx_phi_1 - f_vect = Tuple(f_x, f_y) - - else: - raise ValueError(source_type) - - return f_scal, f_vect, j_scal, u_ex - - -def get_source_and_solution_hcurl( - source_type=None, eta=0, mu=0, nu=0, - domain=None, domain_name=None): - """ - provide source, and exact solutions when available, for: - - Find u in H(curl) such that - - A u = f on \\Omega - n x u = n x u_bc on \\partial \\Omega - - with - - A u := eta * u + mu * curl curl u - nu * grad div u - - see solve_hcurl_source_pbm() - """ - - # exact solutions (if available) - u_ex = None - curl_u_ex = None - div_u_ex = None - - # bc solution: describe the bc on boundary. Inside domain, values should - # not matter. Homogeneous bc will be used if None - u_bc = None - - # source terms - f_vect = None - - # auxiliary term (for more diagnostics) - grad_phi = None - phi = None - - x, y = domain.coordinates - - if source_type == 'manu_maxwell_inhom': - # used for Maxwell equation with manufactured solution - f_vect = Tuple(eta * sin(pi * y) - pi**2 * sin(pi * y) * cos(pi * x) + pi**2 * sin(pi * y), - eta * sin(pi * x) * cos(pi * y) + pi**2 * sin(pi * x) * cos(pi * y)) - if nu == 0: - u_ex = Tuple(sin(pi * y), sin(pi * x) * cos(pi * y)) - curl_u_ex = pi * (cos(pi * x) * cos(pi * y) - cos(pi * y)) - div_u_ex = -pi * sin(pi * x) * sin(pi * y) - else: - raise NotImplementedError - u_bc = u_ex - - elif source_type == 'elliptic_J': - # no manufactured solution for Maxwell pbm - x0 = 1.5 - y0 = 1.5 - s = (x - x0) - (y - y0) - t = (x - x0) + (y - y0) - a = (1 / 1.9)**2 - b = (1 / 1.2)**2 - sigma2 = 0.0121 - tau = a * s**2 + b * t**2 - 1 - phi = exp(-tau**2 / (2 * sigma2)) - dx_tau = 2 * (a * s + b * t) - dy_tau = 2 * (-a * s + b * t) - - f_x = dy_tau * phi - f_y = - dx_tau * phi - f_vect = Tuple(f_x, f_y) - - else: - raise ValueError(source_type) - - # u_ex = Tuple(0, 1) # DEBUG - return f_vect, u_bc, u_ex, curl_u_ex, div_u_ex # , phi, grad_phi - - -def get_source_and_solution_h1(source_type=None, eta=0, mu=0, - domain=None, domain_name=None): - """ - provide source, and exact solutions when available, for: - - Find u in H^1, such that - - A u = f on \\Omega - u = u_bc on \\partial \\Omega - - with - - A u := eta * u - mu * div grad u - - see solve_h1_source_pbm() - """ - - # exact solutions (if available) - u_ex = None - - # bc solution: describe the bc on boundary. Inside domain, values should - # not matter. Homogeneous bc will be used if None - u_bc = None - - # source terms - f_scal = None - - # auxiliary term (for more diagnostics) - grad_phi = None - phi = None - - x, y = domain.coordinates - - if source_type in ['manu_poisson_elliptic']: - x0 = 1.5 - y0 = 1.5 - s = (x - x0) - (y - y0) - t = (x - x0) + (y - y0) - a = (1 / 1.9)**2 - b = (1 / 1.2)**2 - sigma2 = 0.0121 - tau = a * s**2 + b * t**2 - 1 - phi = exp(-tau**2 / (2 * sigma2)) - dx_tau = 2 * (a * s + b * t) - dy_tau = 2 * (-a * s + b * t) - dxx_tau = 2 * (a + b) - dyy_tau = 2 * (a + b) - - dx_phi = (-tau * dx_tau / sigma2) * phi - dy_phi = (-tau * dy_tau / sigma2) * phi - grad_phi = Tuple(dx_phi, dy_phi) - - f_scal = -((tau * dx_tau / sigma2)**2 - (tau * dxx_tau + dx_tau**2) / sigma2 - + (tau * dy_tau / sigma2)**2 - (tau * dyy_tau + dy_tau**2) / sigma2) * phi - - # exact solution of -p'' = f with hom. bc's on pretzel domain - if mu == 1 and eta == 0: - u_ex = phi - else: - print('WARNING (54375385643): exact solution not available in this case!') - - if not domain_name in ['pretzel', 'pretzel_f']: - # we may have non-hom bc's - u_bc = u_ex - - elif source_type == 'manu_poisson_2': - f_scal = -4 - if mu == 1 and eta == 0: - u_ex = x**2 + y**2 - else: - raise NotImplementedError - u_bc = u_ex - - elif source_type == 'manu_poisson_sincos': - u_ex = sin(pi * x) * cos(pi * y) - f_scal = (eta + 2 * mu * pi**2) * u_ex - u_bc = u_ex - - else: - raise ValueError(source_type) - - return f_scal, u_bc, u_ex diff --git a/examples/feec/timedomain_maxwell.py b/examples/feec/timedomain_maxwell.py index 4525b2f04..4b0b24495 100644 --- a/examples/feec/timedomain_maxwell.py +++ b/examples/feec/timedomain_maxwell.py @@ -15,44 +15,30 @@ V0h --grad-> V1h -—curl-> V2h (Eh) (Bh) """ - -from pytest import param -from mpi4py import MPI - import os import numpy as np -import scipy as sp -from collections import OrderedDict -import matplotlib.pyplot as plt -from sympy import lambdify, Matrix +from sympde.calculus import grad, dot, curl, cross +from sympde.topology import NormalVector +from sympde.topology import elements_of +from sympde.topology import Derham +from sympde.expr.expr import integral +from sympde.expr.expr import BilinearForm -from scipy.sparse.linalg import spsolve -from scipy import special +from psydac.linalg.basic import IdentityOperator -from sympde.calculus import dot -from sympde.topology import element_of -from sympde.expr.expr import LinearForm -from sympde.expr.expr import integral, Norm -from sympde.topology import Derham -from psydac.linalg.basic import IdentityOperator - -from psydac.api.settings import PSYDAC_BACKENDS +from psydac.api.settings import PSYDAC_BACKENDS from psydac.api.discretization import discretize - -from psydac.fem.plotting_utilities import plot_field_2d as plot_field -from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain - -from psydac.feec.multipatch.examples.ppc_test_cases import get_source_and_solution_hcurl, get_div_free_pulse, get_curl_free_pulse, get_Delta_phi_pulse, get_Gaussian_beam -from psydac.feec.multipatch.utils_conga_2d import DiagGrid, P0_phys, P1_phys, P2_phys, get_Vh_diags_for -from psydac.feec.multipatch.utilities import time_count -from psydac.fem.basic import FemField -from psydac.feec.multipatch.multipatch_domain_utilities import build_cartesian_multipatch_domain - from psydac.api.postprocessing import OutputManager, PostProcessManager -from psydac.fem.projectors import get_dual_dofs +from psydac.feec.multipatch_domain_utilities import build_multipatch_domain, build_cartesian_multipatch_domain + +from psydac.fem.basic import FemField +from psydac.fem.projectors import get_dual_dofs +#============================================================================== +# Solver for the TD Maxwell problem +#============================================================================== def solve_td_maxwell_pbm(*, nc=4, deg=4, @@ -62,15 +48,10 @@ def solve_td_maxwell_pbm(*, domain_name='pretzel_f', backend='pyccel-gcc', source_type='zero', - source_omega=None, - source_proj='P_L2', - project_sol=False, - filter_source=True, E0_type='pulse_2', - E0_proj='P_L2', plot_dir=None, - plot_time_ranges=None, - domain_lims=None + domain_lims=None, + p_moments=4, ): """ solver for the TD Maxwell problem: find E(t) in H(curl), B in L2, such that @@ -113,77 +94,37 @@ def solve_td_maxwell_pbm(*, Name of the backend used for acceleration of the computational kernels, to be chosen among the available keys of the PSYDAC_BACKENDS dict. - source_type : str {'zero' | 'pulse' | 'cf_pulse' | 'Il_pulse'} + source_type : str {'zero' | 'pulse' | 'cf_pulse' } Name that identifies the space-time profile of the current source, to be chosen among those available in the function get_source_and_solution(). Available options: - 'zero' : no current source - 'pulse' : div-free current source, time-harmonic - 'cf_pulse': curl-free current source, time-harmonic - - 'Il_pulse': Issautier-like pulse, with both a div-free and a - curl-free component, not time-harmonic. - - source_omega : float - Pulsation of the time-harmonic component (if any) of a time-dependent - current source. - - source_proj : str {'P_geom' | 'P_L2'} - Name of the approximation operator for the current source: 'P_geom' is - a geometric projector (based on inter/histopolation) which yields the - primal degrees of freedom; 'P_L2' is an L2 projector which yields the - dual degrees of freedom. Change of basis from primal to dual (and vice - versa) is obtained through multiplication with the proper Hodge matrix. - - project_sol : bool - Whether the solution fields should be projected onto the corresponding - conforming spaces before plotting them. - - filter_source : bool - If True, the current source will be filtered with the conforming - projector operator (or its dual, depending on which basis is used). E0_type : str {'zero', 'pulse'} Initial conditions for the electric field. Choose 'zero' for E0=0 and 'pulse' for a non-zero field localized in a small region. - E0_proj : str {'P_geom' | 'P_L2'} - Name of the approximation operator for the initial electric field E0 - (see source_proj for details). Only relevant if E0 is not zero. - plot_dir : str Path to the directory where the figures will be saved. - plot_time_ranges : list - List of lists, of the form `[[start, end], dtp]`, where `[start, end]` - is a time interval and `dtp` is the time between two successive plots. - domain_lims : list If the domain_name is 'refined_square' or 'square_L_shape', this parameter must be set to the list of the two intervals defining the rectangular domain, i.e. `[[x_min, x_max], [y_min, y_max]]`. - + + p_moments : int + Degree of the polynomial moments used in the conforming projection. """ degree = [deg, deg] - if source_omega is not None: - period_time = 2 * np.pi / source_omega - Nt_pp = period_time // dt_max - - if plot_time_ranges is None: - plot_time_ranges = [ - [[0, final_time], final_time] - ] - print('---------------------------------------------------------------------------------------------------------') print('Starting solve_td_maxwell_pbm function with: ') print(' ncells = {}'.format(nc)) print(' degree = {}'.format(degree)) print(' domain_name = {}'.format(domain_name)) - print(' E0_type = {}'.format(E0_type)) - print(' E0_proj = {}'.format(E0_proj)) - print(' source_type = {}'.format(source_type)) - print(' source_proj = {}'.format(source_proj)) print(' backend = {}'.format(backend)) print('---------------------------------------------------------------------------------------------------------') @@ -191,12 +132,10 @@ def solve_td_maxwell_pbm(*, print() print(' -- building discrete spaces and operators --') - t_stamp = time_count() print(' .. multi-patch domain...') if domain_name == 'refined_square' or domain_name == 'square_L_shape': int_x, int_y = domain_lims domain = build_cartesian_multipatch_domain(nc, int_x, int_y, mapping='identity') - else: domain = build_multipatch_domain(domain_name=domain_name) @@ -209,67 +148,43 @@ def solve_td_maxwell_pbm(*, ncells = {patch.name: [nc[int(patch.name[2])][int(patch.name[4])], nc[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior} - mappings = OrderedDict([(P.logical_domain, P.mapping) - for P in domain.interior]) - mappings_list = list(mappings.values()) - - t_stamp = time_count(t_stamp) print(' .. derham sequence...') derham = Derham(domain, ["H1", "Hcurl", "L2"]) - t_stamp = time_count(t_stamp) print(' .. discrete domain...') domain_h = discretize(domain, ncells=ncells) - t_stamp = time_count(t_stamp) print(' .. discrete derham sequence...') - derham_h = discretize(derham, domain_h, degree=degree) - t_stamp = time_count(t_stamp) print(' .. commuting projection operators...') nquads = [4 * (d + 1) for d in degree] P0, P1, P2 = derham_h.projectors(nquads=nquads) - t_stamp = time_count(t_stamp) print(' .. multi-patch spaces...') V0h, V1h, V2h = derham_h.spaces - t_stamp = time_count(t_stamp) print(' .. Id operator and matrix...') I1 = IdentityOperator(V1h.coeff_space) - t_stamp = time_count(t_stamp) print(' .. Hodge operators...') H0, H1, H2 = derham_h.hodge_operators(kind='linop') dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True) - - t_stamp = time_count(t_stamp) print(' .. conforming Projection operators...') - cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', p_moments = degree[0]+2, hom_bc = False) + cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', p_moments = p_moments, hom_bc = False) - t_stamp = time_count(t_stamp) print(' .. broken differential operators...') bD0, bD1 = derham_h.derivatives(kind='linop') - - if plot_dir is not None and not os.path.exists(plot_dir): - os.makedirs(plot_dir) - print(' .. matrix of the primal curl (in primal bases)...') C = bD1 @ cP1 + print(' .. matrix of the dual curl (also in primal bases)...') dC = dH1 @ C.T @ H2 - ### Silvermueller ABC - from sympde.calculus import grad, dot, curl, cross - from sympde.topology import NormalVector - from sympde.expr.expr import BilinearForm - from sympde.topology import elements_of - u, v = elements_of(derham.V1, names='u, v') nn = NormalVector('nn') boundary = domain.boundary @@ -278,16 +193,15 @@ def solve_td_maxwell_pbm(*, a = BilinearForm((u, v), integral(boundary, expr_b)) ah = discretize(a, domain_h, [V1h, V1h], backend=PSYDAC_BACKENDS[backend],) A_eps = ah.assemble() - # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ - - # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ # Compute stable time step size based on max CFL and max dt dt = compute_stable_dt(C=C, dC=dC, cfl_max=cfl_max, dt_max=dt_max) - # ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ + print(" Reduce time step to match the simulation final time:") + Nt = int(np.ceil(final_time / dt)) + dt = final_time / Nt + print(f" . Time step size : dt = {dt}") + print(' total nb of time steps: Nt = {}, final time: T = {:5.4f}'.format(Nt, final_time)) - # Absorbing dC - CH2 = C.T @ H2 H1A = H1 + dt * A_eps # alternative inverse @@ -303,48 +217,15 @@ def solve_td_maxwell_pbm(*, H1A_inv = SparseMatrixLinearOperator(M.codomain, M.domain, M_inv) #### - dC = H1A_inv @ CH2 + # Absorbing dC + dC = H1A_inv @ C.T @ H2 dCH1 = H1A_inv @ H1 - print(' .. matrix of the dual div (still in primal bases)...') - D = dH0 @ cP0.T @ bD0.T @ H1 - - - print(" Reduce time step to match the simulation final time:") - Nt = int(np.ceil(final_time / dt)) - dt = final_time / Nt - print(f" . Time step size : dt = {dt}") - print(f" . Nb of time steps: Nt = {Nt}") - - # ... - def is_plotting_time(nt, *, dt=dt, Nt=Nt, plot_time_ranges=plot_time_ranges): - if nt in [0, Nt]: - return True - for [start, end], dt_plots in plot_time_ranges: - # number of time steps between two successive plots - ds = max(dt_plots // dt, 1) - if (start <= nt * dt <= end) and (nt % ds == 0): - return True - return False - # ... - - - print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print(' total nb of time steps: Nt = {}, final time: T = {:5.4f}'.format(Nt, final_time)) - print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print(' ------ ------ ------ ------ ------ ------ ------ ------ ') - print(' ------ ------ ------ ------ ------ ------ ------ ------ ') # ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- # source - - t_stamp = time_count(t_stamp) print() print(' -- getting source --') - f0_h = None - f0_harmonic_h = None - rho0_h = None if source_type == 'zero': @@ -359,113 +240,28 @@ def is_plotting_time(nt, *, dt=dt, Nt=Nt, plot_time_ranges=plot_time_ranges): f0 = get_curl_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) - elif source_type == 'Il_pulse': # Issautier-like pulse - # source will be - # J = curl A + cos(om*t) * grad phi - # so that - # dt rho = - div J = - cos(om*t) Delta phi - # for instance, with rho(t=0) = 0 this gives - # rho = - sin(om*t)/om * Delta phi - # and Gauss' law reads - # div E = rho = - sin(om*t)/om * Delta phi - f0 = get_div_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is curl A - f0_harmonic = get_curl_free_pulse( x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is grad phi - - rho0 = get_Delta_phi_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) # this is Delta phi - tilde_rho0_h = get_dual_dofs(Vh=V0h, f=rho0, domain_h=domain_h, backend_language=backend) - tilde_rho0_h = cP0.T @ tilde_rho0_h - rho0_h = dH0.dot(tilde_rho0_h) else: - f0, u_bc, u_ex, curl_u_ex, div_u_ex = get_source_and_solution_hcurl(source_type=source_type, domain=domain, domain_name=domain_name) - assert u_bc is None # only homogeneous BC's for now - - - if source_omega is not None: - f0_harmonic = f0 - f0 = None - - def source_enveloppe(tau): - return 1 - - t_stamp = time_count(t_stamp) - tilde_f0_h = f0_h = None - tilde_f0_harmonic_h = f0_harmonic_h = None - - if source_proj == 'P_geom': - print(' .. projecting the source with commuting projection...') - - if f0 is not None: - f0_h = P1_phys(f0, P1, domain).coeffs - tilde_f0_h = H1.dot(f0_h) - - if f0_harmonic is not None: - f0_harmonic_h = P1_phys(f0_harmonic, P1, domain).coeffs - tilde_f0_harmonic_h = H1.dot(f0_harmonic_h) - - elif source_proj == 'P_L2': - - if f0 is not None: - if source_type == 'Il_pulse': - source_name = 'Il_pulse_f0' - else: - source_name = source_type + raise ValueError(source_type) - print(' .. projecting the source f0 with L2 projection...') - tilde_f0_h = get_dual_dofs(Vh=V1h, f=f0, domain_h=domain_h, backend_language=backend) - if f0_harmonic is not None: - if source_type == 'Il_pulse': - source_name = 'Il_pulse_f0_harmonic' - else: - source_name = source_type + if f0 is not None: + print(' .. projecting the source f0 with L2 projection...') + tilde_f0_h = get_dual_dofs(Vh=V1h, f=f0, domain_h=domain_h, backend_language=backend) - print(' .. projecting the source f0_harmonic with L2 projection...') - tilde_f0_harmonic_h = get_dual_dofs(Vh=V1h, f=f0_harmonic, domain_h=domain_h, backend_language=backend) - - else: - raise ValueError(source_proj) - - t_stamp = time_count(t_stamp) - if filter_source: print(' .. filtering the source...') - if tilde_f0_h is not None: - tilde_f0_h = cP1.T @ tilde_f0_h - - if tilde_f0_harmonic_h is not None: - tilde_f0_harmonic_h = cP1.T @ tilde_f0_harmonic_h + tilde_f0_h = cP1.T @ tilde_f0_h - if tilde_f0_h is not None: f0_h = dH1.dot(tilde_f0_h) - if tilde_f0_harmonic_h is not None: - f0_harmonic_h = dH1.dot(tilde_f0_harmonic_h) - + else: - if f0_h is None: f0_h = V1h.coeff_space.zeros() - t_stamp = time_count(t_stamp) - - # diags arrays - E_norm2_diag = np.zeros(Nt + 1) - B_norm2_diag = np.zeros(Nt + 1) - divE_norm2_diag = np.zeros(Nt + 1) - time_diag = np.zeros(Nt + 1) - PE_norm2_diag = np.zeros(Nt + 1) - I_PE_norm2_diag = np.zeros(Nt + 1) - J_norm2_diag = np.zeros(Nt + 1) - if source_type == 'Il_pulse': - GaussErr_norm2_diag = np.zeros(Nt + 1) - GaussErrP_norm2_diag = np.zeros(Nt + 1) - else: - GaussErr_norm2_diag = None - GaussErrP_norm2_diag = None - # ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- # initial solution - print(' .. initial solution ..') + print(' -- initial solution --') # initial B sol B_h = V2h.coeff_space.zeros() @@ -479,38 +275,31 @@ def source_enveloppe(tau): E0 = get_div_free_pulse(x_0=np.pi/2, y_0=np.pi/2, domain=domain) - if E0_proj == 'P_geom': - print(' .. projecting E0 with commuting projection...') - E0_h = P1_phys(E0, P1, domain) - E_h = E0_h.coeffs - - elif E0_proj == 'P_L2': - - print(' .. projecting E0 with L2 projection...') - tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) - E_h = dH1.dot(tilde_E0_h) + print(' .. projecting E0 with L2 projection...') + tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) + E_h = dH1.dot(tilde_E0_h) elif E0_type == 'pulse_2': E0, B0 = get_Gaussian_beam(y_0=np.pi/2, x_0=np.pi/2, domain=domain) - if E0_proj == 'P_geom': - print(' .. projecting E0 with commuting projection...') + print(' .. projecting E0 with L2 projection...') + tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) + E_h = dH1.dot(tilde_E0_h) - E0_h = P1_phys(E0, P1, domain) - E_h = E0_h.coeffs + tilde_B0_h = get_dual_dofs(Vh=V2h, f=B0, domain_h=domain_h, backend_language=backend) + B_h = dH2.dot(tilde_B0_h) - B0_h = P2_phys(B0, P2, domain) - B_h = B0_h.coeffs + elif E0_type == 'Gaussian': + + E0, B0 = get_Gaussian_beam(y_0=np.pi/2, x_0=np.pi/2, domain=domain) - elif E0_proj == 'P_L2': - - print(' .. projecting E0 with L2 projection...') - tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) - E_h = dH1.dot(tilde_E0_h) + print(' .. projecting E0 with L2 projection...') + tilde_E0_h = get_dual_dofs(Vh=V1h, f=E0, domain_h=domain_h, backend_language=backend) + E_h = dH1.dot(tilde_E0_h) - tilde_B0_h = get_dual_dofs(Vh=V2h, f=B0, domain_h=domain_h, backend_language=backend) - B_h = dH2.dot(tilde_B0_h) + tilde_B0_h = get_dual_dofs(Vh=V2h, f=B0, domain_h=domain_h, backend_language=backend) + B_h = dH2.dot(tilde_B0_h) else: raise ValueError(E0_type) @@ -518,23 +307,9 @@ def source_enveloppe(tau): # ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- # time loop - def compute_diags(E_h, B_h, J_h, nt): - time_diag[nt] = (nt) * dt - PE_h = cP1.dot(E_h) - I_PE_h = E_h - PE_h - E_norm2_diag[nt] = E_h.inner(H1.dot(E_h)) - PE_norm2_diag[nt] = PE_h.inner(H1.dot(PE_h)) - I_PE_norm2_diag[nt] = I_PE_h.inner(H1.dot(I_PE_h)) - J_norm2_diag[nt] = J_h.inner(H1.dot(J_h)) - B_norm2_diag[nt] = B_h.inner(H2.dot(B_h)) - divE_h = D @ E_h - divE_norm2_diag[nt] = divE_h.inner(H0.dot(divE_h)) - if source_type == 'Il_pulse' and source_omega is not None: - rho_h = rho0_h * np.sin(source_omega * nt * dt) / omega - GaussErr = rho_h - divE_h - GaussErrP = rho_h - D @ PE_h - GaussErr_norm2_diag[nt] = GaussErr.inner(H0.dot(GaussErr)) - GaussErrP_norm2_diag[nt] = GaussErrP.inner(H0.dot(GaussErrP)) + + if plot_dir is not None and not os.path.exists(plot_dir): + os.makedirs(plot_dir) if plot_dir: OM1 = OutputManager(plot_dir + '/spaces1.yml', plot_dir + '/fields1.h5') @@ -555,38 +330,35 @@ def compute_diags(E_h, B_h, J_h, nt): f_h = f0_h.copy() + Btemp_h = B_h.copy() + Etemp_h = E_h.copy() + + print(" -- time loop --") for nt in range(Nt): - print(' .. nt+1 = {}/{}'.format(nt + 1, Nt)) + print(' .. nt+1 = {}/{}'.format(nt+1, Nt)) # 1/2 faraday: Bn -> Bn+1/2 - B_h -= (dt / 2) * C @ E_h - - # ampere: En -> En+1 - if f0_harmonic_h is not None and source_omega is not None: - f_harmonic_h = f0_harmonic_h * (np.sin(source_omega * (nt + 1) * dt) - np.sin(source_omega * (nt) * dt)) / (dt * source_omega) # * source_enveloppe(omega*(nt+1/2)*dt) - f_h = f0_h + f_harmonic_h - - E_h = dCH1 @ E_h + dt * (dC @ B_h - f_h) - - # 1/2 faraday: Bn+1/2 -> Bn+1 - B_h -= (dt / 2) * C @ E_h - - # diags: - compute_diags(E_h, B_h, f_h, nt=nt + 1) - - + # B_h -= (dt/2) * C @ E_h + # E_h = A_eps @ E_h + dt * dC @ B_h + # B_h -= (dt/2) * C @ E_h + + C.dot(E_h, out=Btemp_h) + B_h -= (dt/2) * Btemp_h + + dCH1.dot(E_h, out=E_h) + dC.dot(B_h, out=Etemp_h) + E_h += dt * (Etemp_h - f_h) + + C.dot(E_h, out=Btemp_h) + B_h -= (dt/2) * Btemp_h - if is_plotting_time(nt + 1) and plot_dir: - print("Plot fields") - - Eh = FemField(V1h, coeffs=cP1 @ E_h) - OM1.add_snapshot(t=nt * dt, ts=nt) - OM1.export_fields(Eh=Eh) - - Bh = FemField(V2h, coeffs=B_h) - OM2.add_snapshot(t=nt * dt, ts=nt) - OM2.export_fields(Bh=Bh) + Eh = FemField(V1h, coeffs=cP1 @ E_h) + OM1.add_snapshot(t=nt*dt, ts=nt) + OM1.export_fields(Eh = Eh) + Bh = FemField(V2h, coeffs=B_h) + OM2.add_snapshot(t=nt*dt, ts=nt) + OM2.export_fields(Bh=Bh) if plot_dir: OM1.close() @@ -616,8 +388,9 @@ def compute_diags(E_h, B_h, J_h, nt): fields='Bh') PM.close() - - +# ============================================================================== +# Compute stable time step size +# ============================================================================== def compute_stable_dt(*, C, dC, cfl_max, dt_max=None): """ Compute a stable time step size based on the maximum CFL parameter in the @@ -666,7 +439,6 @@ def compute_stable_dt(*, C, dC, cfl_max, dt_max=None): print(' WARNING !!! cfl = {} '.format(cfl)) print(' ****** ****** ****** ****** ****** ****** ') - t_stamp = time_count() V = C.domain from psydac.linalg.utilities import array_to_psydac vv = array_to_psydac(np.random.rand(V.dimension), V) @@ -690,7 +462,6 @@ def compute_stable_dt(*, C, dC, cfl_max, dt_max=None): spectral_rho = norm_vv # approximation conv = abs((spectral_rho - old_spectral_rho) / spectral_rho) < 0.001 print(" ... spectral radius iteration: spectral_rho( dC @ C ) ~= {}".format(spectral_rho)) - t_stamp = time_count(t_stamp) norm_op = np.sqrt(spectral_rho) c_dt_max = 2. / norm_op @@ -707,3 +478,91 @@ def compute_stable_dt(*, C, dC, cfl_max, dt_max=None): print(f" -- and spectral_radius((c*dt)**2* dC @ C ) = {(light_c * dt * norm_op)**2} (should be < 4).") return dt + +# ============================================================================== +# Test Sources +# ============================================================================== +def get_div_free_pulse(x_0, y_0, domain=None): + + from sympy import pi, cos, sin, Tuple, exp + + x, y = domain.coordinates + ds2_0 = (0.02)**2 + sigma_0 = (x - x_0)**2 + (y - y_0)**2 + phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) + dx_sig_0 = 2 * (x - x_0) + dy_sig_0 = 2 * (y - y_0) + dx_phi_0 = - dx_sig_0 * sigma_0 / ds2_0 * phi_0 + dy_phi_0 = - dy_sig_0 * sigma_0 / ds2_0 * phi_0 + f_x = dy_phi_0 + f_y = - dx_phi_0 + f_vect = Tuple(f_x, f_y) + + return f_vect + + +def get_curl_free_pulse(x_0, y_0, domain=None, pp=False): + + from sympy import pi, cos, sin, Tuple, exp + + # return -grad phi_0 + x, y = domain.coordinates + if pp: + # psi=phi + ds2_0 = (0.02)**2 + else: + ds2_0 = (0.1)**2 + sigma_0 = (x - x_0)**2 + (y - y_0)**2 + phi_0 = exp(-sigma_0**2 / (2 * ds2_0)) + dx_sig_0 = 2 * (x - x_0) + dy_sig_0 = 2 * (y - y_0) + dx_phi_0 = - dx_sig_0 * sigma_0 / ds2_0 * phi_0 + dy_phi_0 = - dy_sig_0 * sigma_0 / ds2_0 * phi_0 + f_x = -dx_phi_0 + f_y = -dy_phi_0 + f_vect = Tuple(f_x, f_y) + + return f_vect + +def get_Gaussian_beam(x_0, y_0, domain=None): + + from sympy import pi, cos, sin, Tuple, exp + + # return E = cos(k*x) exp( - x^2 + y^2 / 2 sigma^2) v + x, y = domain.coordinates + + x = x - x_0 + y = y - y_0 + + sigma = 0.1 + + xy = x**2 + y**2 + ef = 1 / (sigma**2) * exp(- xy / (2 * sigma**2)) + + # E = curl exp + E = Tuple(y * ef, -x * ef) + + # B = curl E + B = (xy / (sigma**2) - 2) * ef + + return E, B + +if __name__ == '__main__': + domain_name = 'refined_square' + domain_lims = [[0, np.pi], [0, np.pi]] + + nc = 20 + ncells = np.array([[nc, nc, nc], + [nc, 2*nc, nc], + [nc, nc, nc]]) + + deg = 3 + p_moments = deg+1 + + final_time = 2 + + plot_dir = './td_maxwell_pulse/' + + solve_td_maxwell_pbm(nc=ncells, deg=deg, p_moments=p_moments, final_time=final_time, + domain_name=domain_name, domain_lims=domain_lims, + source_type='zero', E0_type='pulse', plot_dir=plot_dir) From 31a47030cf3fc3a3ac0b9595064f9df90df11aa2 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:06:45 +0100 Subject: [PATCH 29/63] finish multipatch examples --- examples/feec/hcurl_eigen_pbms_dg_2d.py | 2 +- .../tests/test_feec_maxwell_multipatch_2d.py | 27 ++- .../tests/test_feec_poisson_multipatch_2d.py | 2 +- examples/feec/timedomain_maxwell.py | 15 +- examples/feec/timedomain_maxwell_testcase.py | 159 ------------------ 5 files changed, 21 insertions(+), 184 deletions(-) delete mode 100644 examples/feec/timedomain_maxwell_testcase.py diff --git a/examples/feec/hcurl_eigen_pbms_dg_2d.py b/examples/feec/hcurl_eigen_pbms_dg_2d.py index 0566a5804..8faa09a29 100644 --- a/examples/feec/hcurl_eigen_pbms_dg_2d.py +++ b/examples/feec/hcurl_eigen_pbms_dg_2d.py @@ -28,7 +28,7 @@ from psydac.api.discretization import discretize from psydac.api.postprocessing import OutputManager, PostProcessManager -from hcurl_eigen_pbms_conga_2d import get_eigenvalues +from examples.feec.hcurl_eigen_pbms_conga_2d import get_eigenvalues #============================================================================== # Solver for curl-curl eigenvalue problems diff --git a/examples/feec/tests/test_feec_maxwell_multipatch_2d.py b/examples/feec/tests/test_feec_maxwell_multipatch_2d.py index bfb8bc210..9a624e3cf 100644 --- a/examples/feec/tests/test_feec_maxwell_multipatch_2d.py +++ b/examples/feec/tests/test_feec_maxwell_multipatch_2d.py @@ -4,12 +4,11 @@ # for full license details. # #---------------------------------------------------------------------------# import numpy as np -import pytest -from psydac.feec.multipatch.examples.hcurl_source_pbms_conga_2d import solve_hcurl_source_pbm -from psydac.feec.multipatch.examples.hcurl_eigen_pbms_conga_2d import hcurl_solve_eigen_pbm -from psydac.feec.multipatch.examples.hcurl_eigen_pbms_dg_2d import hcurl_solve_eigen_pbm_dg -from psydac.feec.multipatch.examples.timedomain_maxwell import solve_td_maxwell_pbm +from examples.feec.hcurl_source_pbms_conga_2d import solve_hcurl_source_pbm +from examples.feec.hcurl_eigen_pbms_conga_2d import hcurl_solve_eigen_pbm +from examples.feec.hcurl_eigen_pbms_dg_2d import hcurl_solve_eigen_pbm_dg +from examples.feec.timedomain_maxwell import solve_td_maxwell_pbm def test_time_harmonic_maxwell_pretzel_f(): nc = 4 @@ -17,22 +16,20 @@ def test_time_harmonic_maxwell_pretzel_f(): source_type = 'manu_maxwell_inhom' domain_name = 'pretzel_f' - source_proj = 'tilde_Pi' omega = np.pi eta = -omega**2 # source - diags = solve_hcurl_source_pbm( + err = solve_hcurl_source_pbm( nc=nc, deg=deg, eta=eta, nu=0, mu=1, domain_name=domain_name, source_type=source_type, - source_proj=source_proj, backend_language='pyccel-gcc') - assert abs(diags["err"] - 0.0072015081402929445) < 1e-10 + assert abs(err - 0.0072015081402929445) < 1e-10 def test_time_harmonic_maxwell_pretzel_f_nc(): deg = 2 @@ -41,22 +38,20 @@ def test_time_harmonic_maxwell_pretzel_f_nc(): source_type = 'manu_maxwell_inhom' domain_name = 'pretzel_f' - source_proj = 'tilde_Pi' omega = np.pi eta = -omega**2 # source - diags = solve_hcurl_source_pbm( + err = solve_hcurl_source_pbm( nc=nc, deg=deg, eta=eta, nu=0, mu=1, domain_name=domain_name, source_type=source_type, - source_proj=source_proj, backend_language='pyccel-gcc') - assert abs(diags["err"] - 0.004849225522124346) < 5e-7 + assert abs(err - 0.004849225522124346) < 5e-7 def test_maxwell_eigen_curved_L_shape(): domain_name = 'curved_L_shape' @@ -77,7 +72,7 @@ def test_maxwell_eigen_curved_L_shape(): nb_eigs_plot = 7 skip_eigs_threshold = 1e-7 - diags, eigenvalues = hcurl_solve_eigen_pbm( + eigenvalues = hcurl_solve_eigen_pbm( ncells=ncells, degree=degree, gamma_h=0, generalized_pbm=True, @@ -120,7 +115,7 @@ def test_maxwell_eigen_curved_L_shape_nc(): nb_eigs_plot = 7 skip_eigs_threshold = 1e-7 - diags, eigenvalues = hcurl_solve_eigen_pbm( + eigenvalues = hcurl_solve_eigen_pbm( ncells=ncells, degree=degree, gamma_h=0, generalized_pbm=True, @@ -163,7 +158,7 @@ def test_maxwell_eigen_curved_L_shape_dg(): nb_eigs_plot = 7 skip_eigs_threshold = 1e-7 - diags, eigenvalues = hcurl_solve_eigen_pbm_dg( + eigenvalues = hcurl_solve_eigen_pbm_dg( ncells=ncells, degree=degree, nu=0, mu=1, diff --git a/examples/feec/tests/test_feec_poisson_multipatch_2d.py b/examples/feec/tests/test_feec_poisson_multipatch_2d.py index 29cab81d1..142ff5ccc 100644 --- a/examples/feec/tests/test_feec_poisson_multipatch_2d.py +++ b/examples/feec/tests/test_feec_poisson_multipatch_2d.py @@ -5,7 +5,7 @@ #---------------------------------------------------------------------------# import numpy as np -from psydac.feec.multipatch.examples.h1_source_pbms_conga_2d import solve_h1_source_pbm +from examples.feec.h1_source_pbms_conga_2d import solve_h1_source_pbm def test_poisson_pretzel_f(): diff --git a/examples/feec/timedomain_maxwell.py b/examples/feec/timedomain_maxwell.py index 4b0b24495..658dc8bfe 100644 --- a/examples/feec/timedomain_maxwell.py +++ b/examples/feec/timedomain_maxwell.py @@ -51,7 +51,7 @@ def solve_td_maxwell_pbm(*, E0_type='pulse_2', plot_dir=None, domain_lims=None, - p_moments=4, + p_moments=-1, ): """ solver for the TD Maxwell problem: find E(t) in H(curl), B in L2, such that @@ -352,13 +352,14 @@ def solve_td_maxwell_pbm(*, C.dot(E_h, out=Btemp_h) B_h -= (dt/2) * Btemp_h - Eh = FemField(V1h, coeffs=cP1 @ E_h) - OM1.add_snapshot(t=nt*dt, ts=nt) - OM1.export_fields(Eh = Eh) + if plot_dir: + Eh = FemField(V1h, coeffs=cP1 @ E_h) + OM1.add_snapshot(t=nt*dt, ts=nt) + OM1.export_fields(Eh = Eh) - Bh = FemField(V2h, coeffs=B_h) - OM2.add_snapshot(t=nt*dt, ts=nt) - OM2.export_fields(Bh=Bh) + Bh = FemField(V2h, coeffs=B_h) + OM2.add_snapshot(t=nt*dt, ts=nt) + OM2.export_fields(Bh=Bh) if plot_dir: OM1.close() diff --git a/examples/feec/timedomain_maxwell_testcase.py b/examples/feec/timedomain_maxwell_testcase.py deleted file mode 100644 index 4a1b5a58e..000000000 --- a/examples/feec/timedomain_maxwell_testcase.py +++ /dev/null @@ -1,159 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -""" - Runner script for solving the time-domain Maxwell problem. -""" - -import numpy as np - -from psydac.feec.multipatch.examples.timedomain_maxwell import solve_td_maxwell_pbm -from psydac.feec.multipatch.utilities import get_run_dir, get_plot_dir - -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- -# - -test_case = 'E0_pulse_no_source' -# test_case = 'Issautier_like_source' -# J_proj_case = 'P_geom' -J_proj_case = 'P_L2' - -# -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -# Parameters to be changed in the batch run -deg = 3 - -# Common simulation parameters -# domain_name = 'square_6' -# ncells = [4,4,4,4,4,4] -# domain_name = 'pretzel_f' - -# non-conf domains -domain = [[0, np.pi], [0, np.pi]] # interval in x- and y-direction -domain_name = 'refined_square' -# use isotropic meshes (probably with a square domain) -# 4x8= 64 patches -# care for the transpose -ncells = np.array([[10, 10, 10], - [10, 20, 10], - [10, 10, 10]]) - -cfl_max = 0.8 - -# 'P_geom' # projection used for initial E0 (B0 = 0 in all cases) -E0_proj = 'P_L2' -backend = 'pyccel-gcc' -project_sol = True # whether cP1 E_h is plotted instead of E_h - -# Parameters that depend on test case -if test_case == 'E0_pulse_no_source': - - E0_type = 'pulse_2' # non-zero initial conditions - source_type = 'zero' # no current source - source_omega = None - final_time = 2 # wave transit time in domain is > 4 - dt_max = None - - plot_a_lot = True - if plot_a_lot: - plot_time_ranges = [[[0, final_time], 0.1]] - else: - plot_time_ranges = [ - [[0, 2], 0.1], - [[final_time - 1, final_time], 0.1], - ] - -# TODO: check -elif test_case == 'Issautier_like_source': - - E0_type = 'zero' # zero initial conditions - source_type = 'Il_pulse' - source_omega = None - final_time = 20 - dt_max = None - - if deg == 3 and final_time == 20: - - plot_time_ranges = [ - [[1.9, 2], 0.1], - [[4.9, 5], 0.1], - [[9.9, 10], 0.1], - [[19.9, 20], 0.1], - ] - -else: - raise ValueError(test_case) - - -# projection used for the source J -if J_proj_case == 'P_geom': - source_proj = 'P_geom' - filter_source = False - -elif J_proj_case == 'P_L2': - source_proj = 'P_L2' - filter_source = False - -elif J_proj_case == 'tilde Pi_1': - source_proj = 'P_L2' - filter_source = True - -else: - raise ValueError(J_proj_case) - -case_dir = 'tdmaxwell_' + test_case + '_J_proj=' + J_proj_case - -if filter_source: - case_dir += '_Jfilter' -else: - case_dir += '_Jnofilter' -if not project_sol: - case_dir += '_E_noproj' - -if source_omega is not None: - case_dir += f'_omega={source_omega}' - -case_dir += f'_tend={final_time}' - -# -# ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- ---- - -run_dir = get_run_dir( - domain_name, - sum(ncells), - deg, - source_type=source_type, - conf_proj="") - -plot_dir = get_plot_dir(case_dir, run_dir) - - -# -params = { - 'nc': ncells, - 'deg': deg, - 'final_time': final_time, - 'cfl_max': cfl_max, - 'dt_max': dt_max, - 'domain_name': domain_name, - 'backend': backend, - 'source_type': source_type, - 'source_omega': source_omega, - 'source_proj': source_proj, - 'project_sol': project_sol, - 'filter_source': filter_source, - 'E0_type': E0_type, - 'E0_proj': E0_proj, - 'plot_dir': plot_dir, - 'plot_time_ranges': plot_time_ranges, - 'domain_lims': domain -} - -print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') -print(' Calling solve_td_maxwell_pbm() with params = {}'.format(params)) -print('\n --- --- --- --- --- --- --- --- --- --- --- --- --- --- \n') - -solve_td_maxwell_pbm(**params) From ffaf555c5d590110dc9550814f8c49fca767dae0 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:16:55 +0100 Subject: [PATCH 30/63] add examples to test workflow --- .github/workflows/testing.yml | 5 +++++ 1 file changed, 5 insertions(+) diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index c3c2da8a4..22b9eb157 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -236,6 +236,11 @@ jobs: run: | python mpi_tester.py --mpirun="mpiexec -n 4 ${MPI_OPTS}" --pyargs psydac -m "parallel and petsc" + - name: Run tests in examples/feec + working-directory: ./pytest + run: | + python -m pytest examples/feec + - name: Remove test directory if: always() run: | From 580c5244d993b66bae61c7331575ad1245de18af Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:23:00 +0100 Subject: [PATCH 31/63] purge feec/multipatch --- docs/source/modules/feec.multipatch.rst | 12 - docs/source/modules/feec.rst | 7 - psydac/feec/multipatch/__init__.py | 5 - psydac/feec/multipatch/utilities.py | 160 --------- psydac/feec/multipatch/utils_conga_2d.py | 392 ----------------------- 5 files changed, 576 deletions(-) delete mode 100644 docs/source/modules/feec.multipatch.rst delete mode 100644 psydac/feec/multipatch/__init__.py delete mode 100644 psydac/feec/multipatch/utilities.py delete mode 100644 psydac/feec/multipatch/utils_conga_2d.py diff --git a/docs/source/modules/feec.multipatch.rst b/docs/source/modules/feec.multipatch.rst deleted file mode 100644 index 85bf08af1..000000000 --- a/docs/source/modules/feec.multipatch.rst +++ /dev/null @@ -1,12 +0,0 @@ -feec.multipatch -=============== - -.. currentmodule:: psydac.feec -.. autosummary:: - :nosignatures: - :toctree: STUBDIR - :template: autosummary/module.rst - - multipatch.multipatch_domain_utilities - multipatch.utilities - multipatch.utils_conga_2d diff --git a/docs/source/modules/feec.rst b/docs/source/modules/feec.rst index f75dfb8cc..c3f50aaba 100644 --- a/docs/source/modules/feec.rst +++ b/docs/source/modules/feec.rst @@ -13,10 +13,3 @@ feec feec.hodge feec.pull_push feec.pushforward - -feec submodules ---------------- -.. toctree:: - :maxdepth: 1 - - feec.multipatch diff --git a/psydac/feec/multipatch/__init__.py b/psydac/feec/multipatch/__init__.py deleted file mode 100644 index 419109b64..000000000 --- a/psydac/feec/multipatch/__init__.py +++ /dev/null @@ -1,5 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# diff --git a/psydac/feec/multipatch/utilities.py b/psydac/feec/multipatch/utilities.py deleted file mode 100644 index 22182c2c7..000000000 --- a/psydac/feec/multipatch/utilities.py +++ /dev/null @@ -1,160 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -import time - - -def time_count(t_stamp=None, msg=None): - new_t_stamp = time.time() - if msg is None: - msg = '' - else: - msg = '[' + msg + ']' - if t_stamp: - print('time elapsed ' + msg + ': ' + repr(new_t_stamp - t_stamp)) - elif len(msg) > 0: - print('time stamp set for ' + msg) - return new_t_stamp - -# --------------------------------------------------------------------------------------------------------------- -# small/temporary utility for saving/loading sparse matrices, plots... -# (should be cleaned !) - - -def source_name(source_type=None, source_proj=None): - """ Get the source term name""" - assert source_type and source_proj - return source_type + '_' + source_proj - - -def sol_ref_fn(source_type, N_diag, source_proj=None): - """ Get the reference solution filename based on the source term type""" - fn = 'u_ref_' + source_name(source_type, - source_proj) + '_N' + repr(N_diag) + '.npz' - return fn - - -def error_fn( - source_type=None, - method=None, - conf_proj=None, - k=None, - domain_name=None, - deg=None): - """ Get the error filename based on the method used to solve the multpatch problem""" - return 'errors/error_' + domain_name + '_' + source_type + '_' + '_deg' + \ - repr(deg) + '_' + get_method_name(method, k, conf_proj=conf_proj) + '.txt' - - -def get_method_name(method=None, k=None, conf_proj=None, penal_regime=None): - """ Get method name used to solve the multpatch problem""" - if method == 'nitsche': - method_name = method - if k == 1: - method_name += '_SIP' - elif k == -1: - method_name += '_NIP' - elif k == 0: - method_name += '_IIP' - else: - assert k is None - elif method == 'conga': - method_name = method - if conf_proj is not None: - method_name += '_' + conf_proj - else: - raise ValueError(method) - if penal_regime is not None: - method_name += '_pr' + repr(penal_regime) - - return method_name - - -def get_fem_name( - method=None, - k=None, - DG_full=False, - conf_proj=None, - domain_name=None, - nc=None, - deg=None, - hom_seq=True): - """ Get Fem name used to solve the multipatch problem""" - assert domain_name - fn = domain_name + (('_nc' + repr(nc)) if nc else '') + \ - (('_deg' + repr(deg)) if deg else '') - if DG_full: - fn += '_fDG' - if method is not None: - fn += '_' + get_method_name(method, k, conf_proj) - if not hom_seq: - fn += '_inhom' - return fn - - -def FEM_sol_fn(source_type=None, source_proj=None): - """ Get the filename for FEM solution coeffs in numpy array format """ - fn = 'sol_' + source_name(source_type, source_proj) + '.npy' - return fn - - -def get_load_dir( - method=None, - DG_full=False, - domain_name=None, - nc=None, - deg=None, - data='matrices'): - """ get load directory name based on the fem name""" - assert data in ['matrices', 'solutions', 'rhs'] - if method is None: - assert data == 'rhs' - fem_name = get_fem_name( - domain_name=domain_name, - method=method, - nc=nc, - deg=deg, - DG_full=DG_full) - return './saved_' + data + '/' + fem_name + '/' - - -def get_run_dir(domain_name, nc, deg, source_type=None, conf_proj=None): - """ Get the run directory name""" - rdir = domain_name - if source_type: - rdir += '_' + source_type - if conf_proj: - rdir += '_P=' + conf_proj - rdir += '_nc={}_deg={}'.format(nc, deg) - return rdir - - -def get_plot_dir(case_dir, run_dir): - """ Get the plot directory name""" - return './plots/' + case_dir + '/' + run_dir - - -def get_mat_dir(domain_name, nc, deg, quad_param=None): - """ Get the directory name where matrices are stored""" - mat_dir = './saved_matrices/matrices_{}_nc={}_deg={}'.format( - domain_name, nc, deg) - if quad_param is not None: - mat_dir += '_qp={}'.format(quad_param) - return mat_dir - - -def get_sol_dir(case_dir, domain_name, nc, deg): - """ Get the directory name where solutions are stored""" - return './saved_solutions/' + case_dir + \ - '/solutions_{}_nc={}_deg={}'.format(domain_name, nc, deg) - - -def diag_fn(source_type=None, source_proj=None): - """ Get the diagnostics filename""" - if source_type is not None: - fn = 'diag_' + source_name(source_type, source_proj) + '.txt' - else: - fn = 'diag.txt' - return fn diff --git a/psydac/feec/multipatch/utils_conga_2d.py b/psydac/feec/multipatch/utils_conga_2d.py deleted file mode 100644 index 7907dea57..000000000 --- a/psydac/feec/multipatch/utils_conga_2d.py +++ /dev/null @@ -1,392 +0,0 @@ -#---------------------------------------------------------------------------# -# This file is part of PSYDAC which is released under MIT License. See the # -# LICENSE file or go to https://github.com/pyccel/psydac/blob/devel/LICENSE # -# for full license details. # -#---------------------------------------------------------------------------# -import os -import datetime - -import numpy as np - -from sympy import lambdify -from sympde.topology import Derham -from sympde.topology.callable_mapping import BasicCallableMapping - -from psydac.api.settings import PSYDAC_BACKENDS -from psydac.feec.pull_push import pull_2d_h1, pull_2d_hcurl, pull_2d_l2 - -from psydac.api.discretization import discretize -from psydac.feec.multipatch.utilities import time_count -from psydac.linalg.utilities import array_to_psydac -from psydac.fem.basic import FemField -from psydac.fem.plotting_utilities import get_plotting_grid, get_grid_quad_weights, get_grid_vals - -from scipy.sparse import kron, block_diag -from psydac.core.bsplines import collocation_matrix, histopolation_matrix -from psydac.linalg.solvers import inverse - - -# commuting projections on the physical domain (should probably be in the -# interface) -def P0_phys(f_phys, P0, domain): - f = lambdify(domain.coordinates, f_phys) - - return P0(f) - - -def P1_phys(f_phys, P1, domain): - f_x = lambdify(domain.coordinates, f_phys[0]) - f_y = lambdify(domain.coordinates, f_phys[1]) - - return P1([f_x, f_y]) - - -def P2_phys(f_phys, P2, domain): - f = lambdify(domain.coordinates, f_phys) - - return P2(f) - - -def get_kind(space='V*'): - # temp helper - if space == 'V0': - kind = 'h1' - elif space == 'V1': - kind = 'hcurl' - elif space == 'V2': - kind = 'l2' - else: - raise ValueError(space) - return kind - -# =============================================================================== -def get_K0_and_K0_inv(V0h, uniform_patches=False): - """ - Compute the change of basis matrices K0 and K0^{-1} in V0h. - - With - K0_ij = sigma^0_i(B_j) = B_jx(n_ix) * B_jy(n_iy) - where sigma_i is the geometric (interpolation) dof - and B_j is the tensor-product B-spline - """ - if uniform_patches: - print(' [[WARNING -- hack in get_K0_and_K0_inv: using copies of 1st-patch matrices in every patch ]] ') - - V0 = V0h.symbolic_space # VOh is FemSpace - domain = V0.domain - K0_blocks = [] - K0_inv_blocks = [] - for k, D in enumerate(domain.interior): - if uniform_patches and k > 0: - K0_k = K0_blocks[0].copy() - K0_inv_k = K0_inv_blocks[0].copy() - - else: - V0_k = V0h.spaces[k] # fem space on patch k: (TensorFemSpace) - K0_k_factors = [None, None] - for d in [0, 1]: - # 1d fem space alond dim d (SplineSpace) - V0_kd = V0_k.spaces[d] - K0_k_factors[d] = collocation_matrix( - knots=V0_kd.knots, - degree=V0_kd.degree, - periodic=V0_kd.periodic, - normalization=V0_kd.basis, - xgrid=V0_kd.greville - ) - K0_k = kron(*K0_k_factors) - K0_k.eliminate_zeros() - K0_inv_k = inv(K0_k.tocsc()) - K0_inv_k.eliminate_zeros() - - K0_blocks.append(K0_k) - K0_inv_blocks.append(K0_inv_k) - K0 = block_diag(K0_blocks) - K0_inv = block_diag(K0_inv_blocks) - return K0, K0_inv - - -# =============================================================================== -def get_K1_and_K1_inv(V1h, uniform_patches=False): - """ - Compute the change of basis matrices K1 and K1^{-1} in Hcurl space V1h. - - With - K1_ij = sigma^1_i(B_j) = int_{e_ix}(M_jx) * B_jy(n_iy) - if i = horizontal edge [e_ix, n_iy] and j = (M_jx o B_jy) x-oriented MoB spline - or - = B_jx(n_ix) * int_{e_iy}(M_jy) - if i = vertical edge [n_ix, e_iy] and j = (B_jx o M_jy) y-oriented BoM spline - (above, 'o' denotes tensor-product for functions) - """ - if uniform_patches: - print(' [[WARNING -- hack in get_K1_and_K1_inv: using copies of 1st-patch matrices in every patch ]] ') - - V1 = V1h.symbolic_space # V1h is FemSpace - domain = V1.domain - K1_blocks = [] - K1_inv_blocks = [] - for k, D in enumerate(domain.interior): - if uniform_patches and k > 0: - K1_k = K1_blocks[0].copy() - K1_inv_k = K1_inv_blocks[0].copy() - - else: - # fem space on patch k: - V1_k = V1h.spaces[k] - K1_k_blocks = [] - for c in [0, 1]: # dim of component - # fem space for comp. dc (TensorFemSpace) - V1_kc = V1_k.spaces[c] - K1_kc_factors = [None, None] - for d in [0, 1]: # dim of variable - # 1d fem space for comp c alond dim d (SplineSpace) - V1_kcd = V1_kc.spaces[d] - if c == d: - K1_kc_factors[d] = histopolation_matrix( - knots=V1_kcd.knots, - degree=V1_kcd.degree, - periodic=V1_kcd.periodic, - normalization=V1_kcd.basis, - xgrid=V1_kcd.ext_greville - ) - else: - K1_kc_factors[d] = collocation_matrix( - knots=V1_kcd.knots, - degree=V1_kcd.degree, - periodic=V1_kcd.periodic, - normalization=V1_kcd.basis, - xgrid=V1_kcd.greville - ) - K1_kc = kron(*K1_kc_factors) - K1_kc.eliminate_zeros() - K1_k_blocks.append(K1_kc) - K1_k = block_diag(K1_k_blocks) - K1_k.eliminate_zeros() - K1_inv_k = inv(K1_k.tocsc()) - K1_inv_k.eliminate_zeros() - - K1_blocks.append(K1_k) - K1_inv_blocks.append(K1_inv_k) - - K1 = block_diag(K1_blocks) - K1_inv = block_diag(K1_inv_blocks) - return K1, K1_inv - -# =============================================================================== - - -def ortho_proj_Hcurl(EE, V1h, domain_h, M1, backend_language='python'): - """ - return orthogonal projection of E on V1h, given M1 the mass matrix - """ - assert isinstance(EE, Tuple) - V1 = V1h.symbolic_space - v = element_of(V1, name='v') - l = LinearForm(v, integral(V1.domain, dot(v, EE))) - lh = discretize( - l, - domain_h, - V1h, - backend=PSYDAC_BACKENDS[backend_language]) - b = lh.assemble() - M1_inv = inverse(M1.mat(), 'pcg', pc='jacobi', tol=1e-10) - sol_coeffs = M1_inv @ b - - return FemField(V1h, coeffs=sol_coeffs) - - -# =============================================================================== -class DiagGrid(): - """ - Class storing: - - a diagnostic cell-centered grid - - writing / quadrature utilities - - a ref solution - - to compare solutions from different FEM spaces on same domain - """ - - def __init__(self, mappings=None, N_diag=None): - - mappings_list = list(mappings.values()) - etas, xx, yy, patch_logvols = get_plotting_grid( - mappings, N=N_diag, centered_nodes=True, return_patch_logvols=True) - quad_weights = get_grid_quad_weights( - etas, patch_logvols, mappings_list) - - self.etas = etas - self.xx = xx - self.yy = yy - self.patch_logvols = patch_logvols - self.quad_weights = quad_weights - self.mappings_list = mappings_list - - self.sol_ref = {} # Fem fields - self.sol_vals = {} # values on diag grid - self.sol_ref_vals = {} # values on diag grid - - def grid_vals_h1(self, v): - return get_grid_vals(v, self.etas, self.mappings_list, space_kind='h1') - - def grid_vals_hcurl(self, v): - return get_grid_vals( - v, - self.etas, - self.mappings_list, - space_kind='hcurl') - - def create_ref_fem_spaces(self, domain=None, ref_nc=None, ref_deg=None): - print('[DiagGrid] Discretizing the ref FEM space...') - degree = [ref_deg, ref_deg] - derham = Derham(domain, ["H1", "Hcurl", "L2"]) - ref_nc = {patch.name: [ref_nc, ref_nc] for patch in domain.interior} - - domain_h = discretize(domain, ncells=ref_nc) - # , backend=PSYDAC_BACKENDS[backend_language]) - derham_h = discretize(derham, domain_h, degree=degree) - self.V0h = derham_h.V0 - self.V1h = derham_h.V1 - - def import_ref_sol_from_coeffs(self, sol_ref_filename=None, space='V*'): - print('[DiagGrid] loading coeffs of ref_sol from {}...'.format( - sol_ref_filename)) - if space == 'V0': - Vh = self.V0h - elif space == 'V1': - Vh = self.V1h - else: - raise ValueError(space) - try: - coeffs = np.load(sol_ref_filename) - except OSError: - print("-- WARNING: file not found, setting sol_ref = 0") - coeffs = np.zeros(Vh.nbasis) - if space in self.sol_ref: - print( - 'WARNING !! sol_ref[{}] exists -- will be overwritten !! '.format(space)) - print('use refined labels if several solutions are needed in the same space') - self.sol_ref[space] = FemField( - Vh, coeffs=array_to_psydac( - coeffs, Vh.coeff_space)) - - def write_sol_values(self, v, space='V*'): - """ - v: FEM field - """ - if space in self.sol_vals: - print( - 'WARNING !! sol_vals[{}] exists -- will be overwritten !! '.format(space)) - print('use refined labels if several solutions are needed in the same space') - self.sol_vals[space] = get_grid_vals( - v, self.etas, self.mappings_list, space_kind=get_kind(space)) - - def write_sol_ref_values(self, v=None, space='V*'): - """ - if no FemField v is provided, then use the self.sol_ref (must have been imported) - """ - if space in self.sol_vals: - print( - 'WARNING !! sol_ref_vals[{}] exists -- will be overwritten !! '.format(space)) - print('use refined labels if several solutions are needed in the same space') - if v is None: - # then sol_ref must have been imported - v = self.sol_ref[space] - self.sol_ref_vals[space] = get_grid_vals( - v, self.etas, self.mappings_list, space_kind=get_kind(space)) - - def compute_l2_error(self, space='V*'): - if space in ['V0', 'V2']: - u = self.sol_ref_vals[space] - uh = self.sol_vals[space] - abs_u = [np.abs(p) for p in u] - abs_uh = [np.abs(p) for p in uh] - errors = [np.abs(p - q) for p, q in zip(u, uh)] - elif space == 'V1': - u_x, u_y = self.sol_ref_vals[space] - uh_x, uh_y = self.sol_vals[space] - abs_u = [np.sqrt((u1)**2 + (u2)**2) for u1, u2 in zip(u_x, u_y)] - abs_uh = [np.sqrt((u1)**2 + (u2)**2) for u1, u2 in zip(uh_x, uh_y)] - errors = [np.sqrt((u1 - v1)**2 + (u2 - v2)**2) - for u1, v1, u2, v2 in zip(u_x, uh_x, u_y, uh_y)] - else: - raise ValueError(space) - - l2_norm_uh = ( - np.sum([J_F * v**2 for v, J_F in zip(abs_uh, self.quad_weights)]))**0.5 - l2_norm_u = ( - np.sum([J_F * v**2 for v, J_F in zip(abs_u, self.quad_weights)]))**0.5 - l2_error = ( - np.sum([J_F * v**2 for v, J_F in zip(errors, self.quad_weights)]))**0.5 - - return l2_norm_uh, l2_norm_u, l2_error - - def get_diags_for(self, v, space='V*', print_diags=True): - self.write_sol_values(v, space) - sol_norm, sol_ref_norm, l2_error = self.compute_l2_error(space) - rel_l2_error = l2_error / (max(sol_norm, sol_ref_norm)) - diags = { - 'sol_norm': sol_norm, - 'sol_ref_norm': sol_ref_norm, - 'rel_l2_error': rel_l2_error, - } - if print_diags: - print(' .. l2 norms (computed via quadratures on diag_grid): ') - print(diags) - - return diags - - -def get_Vh_diags_for( - v=None, - v_ref=None, - M_m=None, - print_diags=True, - msg='error between ?? and ?? in Vh'): - """ - v, v_ref: FemField - M_m: mass matrix in scipy format - """ - uh_c = v.coeffs.toarray() - uh_ref_c = v_ref.coeffs.toarray() - err_c = uh_c - uh_ref_c - l2_error = np.dot(err_c, M_m.dot(err_c))**0.5 - sol_norm = np.dot(uh_c, M_m.dot(uh_c))**0.5 - sol_ref_norm = np.dot(uh_ref_c, M_m.dot(uh_ref_c))**0.5 - rel_l2_error = l2_error / (max(sol_norm, sol_ref_norm)) - diags = { - 'sol_norm': sol_norm, - 'sol_ref_norm': sol_ref_norm, - 'rel_l2_error': rel_l2_error, - } - if print_diags: - print(' .. l2 norms ({}): '.format(msg)) - print(diags) - - return diags - - -def write_diags_to_file(diags, script_filename, diag_filename, params=None): - """ write diagnostics to file """ - print(' -- writing diags to file {} --'.format(diag_filename)) - if not os.path.exists(diag_filename): - open(diag_filename, 'w') - - with open(diag_filename, 'a') as a_writer: - a_writer.write('\n') - a_writer.write( - ' ---------- ---------- ---------- ---------- ---------- ---------- \n') - a_writer.write(' run script: \n {}\n'.format(script_filename)) - a_writer.write( - ' executed on: \n {}\n\n'.format( - datetime.datetime.now())) - a_writer.write(' params: \n') - for key, value in params.items(): - a_writer.write(' {}: {} \n'.format(key, value)) - a_writer.write('\n') - a_writer.write(' diags: \n') - for key, value in diags.items(): - a_writer.write(' {}: {} \n'.format(key, value)) - a_writer.write( - ' ---------- ---------- ---------- ---------- ---------- ---------- \n') - a_writer.write('\n') From afbd14cc21bcfbe3495626e4a5680a4f137cdef1 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:23:56 +0100 Subject: [PATCH 32/63] update feec doc --- docs/source/modules/feec.rst | 1 + 1 file changed, 1 insertion(+) diff --git a/docs/source/modules/feec.rst b/docs/source/modules/feec.rst index c3f50aaba..42313895c 100644 --- a/docs/source/modules/feec.rst +++ b/docs/source/modules/feec.rst @@ -11,5 +11,6 @@ feec feec.derivatives feec.global_geometric_projectors feec.hodge + feec.multipatch_domain_utilities feec.pull_push feec.pushforward From 6035e9aa8471e9328ac53b20b4db287071a728dc Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:28:39 +0100 Subject: [PATCH 33/63] fix broken imports --- psydac/api/tests/build_domain.py | 2 +- psydac/fem/tests/test_dirichlet_projectors.py | 2 +- 2 files changed, 2 insertions(+), 2 deletions(-) diff --git a/psydac/api/tests/build_domain.py b/psydac/api/tests/build_domain.py index 7a77f7c7f..3301294c1 100644 --- a/psydac/api/tests/build_domain.py +++ b/psydac/api/tests/build_domain.py @@ -12,7 +12,7 @@ from sympde.topology import IdentityMapping, PolarMapping, AffineMapping, Mapping # remove after sympde PR #155 is merged and call Domain.join instead -from psydac.feec.multipatch.multipatch_domain_utilities import sympde_Domain_join +from psydac.feec.multipatch_domain_utilities import sympde_Domain_join #============================================================================== # small extension to SymPDE: diff --git a/psydac/fem/tests/test_dirichlet_projectors.py b/psydac/fem/tests/test_dirichlet_projectors.py index bea727244..e2fc41fa8 100644 --- a/psydac/fem/tests/test_dirichlet_projectors.py +++ b/psydac/fem/tests/test_dirichlet_projectors.py @@ -445,7 +445,7 @@ def test_discrete_derham_boundary_projector_multipatch(): comm = None backend = PSYDAC_BACKEND_GPYCCEL - from psydac.feec.multipatch.multipatch_domain_utilities import build_multipatch_domain + from psydac.feec.multipatch_domain_utilities import build_multipatch_domain domain = build_multipatch_domain(domain_name='annulus_3') rng = np.random.default_rng(42) From c002659e3971622a04f0539c7fa75c997d982fb2 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 15:37:50 +0100 Subject: [PATCH 34/63] remove feec.multipatch from script --- docs/update_links.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/update_links.py b/docs/update_links.py index 3ff71a899..cdea472ec 100644 --- a/docs/update_links.py +++ b/docs/update_links.py @@ -5,7 +5,7 @@ 'cmd', 'core', 'ddm', - 'feec', 'feec.multipatch', + 'feec', 'fem', 'linalg', 'linalg.kernels', 'mapping', From 799c757cbcbbbe5ec6fd9108f2819f33f87f0f89 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Wed, 3 Dec 2025 16:45:20 +0100 Subject: [PATCH 35/63] remove failing example testing --- .github/workflows/testing.yml | 5 ----- 1 file changed, 5 deletions(-) diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index 22b9eb157..c3c2da8a4 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -236,11 +236,6 @@ jobs: run: | python mpi_tester.py --mpirun="mpiexec -n 4 ${MPI_OPTS}" --pyargs psydac -m "parallel and petsc" - - name: Run tests in examples/feec - working-directory: ./pytest - run: | - python -m pytest examples/feec - - name: Remove test directory if: always() run: | From 34620f8cf2e115c093c1fa5505bb7cc2b88a16b6 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Thu, 4 Dec 2025 11:19:49 +0100 Subject: [PATCH 36/63] move script and add examples test --- .github/workflows/testing.yml | 7 ++++++- mpi_tester.py => scripts/mpi_tester.py | 0 2 files changed, 6 insertions(+), 1 deletion(-) rename mpi_tester.py => scripts/mpi_tester.py (100%) diff --git a/.github/workflows/testing.yml b/.github/workflows/testing.yml index c3c2da8a4..86e729f1b 100644 --- a/.github/workflows/testing.yml +++ b/.github/workflows/testing.yml @@ -190,7 +190,7 @@ jobs: - name: Initialize test directory run: | mkdir pytest - cp mpi_tester.py pytest + cp scripts/mpi_tester.py pytest - name: Run coverage tests on macOS if: matrix.os == 'macos-14' @@ -236,6 +236,11 @@ jobs: run: | python mpi_tester.py --mpirun="mpiexec -n 4 ${MPI_OPTS}" --pyargs psydac -m "parallel and petsc" + - name: Run single-process example tests with Pytest on Ubuntu + if: matrix.os == 'ubuntu-24.04' + run: | + python -m pytest examples/feec + - name: Remove test directory if: always() run: | diff --git a/mpi_tester.py b/scripts/mpi_tester.py similarity index 100% rename from mpi_tester.py rename to scripts/mpi_tester.py From 1131dc1384676c6867437e99a053cc6a3db52f5e Mon Sep 17 00:00:00 2001 From: elmosa Date: Thu, 4 Dec 2025 19:52:21 +0100 Subject: [PATCH 37/63] add example 3D VTK positive Helmholtz --- .../positive_Helmholtz_3D_fx.png | Bin 0 -> 1973988 bytes .../positive_Helmholtz_3D_fy.png | Bin 0 -> 1973988 bytes .../positive_Helmholtz_3D_fz.png | Bin 0 -> 1973988 bytes .../positive_Helmholtz_3D_ux.png | Bin 0 -> 1973988 bytes .../positive_Helmholtz_3D_uy.png | Bin 0 -> 1973988 bytes .../positive_Helmholtz_3D_uz.png | Bin 0 -> 1973988 bytes .../notebooks/positive_Helmholtz_3D_VTK.ipynb | 295 ++++++++++++++++++ 7 files changed, 295 insertions(+) create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fy.png create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fz.png create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_ux.png create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_uy.png create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_uz.png create mode 100644 examples/notebooks/positive_Helmholtz_3D_VTK.ipynb diff --git a/examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png b/examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png new file mode 100644 index 0000000000000000000000000000000000000000..00d948219f177a26418846e1a6c0854d6a4025cb GIT binary patch literal 1973988 zcmeEv2bfmH_5M<%!!AvcW;;4Whz(4lMx$snighs> zV~nv27)1rdf-PbLv7iVFQWWXz{@>lp&Ntt!b9;NgXCIh5bLPxB?|kfiIdf*_h9Sou z*}O^nCM6{$%?BMda9Bx6-DM>u^)75w7d6Y?saJ--+KfH?H)9XI=%Vw+j6QAbmN_H$6H1N<9F0WHkKCxnaovNxTbm4~x5CI}U1c(3;AOa~u zpqlvbLj;Hb5g-CYfCvzQbRj?nldk!qwM2jj5CI}U1c*R20%S1!9uNT{Km<~QK$~li zc&j!SAT>tQP$CdM0%SAcW6TkV01+SpM1TkofuIo}g9#c@>LUU~fCvx)B0vPfM}Q0_ ze2h5)5g-CYfCvx)A`mnJWH3P^N_`w4MkM z0U|&Ih(JCOAcM*0ywhtUKm>>Y5g-ETMt}?^-SbE5i2xBG0z`laBo=`oyG{Q?B)I@& zGl~5U&@duE1c(3;AOb|d5&<$8OK8|Y1c(3;AOb{y2qYE(GML0p4Gkj#M1Tko0U|&I zED<1sv4n;VM1Tko0q+Q0+H8m8BgqBuZX$aUfeax~KCxmvDNTkZl&%l~B0vO)01?Oy z0%S0`nQA&p1c(3;AOb`nLkN(;WN0$!3K1XzM1Tkof!rWK29ukqj>OUWmws>+a{(fO znu8DlB0vO)fIxt3MnJ&=5g-CYfCvx)B9Iyc$Y4@4RWy_c5CI}U1c(3;5D1XL2q;(} z0z`la5CI~PLj*bu{p`oI=K_$;?D>JcD=N&OVk0U|&IJR|VKF|+qhdoF-y=h=}6WC#JWnG8)P zT_FNQfCvx)B9I#d$Y63a)pV2y5CI}U1c*R}5Fmre&}7mTB0vO)01+Spxj}#oCO1>9 zb9CaOH@0UkfDRNs5&gRudJ zO+y}=)`Dd-Q4Q>Uo#gV(Njd@hyW2F0z@Ew1juIMp95Mz1c(3; zAOb{y2)IRn48|>DlqUj2fCvx)B0vP>Y5g-CVAW%NBVmxU~5J*x75g-CYfCvx)A`mSCWH8a<&C!Se5g-CY zfCvzQAP^vf2?9mxAOb{S#F{Z@G8cf~10p~K;z6K(Ji~HSB0vP9LSXIMwXfHF-hTV- zx^?UJ>C>lg-@ZM1^k~wgNmM3q93nsjh(PcN)Tyef3SKKU5&eZVwXU^u$n}-h{K5W=95SnC|Nh^o|5g-Dt5nv3)HDv5S1X6^+>eZ_k zE?n5HTeoA5IcBfD_JZZ$F;71EB;qkg9C1X87A;cb3r!^gM1Tm$2=ISkG8*2>_y6Df z-!T`!8+Pm!B?7Z&&tATKdH3$!4?OU|#xRW18#Y|CW{q6QG7%sGL?B%Vkin#DzGy8GaEHLpKmWYVHrupo z*G}$+7z`MUT*ERE$Q=T0%jfRQT!8FMJ2QN_i=2-z;X>>?ca?z`_cZrmsySs(&LfC!`!0Wz30 z&KhkF3xN(bA5A+Bh?_TW-fg$tcFHNIbnV(TtRX|z3#I}`K*eMRgGbPsva+&}2d8=> zKm>?DhzKwzCPZ+lI@JguYvl3AA4d!WOGrp7NvSW$=fzg)#fuk9_OIxC;Nc<{0E=bV zbgkRCBnh)f1c(3;NC5(5GbxxPnivZLScSn>lZC20z`lakiqafKm<$>c;ST?X3Us@ zD~4LOY-!RQXchPbB0jIa`YQHCfh`?!$RQXP89ISn(TFRO4nO?x($Z2Whf}yuX}|sU z+k5Z5QCX)>ok0DdG9o|(h(M$Wk&hzxsPvgA08*jW3mju{!WD^k}0z@F^2rwR#^DhA1H$h;^ zlquNCbJ9sCg-u^DHZ~05gqqf^TaOww3g^*)&2oQl< z1en@eiv<5B0yPNWwA+_oei=7F4<9}}0!ZF}|9u?Y0@l*Ickf1x8sU=0Hf`D*eDJ|9 zzWCynEn6ZmfI|=gB0vOEiU1i*N+*tHhk^i7MsB|OW?b+*X3Usq4(P`wZY0SNMH83{kk7ey=`~lBTmnY%Oe3&-`SNF;d1l0j5!-FI z-7mlV0zy;2ez^ZekZ+5R3@T1?fej!uEn2jY>sclOM1Tko0U3dCe>=+~u}lP#kHA0v z@eiC5_tjTlAtj}A=gxvdU~@7y4Mku-4%%I~aN)9L%dkxe+lwL?kwXvxB0vOEiU1i* zN+*tHhk^jsclz|{^Vw&gz5DLFD^{#PvTdtYt#;jYS0tBE7kqaq?e1c*R<2;^p$b$k$WWFjCCz_pSqSFRL~phvjgKzqbS z?oU4X3xF#DKmap;#vn)Z<4VeFRllDMK76D4o

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callable function for the source. In practice, the source could be the interpolation of some experimental data. Besides, we impose periodic boundary conditions everywhere in the boundary.\n", + "\n", + "Let $\\Omega=[0, 10] \\times [-2\\pi, 2\\pi]\\times [-3, 1]$. We want to find $u\\in H(\\mathrm{curl}, \\Omega)$ such that\n", + "\n", + "$$ \\mathrm{curl} \\mathrm{curl} u + \\mu u = f, $$\n", + "\n", + "where $\\mu = \\pi$, and $f$ is a callable function in terms of the domain coordinates, the expression of which is a priori not known. \n", + "\n", + "Only for illustration here we use the callable function\n", + "$$f(x,y,z) = (10e^{-0.5(x-4)^2 - 1.5z^2 - 0.1y^2}, 0, \\cos(y)\\sin(\\pi x / 5)),$$\n", + "\n", + "and project it from $H(\\mathrm{curl}, \\Omega)$ to the corresponding discretized space. This process is analogous with any callable vectorial function.\n", + "\n", + "\n", + "\n", + "## Step 1 : define the domain and spaces and discretize them\n", + "\n", + "This is similar to what is done in other examples" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "39c21151", + "metadata": {}, + "outputs": [ + { + "ename": "", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[1;31mRunning cells with 'Python 3.12.3' requires the ipykernel package.\n", + "\u001b[1;31mCreate a Python Environment with the required packages.\n", + "\u001b[1;31mOr install 'ipykernel' using the command: '/usr/bin/python3 -m pip install ipykernel -U --user --force-reinstall'" + ] + } + ], + "source": [ + "import numpy as np\n", + "from mpi4py import MPI\n", + "from sympde.topology import Cube\n", + "from sympde.topology import VectorFunctionSpace\n", + "from psydac.api.discretization import discretize\n", + "\n", + "comm = MPI.COMM_WORLD # MPI communicator\n", + "\n", + "Omega = Cube('Omega', bounds1=(0, 10), bounds2=(-2*np.pi, 2*np.pi), bounds3=(-3, 1)) # 3D cubic domain\n", + "\n", + "W = VectorFunctionSpace('W', Omega, kind='hcurl') # Hcurl space\n", + "\n", + "ncells = [25, 30, 11] # number of cells in each direction\n", + "degree = [3, 2, 2] # B-spline degree in each direction\n", + "\n", + "periodic = [True, True, True] # set periodic BC in every direction\n", + "\n", + "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic, comm=comm)\n", + "Wh = discretize(W, Omega_h, degree=degree)" + ] + }, + { + "cell_type": "markdown", + "id": "36a9632b", + "metadata": {}, + "source": [ + "## Step 2 : compute the matrix\n", + "\n", + "We assemble the mass and curl curl matrices." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "091d4560", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.topology import elements_of, element_of\n", + "from sympde.expr.expr import BilinearForm, LinearForm, integral\n", + "from sympde.calculus import dot, curl\n", + "from psydac.api.settings import PSYDAC_BACKENDS\n", + "from psydac.fem.basic import FemField\n", + "\n", + "backend_language = 'python'\n", + "backend = PSYDAC_BACKENDS[backend_language]\n", + "\n", + "u, v = elements_of(W, names='u, v') #trial and test functions\n", + "\n", + "m = BilinearForm((u, v), integral(Omega, dot(u, v)))\n", + "mh = discretize(m, Omega_h, [Wh, Wh], backend=backend)\n", + "M = mh.assemble() # Mass matrix\n", + "\n", + "k = BilinearForm((u, v), integral(Omega, dot(curl(u), curl(v))))\n", + "kh = discretize(k, Omega_h, [Wh, Wh], backend=backend)\n", + "K = kh.assemble() # Curl curl matrix\n", + "\n", + "mu = np.pi\n", + "\n", + "A = K + mu*M # system matrix, positive-definite" + ] + }, + { + "cell_type": "markdown", + "id": "8927f88c", + "metadata": {}, + "source": [ + "## Step 3 : compute the right-hand size\n", + "\n", + "We project a callable function to the vector space and use it to assemble the right-hand side of the system." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a13044fa", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl\n", + "f_callable = [lambda x, y, z: 10*np.exp(-0.5*(x-4)**2 - 1.5*z**2 - 1e-1*y**2),\n", + " lambda x, y, z: 0,\n", + " lambda x, y, z: np.cos(y)*np.sin(x*np.pi/5)]\n", + "\n", + "proj_Wh = GlobalGeometricProjectorHcurl(Wh, nquads=[p+1 for p in degree]) # get Hcurl projector, nquads is the number of points for the Gauss quadrature.\n", + "fh = proj_Wh(f_callable) # project callable to field in Wh\n", + "\n", + "f = element_of(W, name='f') # free variable for the FemField\n", + "\n", + "l = LinearForm(v, integral(Omega, dot(f,v)))\n", + "lh = discretize(l, Omega_h, Wh, backend=backend)\n", + "rhs = lh.assemble(f=fh) # assmble RHS, f is a free parameter" + ] + }, + { + "cell_type": "markdown", + "id": "8258971a", + "metadata": {}, + "source": [ + "## Step 4 : solve the system\n", + "Solve the system using Conjugate Gradient" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f0f103d", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.linalg.solvers import inverse\n", + "\n", + "inv_A = inverse(A, solver='cg', tol=1e-2, maxiter=100) # invert using Conjugate Gradient\n", + "\n", + "u = inv_A @ rhs # array of coefficients\n", + "\n", + "uh = FemField(Wh, coeffs=u) # finite element field, callable" + ] + }, + { + "cell_type": "markdown", + "id": "e0c73790", + "metadata": {}, + "source": [ + "## Step 5 : Save results to HDF5 format\n", + "We save the coefficients of the solution and the field used in the right-hand size. This step generates a YAML file containing the space information, and a HDF5 file that stores the coefficients. The fields are saved in parallel. This step does not include an evaluation of the fields on a grid." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c77d25a", + "metadata": {}, + "outputs": [], + "source": [ + "# Save the results using OutputManager\n", + "from psydac.api.postprocessing import OutputManager\n", + "import os\n", + "\n", + "os.makedirs('results_positive_Helmholtz', exist_ok=True)\n", + "\n", + "Om = OutputManager(\n", + " f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm,\n", + " save_mpi_rank=True, \n", + " mode = 'w' \n", + ")\n", + "\n", + "Om.add_spaces(V=Wh)\n", + "Om.export_space_info()\n", + "\n", + "Om.set_static() # the fields do not depend on time\n", + "\n", + "save_fields = {\n", + " 'u': uh,\n", + " 'f': fh\n", + "}\n", + "\n", + "Om.export_fields(**save_fields) # saves the coefficients of the fields\n", + "\n", + "Om.close()\n", + "\n", + "# This generates a YAML file containing the space information, and a HDF5 file that stores the solution coefficients. \n", + "# At this point the solution has not been evaluated on any grid." + ] + }, + { + "cell_type": "markdown", + "id": "a619a838", + "metadata": {}, + "source": [ + "## Step 6 : Evaluate fields on a grid and export to VTK\n", + "Evaluate the saved fields on a grid and export the result to VTK format." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "86a1c531", + "metadata": {}, + "outputs": [], + "source": [ + "# Export the results to VTK using PostProcessManager\n", + "from psydac.api.postprocessing import PostProcessManager\n", + "\n", + "Pm = PostProcessManager(\n", + " domain=Omega,\n", + " space_file=f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm\n", + ")\n", + "\n", + "Pm.export_to_vtk(\n", + " f'results_positive_Helmholtz/visu_{Omega.name}',\n", + " grid=None,\n", + " npts_per_cell=[4,2,4],\n", + " fields=save_fields.keys() # evaluate all the fields that were saved\n", + ")\n", + "\n", + "Pm.close()\n", + "# If this file is run in sequential, then this step will generate a single .vtu file that can be opened with ParaView.\n", + "# If it is run in parallel, it generates a .vtu file per process (containing the local grid) and a .pvtu file. To visualize it in ParaView, open the .pvtu file." + ] + }, + { + "cell_type": "markdown", + "id": "af41d09b", + "metadata": {}, + "source": [ + "## Visualization of the solution in ParaView\n", + "

\n", + " \n", + " \n", + " \n", + "

" + ] + }, + { + "cell_type": "markdown", + "id": "0bb786a7", + "metadata": {}, + "source": [ + "## Visualization of the source in ParaView\n", + "

\n", + " \n", + " \n", + " \n", + "

" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "name": "python", + "version": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} From bd0043b47e4cc84542153a3c2ec9eb863e6d4c9b Mon Sep 17 00:00:00 2001 From: elmosa Date: Thu, 4 Dec 2025 19:57:18 +0100 Subject: [PATCH 38/63] clear output cells --- .../notebooks/positive_Helmholtz_3D_VTK.ipynb | 15 ++------------- 1 file changed, 2 insertions(+), 13 deletions(-) diff --git a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb index c6fe4b219..445e9c09d 100644 --- a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb +++ b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb @@ -5,7 +5,7 @@ "id": "2443e734", "metadata": {}, "source": [ - "# 3D example with VTK and Paraview \n", + "# 3D example with VTK and ParaView \n", "\n", "In this notebook we show how to solve a 3D problem in parallel, save the solution in HDF5 format and export it to VTK. \n", "\n", @@ -34,18 +34,7 @@ "execution_count": null, "id": "39c21151", "metadata": {}, - "outputs": [ - { - "ename": "", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[1;31mRunning cells with 'Python 3.12.3' requires the ipykernel package.\n", - "\u001b[1;31mCreate a Python Environment with the required packages.\n", - "\u001b[1;31mOr install 'ipykernel' using the command: '/usr/bin/python3 -m pip install ipykernel -U --user --force-reinstall'" - ] - } - ], + "outputs": [], "source": [ "import numpy as np\n", "from mpi4py import MPI\n", From 7d7610f8090f4681327ed4bdaecb4fefcfb746ef Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Thu, 4 Dec 2025 20:32:53 +0100 Subject: [PATCH 39/63] nb-clean and put new notebook in docs --- docs/source/examples.rst | 2 +- examples/notebooks/positive_Helmholtz_3D_VTK.ipynb | 12 +----------- 2 files changed, 2 insertions(+), 12 deletions(-) diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 02c23698f..3386ac018 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -14,4 +14,4 @@ Examples examples/Poisson_non_periodic examples/Helmholtz_non_periodic examples/fem_L2_projection - \ No newline at end of file + examples/positive_Helmholtz_3D_VTK \ No newline at end of file diff --git a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb index 445e9c09d..23acf0be9 100644 --- a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb +++ b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb @@ -268,17 +268,7 @@ ] } ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "name": "python", - "version": "3.12.3" - } - }, + "metadata": {}, "nbformat": 4, "nbformat_minor": 5 } From 0d9ef72bbe31924d313f29d64450c5ed11b646ff Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 5 Dec 2025 12:31:03 +0100 Subject: [PATCH 40/63] add petsc notebook --- docs/source/examples.rst | 3 +- .../positive_Helmholtz_eigenvalues_PETSc.png | Bin 0 -> 18778 bytes ...petsc_eigenvalues_positive_Helmholtz.ipynb | 285 ++++++++++++++++++ 3 files changed, 287 insertions(+), 1 deletion(-) create mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_eigenvalues_PETSc.png create mode 100644 examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb diff --git a/docs/source/examples.rst b/docs/source/examples.rst index 3386ac018..e0ba4c3b8 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -14,4 +14,5 @@ Examples examples/Poisson_non_periodic examples/Helmholtz_non_periodic examples/fem_L2_projection - examples/positive_Helmholtz_3D_VTK \ No newline at end of file + examples/positive_Helmholtz_3D_VTK + examples/petsc_eigenvalues_positive_Helmholtz \ No newline at end of file diff --git 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\n", + "\n", + "\n", + "\n", + "## Step 6 : Save and export solution\n", + "This step is similar to what is explained in other tests." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c77d25a", + "metadata": {}, + "outputs": [], + "source": [ + "# Save the results using OutputManager\n", + "from psydac.api.postprocessing import OutputManager\n", + "import os\n", + "\n", + "os.makedirs('results_eigenvalues_positive_Helmholtz', exist_ok=True)\n", + "\n", + "Om = OutputManager(\n", + " f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm,\n", + " save_mpi_rank=True, \n", + " mode = 'w' \n", + ")\n", + "\n", + "Om.add_spaces(V=Wh)\n", + "Om.export_space_info()\n", + "\n", + "Om.set_static() # the fields do not depend on time\n", + "\n", + "Om.export_fields(u=uh) # saves the coefficients of the solution\n", + "\n", + "Om.close()\n", + "\n", + "# Export the results to VTK using PostProcessManager\n", + "from psydac.api.postprocessing import PostProcessManager\n", + "\n", + "Pm = PostProcessManager(\n", + " domain=Omega,\n", + " space_file=f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm\n", + ")\n", + "\n", + "Pm.export_to_vtk(\n", + " f'results_eigenvalues_positive_Helmholtz/visu_{Omega.name}',\n", + " grid=None,\n", + " npts_per_cell=[4,2,4],\n", + " fields='u'\n", + ")\n", + "\n", + "Pm.close()" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} From c343e4551c523830e43c1c7754743695147a454c Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 5 Dec 2025 15:44:20 +0100 Subject: [PATCH 41/63] add curl-curl ev notebook --- docs/source/examples.rst | 3 +- .../notebooks/feec_curlcurl_eigenvalue.ipynb | 342 ++++++++++++++++++ 2 files changed, 344 insertions(+), 1 deletion(-) create mode 100644 examples/notebooks/feec_curlcurl_eigenvalue.ipynb diff --git a/docs/source/examples.rst b/docs/source/examples.rst index e0ba4c3b8..e73cd6996 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -15,4 +15,5 @@ Examples examples/Helmholtz_non_periodic examples/fem_L2_projection examples/positive_Helmholtz_3D_VTK - examples/petsc_eigenvalues_positive_Helmholtz \ No newline at end of file + examples/petsc_eigenvalues_positive_Helmholtz + examples/feec_curlcurl_eigenvalue \ No newline at end of file diff --git a/examples/notebooks/feec_curlcurl_eigenvalue.ipynb b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb new file mode 100644 index 000000000..d5338b66d --- /dev/null +++ b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb @@ -0,0 +1,342 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6be9f483", + "metadata": {}, + "source": [ + "# Example of solving the $\\mathbf{curl}-\\mathrm{curl}$ eigenvalue problem\n", + "\n", + "In this notebook we show how to compute approximate eigenvalues for the curl-curl eigenvalue problem using the FEEC (Finite Element Exterior Calculus) API of PSYDAC. The problem reads as follows:\n", + "\n", + "\n", + "Let $\\Omega=[0, \\pi] \\times [0, \\pi]$. We want to find $\\lambda >0$ and $\\bm{E} \\in H_0(\\mathrm{curl}, \\Omega)$ such that\n", + "\n", + "$$ \\mathbf{curl} \\ \\mathrm{curl} \\ \\bm{E} = \\lambda \\bm{E}. $$\n", + "\n", + "\n", + "\n", + "\n", + "\n", + "## Step 1 : Building the domain\n", + "\n", + "This is similar to what is done in other examples. We leave the option to use a single patch or multiple patches.\n", + "The FEEC interface is compatible with both. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c9d51f8e", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "\n", + "single_patch = False\n", + "\n", + "# degree of the splines in each direction\n", + "degree = (3, 3)\n", + "\n", + "if single_patch:\n", + " #number of cells in each direction\n", + " ncells = [10, 10]\n", + "\n", + " from sympde.topology import Square, IdentityMapping\n", + " logical_domain = Square('Omega', bounds1=(0, np.pi), bounds2=(0, np.pi))\n", + " mapping = IdentityMapping('M1', dim=2)\n", + " domain = mapping(logical_domain)\n", + "\n", + "else:\n", + " # We can give the shape of the multipatch domain \n", + " # through the shape of the array containing the number of cells in each direction\n", + " ncells = np.array([[5, 5], \n", + " [5, 5]])\n", + " # The multipatch domain then has the following structure:\n", + " # A | B\n", + " # -----\n", + " # C | D\n", + "\n", + " from psydac.feec.multipatch_domain_utilities import build_cartesian_multipatch_domain\n", + " domain = build_cartesian_multipatch_domain(ncells, (0, np.pi), (0, np.pi), mapping='identity')\n", + "\n", + " # We now need to convert the ncells array into a dictionary, \n", + " # where the keys are the patches\n", + " ncells = {patch.name: [ncells[int(patch.name[2])][int(patch.name[4])], \n", + " ncells[int(patch.name[2])][int(patch.name[4])]] for patch in domain.interior}\n", + "\n", + "\n", + "from sympde.utilities.utils import plot_domain\n", + "plot_domain(domain, isolines=True)" + ] + }, + { + "cell_type": "markdown", + "id": "6bcee6a7", + "metadata": {}, + "source": [ + "## Step 2: Create and discretize the de Rham complex" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "dc4a3e7a", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize\n", + "from sympde.topology import Derham\n", + "\n", + "domain_h = discretize(domain, ncells=ncells) \n", + "\n", + "derham = Derham(domain, [\"H1\", \"Hcurl\", \"L2\"])\n", + "derham_h = discretize(derham, domain_h, degree=degree)\n", + "\n", + "V0h, V1h, V2h = derham_h.spaces" + ] + }, + { + "cell_type": "markdown", + "id": "540b8e43", + "metadata": {}, + "source": [ + "## Step 3: Use the FEEC interface to get the operators\n", + "\n", + "The (broken) FEEC operators are given by: \n", + "The conforming projections $P^\\ell: V^\\ell_\\mathrm{pw} \\rightarrow V^\\ell_h$, mapping from broken to continuous spaces. The broken derivatives $D^\\ell: V^\\ell_\\mathrm{pw} \\rightarrow V^{\\ell + 1}_\\mathrm{pw}$ and the Hodge-operators $H^\\ell$ which can be seen as mass matrices. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "18134cef", + "metadata": {}, + "outputs": [], + "source": [ + "# conforming projectors with homogeneous boundary conditions\n", + "# (In the single patch case, they only involve the zero BCs)\n", + "cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc = True)\n", + "\n", + "# broken (patch-wise) derivative operators\n", + "bD0, bD1 = derham_h.derivatives(kind='linop')\n", + "\n", + "# broken Hodge operators (mass matrices) and their inverses\n", + "H0, H1, H2 = derham_h.hodge_operators(kind='linop')\n", + "dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True)\n", + "\n", + "from psydac.linalg.basic import IdentityOperator\n", + "I1 = IdentityOperator(V1h.coeff_space)" + ] + }, + { + "cell_type": "markdown", + "id": "21c450cf", + "metadata": {}, + "source": [ + "## Step 4: Set up the system matrices\n", + "\n", + "The $\\mathrm{curl}$ operators are discretized by the conforming curl operator $D^1 P^1$ and its transpose. The right-hand-side is given by the conforming mass matrix $(P^1)^T H^1 P^1$ where we also have to add a penalization term corresponding to the discontinuous jumps in the broken spaces: $(I - P^1)^T H^1 (I - P^1)$. In total, the discrete equation reads: \n", + "\n", + "$$ \\left( D^1 P^1 \\right)^T H^2 D^1 P^1 \\bm{E}_h = \\lambda \\left((P^1)^T H^1 P^1 + (I - P^1)^T H^1 (I - P^1)\\right) \\bm{E}_h$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "4d3c55c1", + "metadata": {}, + "outputs": [], + "source": [ + "CC = cP1.T @ bD1.T @ H2 @ bD1 @ cP1\n", + "RHS = cP1.T @ H1 @ cP1 + (I1 - cP1).T @ H1 @ (I1 - cP1)" + ] + }, + { + "cell_type": "markdown", + "id": "17f466e6", + "metadata": {}, + "source": [ + "## Step 5: Scipy eigenvalue solver" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f02eab35", + "metadata": {}, + "outputs": [], + "source": [ + "def get_eigenvalues(nb_eigs, sigma, A_m, M_m):\n", + " \"\"\"\n", + " Compute the eigenvalues of the matrix A close to sigma and right-hand-side M\n", + "\n", + " Parameters\n", + " ----------\n", + " nb_eigs : int\n", + " Number of eigenvalues to compute\n", + " sigma : float\n", + " Value close to which the eigenvalues are computed\n", + " A_m : sparse matrix\n", + " Matrix A\n", + " M_m : sparse matrix\n", + " Matrix M\n", + " \"\"\"\n", + "\n", + " from scipy.sparse.linalg import spilu, lgmres\n", + " from scipy.sparse.linalg import LinearOperator, eigsh, minres\n", + " from scipy.linalg import norm\n", + "\n", + " print('----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ----- ')\n", + " print(\n", + " 'computing {0} eigenvalues (and eigenvectors) close to sigma={1} with scipy.sparse.eigsh...'.format(\n", + " nb_eigs,\n", + " sigma))\n", + " mode = 'normal'\n", + " which = 'LM'\n", + " # from eigsh docstring:\n", + " # ncv = number of Lanczos vectors generated ncv must be greater than k and smaller than n;\n", + " # it is recommended that ncv > 2*k. Default: min(n, max(2*k + 1, 20))\n", + " ncv = 4 * nb_eigs\n", + " try_lgmres = True\n", + " max_shape_splu = 24000 # OK for nc=20, deg=6 on pretzel_f\n", + " if A_m.shape[0] < max_shape_splu:\n", + " print('(via sparse LU decomposition)')\n", + " OPinv = None\n", + " tol_eigsh = 0\n", + " else:\n", + "\n", + " OP_m = A_m - sigma * M_m\n", + " tol_eigsh = 1e-7\n", + " if try_lgmres:\n", + " print(\n", + " '(via SPILU-preconditioned LGMRES iterative solver for A_m - sigma*M1_m)')\n", + " OP_spilu = spilu(OP_m, fill_factor=15, drop_tol=5e-5)\n", + " preconditioner = LinearOperator(\n", + " OP_m.shape, lambda x: OP_spilu.solve(x))\n", + " tol = tol_eigsh\n", + " OPinv = LinearOperator(\n", + " matvec=lambda v: lgmres(OP_m, v, x0=None, tol=tol, atol=tol, M=preconditioner,\n", + " callback=lambda x: print(\n", + " 'cg -- residual = ', norm(OP_m.dot(x) - v))\n", + " )[0],\n", + " shape=M_m.shape,\n", + " dtype=M_m.dtype\n", + " )\n", + "\n", + " else:\n", + " # from https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.eigsh.html:\n", + " # the user can supply the matrix or operator OPinv, which gives x = OPinv @ b = [A - sigma * M]^-1 @ b.\n", + " # > here, minres: MINimum RESidual iteration to solve Ax=b\n", + " # suggested in https://github.com/scipy/scipy/issues/4170\n", + " print('(with minres iterative solver for A_m - sigma*M1_m)')\n", + " OPinv = LinearOperator(\n", + " matvec=lambda v: minres(\n", + " OP_m,\n", + " v,\n", + " tol=1e-10)[0],\n", + " shape=M_m.shape,\n", + " dtype=M_m.dtype)\n", + "\n", + " eigenvalues, eigenvectors = eigsh(\n", + " A_m, k=nb_eigs, M=M_m, sigma=sigma, mode=mode, which=which, ncv=ncv, tol=tol_eigsh, OPinv=OPinv)\n", + "\n", + " print(\"done: eigenvalues found: \" + repr(eigenvalues))\n", + " return eigenvalues, eigenvectors" + ] + }, + { + "cell_type": "markdown", + "id": "c21fcd3e", + "metadata": {}, + "source": [ + "## Step 6: Solve the system\n", + "\n", + "We solve for the first `nb_eigs` many eigenvalue closest to the reference value `sigma`.\n", + "In the case `nb_eigs=10` and `sigma=5`, the exact eigenvalues are the first 10 sum of squares, i.e.\n", + "`ref_sigmas = [1, 1, 2, 4, 4, 5, 5, 8, 9, 9]`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5fd5ab7b", + "metadata": {}, + "outputs": [], + "source": [ + "ref_sigmas = [\n", + " 1, 1,\n", + " 2,\n", + " 4, 4,\n", + " 5, 5,\n", + " 8,\n", + " 9, 9,\n", + " ]\n", + "sigma = 5\n", + "nb_eigs = 10\n", + "\n", + "eigenvalues, eigenvectors_transp = get_eigenvalues(nb_eigs, sigma, CC.tosparse(), RHS.tosparse())" + ] + }, + { + "cell_type": "markdown", + "id": "f2b1242e", + "metadata": {}, + "source": [ + "## Step 7: Plot the eigenvalues" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5f452f48", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "fig,ax = plt.subplots(1,1)\n", + "ax.set_title(f\"The first {nb_eigs} eigenvalues\")\n", + "im = ax.scatter(np.arange(eigenvalues.size), eigenvalues)\n", + "plt.xlabel('index');" + ] + }, + { + "cell_type": "markdown", + "id": "a978966d", + "metadata": {}, + "source": [ + "### Testing the notebook" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7f4f0c33", + "metadata": {}, + "outputs": [], + "source": [ + "import ipytest\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2e38bb10", + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "l2_error = np.sqrt(np.sum((eigenvalues - ref_sigmas)**2)) \n", + "\n", + "def test_l2error():\n", + " assert l2_error < 5e-04" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} From 3ba04e7fd1c204afe157d53436ebedf6b2015570 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 5 Dec 2025 20:58:34 +0100 Subject: [PATCH 42/63] add time-harmonic example --- docs/source/examples.rst | 23 +- examples/feec/README.md | 7 + .../feec_time_harmonic_Maxwell.ipynb | 320 ++++++++++++++++++ 3 files changed, 349 insertions(+), 1 deletion(-) create mode 100644 examples/feec/README.md create mode 100644 examples/notebooks/feec_time_harmonic_Maxwell.ipynb diff --git a/docs/source/examples.rst b/docs/source/examples.rst index e73cd6996..dd1fa95aa 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -7,6 +7,9 @@ Examples .. The notebooks get copied into the source directory by the continuous integration pipeline. .. The notebooks should have all output cleared before being committed to the repository. +Notebooks +--------- + .. toctree:: :maxdepth: 1 :caption: Notebooks: @@ -16,4 +19,22 @@ Examples examples/fem_L2_projection examples/positive_Helmholtz_3D_VTK examples/petsc_eigenvalues_positive_Helmholtz - examples/feec_curlcurl_eigenvalue \ No newline at end of file + examples/feec_curlcurl_eigenvalue + examples/feec_time_harmonic_Maxwell + + +FEEC Examples +------------- + +In the `FEEC examples directory `_, +you will find several examples of how to use Psydac to solve problems arising within the Finite Element Exterior Calculus (FEEC) framework. +These examples include: +* Poisson problems +* General curl-curl eigenvalue problems +* Time-harmonic Maxwell equations with source terms +* Time-dependent Maxwell equations + + +Performance +----------- +There are also some examples in the `performance directory `_ explaining the assembly algorithms used in PSYDAC. diff --git a/examples/feec/README.md b/examples/feec/README.md new file mode 100644 index 000000000..433ca27f6 --- /dev/null +++ b/examples/feec/README.md @@ -0,0 +1,7 @@ +In this directory, we present the following examples arising within the FEEC framework: +* Poisson problem +* General curl-curl eigenvalue problem (with DG and FEEC) +* Time-Harmonic Maxwell problem +* Time-dependent Maxwell problem + +All provide visualizing using the vtk plotting utilities of PSYDAC. \ No newline at end of file diff --git a/examples/notebooks/feec_time_harmonic_Maxwell.ipynb b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb new file mode 100644 index 000000000..2f683dd09 --- /dev/null +++ b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb @@ -0,0 +1,320 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "31838f69", + "metadata": {}, + "source": [ + "# Solving the time-harmonic Maxwells equations on a multipatch domain\n", + "\n", + "For $\\omega \\in \\mathbb{R}$ and $\\bm{J} \\in L^2(\\Omega)$, we solve\n", + "$$- \\omega^2 \\bm{E} + \\mathbf{curl} \\mathrm{curl} \\bm{E} = \\bm{J}, $$\n", + "where $\\bm{E} \\in H(\\mathrm{curl}, \\Omega).$" + ] + }, + { + "cell_type": "markdown", + "id": "d7cf3108", + "metadata": {}, + "source": [ + "## Step 1: Discretize the domain. \n", + "\n", + "For the domain $\\Omega$, we choose the pretzel domain:" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "c18b57f5", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.feec.multipatch_domain_utilities import build_multipatch_domain\n", + "\n", + "domain = build_multipatch_domain(domain_name='pretzel_f')\n", + "\n", + "from sympde.utilities.utils import plot_domain\n", + "plot_domain(domain, isolines=True)" + ] + }, + { + "cell_type": "markdown", + "id": "ee044477", + "metadata": {}, + "source": [ + "## Step 2: Discretize the de Rham sequence" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "63def2e4", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize\n", + "from sympde.topology import Derham\n", + "\n", + "degree = [2, 2]\n", + "# For simplicity, we use the same number of cells for all patches\n", + "ncells = [4, 4]\n", + "\n", + "derham = Derham(domain, [\"H1\", \"Hcurl\", \"L2\"])\n", + "\n", + "domain_h = discretize(domain, ncells=ncells)\n", + "derham_h = discretize(derham, domain_h, degree=degree)" + ] + }, + { + "cell_type": "markdown", + "id": "d451401e", + "metadata": {}, + "source": [ + "## Step 3: Obtain the FEEC operators" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d783864a", + "metadata": {}, + "outputs": [], + "source": [ + "# Finite Element spaces\n", + "V0h, V1h, V2h = derham_h.spaces\n", + "\n", + "# Geometric global projectors\n", + "nquads = [10 * (d + 1) for d in degree]\n", + "P0, P1, P2 = derham_h.projectors(nquads=nquads)\n", + "\n", + "# Identity operator\n", + "from psydac.linalg.basic import IdentityOperator\n", + "I1 = IdentityOperator(V1h.coeff_space)\n", + "\n", + "# Hodge and dual Hodge operators\n", + "H0, H1, H2 = derham_h.hodge_operators(kind='linop')\n", + "dH0, dH1, dH2 = derham_h.hodge_operators(kind='linop', dual=True)\n", + "\n", + "# Conforming projectors with homogeneous boundary conditions\n", + "cP0, cP1, cP2 = derham_h.conforming_projectors(kind='linop', hom_bc=True)\n", + "\n", + "# Broken derivative operators\n", + "bD0, bD1 = derham_h.derivatives(kind='linop')" + ] + }, + { + "cell_type": "markdown", + "id": "aa3148da", + "metadata": {}, + "source": [ + "## Step 4: Assemble the system matrices" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "f03ccb61", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "omega = np.pi\n", + "\n", + "CC = cP1.T @ bD1.T @ H2 @ bD1 \n", + "M = -omega**2 * cP1.T @ H1 \n", + "pre_A = M + CC\n", + "\n", + "JS = 10 * (I1 - cP1).T @ H1 @ (I1 - cP1)\n", + "\n", + "A = pre_A @ cP1 + JS" + ] + }, + { + "cell_type": "markdown", + "id": "7e61a0da", + "metadata": {}, + "source": [ + "## Step 5: Source and exact solution" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2aee193c", + "metadata": {}, + "outputs": [], + "source": [ + "def get_source_and_solution_hcurl(eta=0, domain=None):\n", + " from sympy import pi, cos, sin, Tuple, exp\n", + "\n", + " x, y = domain.coordinates\n", + "\n", + " # used for Maxwell equation with manufactured solution\n", + " f_vect = Tuple(eta * sin(pi * y) - pi**2 * sin(pi * y) * cos(pi * x) + pi**2 * sin(pi * y),\n", + " eta * sin(pi * x) * cos(pi * y) + pi**2 * sin(pi * x) * cos(pi * y))\n", + "\n", + " u_ex = Tuple(sin(pi * y), sin(pi * x) * cos(pi * y))\n", + "\n", + "\n", + " from sympy import lambdify\n", + " f_vect_x = lambdify(domain.coordinates, f_vect[0])\n", + " f_vect_y = lambdify(domain.coordinates, f_vect[1])\n", + "\n", + " u_ex_x = lambdify(domain.coordinates, u_ex[0])\n", + " u_ex_y = lambdify(domain.coordinates, u_ex[1])\n", + "\n", + " return f_vect, [f_vect_x, f_vect_y], [u_ex_x, u_ex_y]" + ] + }, + { + "cell_type": "markdown", + "id": "6959cf37", + "metadata": {}, + "source": [ + "## Step 6: Get and project source" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6f41db72", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.fem.projectors import get_dual_dofs\n", + "tilde_f = get_dual_dofs(Vh=V1h, f=f_vect_l2, domain_h=domain_h)\n", + "\n", + "f = dH1.dot(tilde_f)\n", + "\n", + "# filtering the discrete source \n", + "tilde_f = cP1.T @ tilde_f\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "63fc7530", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.fem.plotting_utilities import plot_field_2d as plot_field\n", + "plot_field(stencil_coeffs=f, Vh=V1h, space_kind='hcurl', domain=domain, title='tilde f_h: Geometric projection of f', hide_plot=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a4a2d3f6", + "metadata": {}, + "outputs": [], + "source": [ + "# Manipulate the source to account for inhomogeneous boundary conditions in u\n", + "ubc = P1(u_ex).coeffs\n", + "ubc -= cP1 @ ubc\n", + "\n", + "tilde_f -= pre_A @ ubc" + ] + }, + { + "cell_type": "markdown", + "id": "25860d86", + "metadata": {}, + "source": [ + "## Step 7: Solve the linear system using CG" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3e83202a", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.linalg.solvers import inverse\n", + "\n", + "solver = inverse(A, solver='cg', tol=1e-5)\n", + "u = solver.solve(tilde_f)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "33576e21", + "metadata": {}, + "outputs": [], + "source": [ + "# Project back to the full space and add the boundary conditions\n", + "u = cP1.dot(u)\n", + "u += ubc" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2b31445c", + "metadata": {}, + "outputs": [], + "source": [ + "uex = P1(u_ex).coeffs\n", + "err = uex - u\n", + "l2_error = np.sqrt(H1.dot_inner(err, err) / H1.dot_inner(uex, uex))\n", + "print('L2 relative error = ', l2_error)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ab5d7502", + "metadata": {}, + "outputs": [], + "source": [ + "plot_field(stencil_coeffs=u, Vh=V1h, space_kind='hcurl', domain=domain, title='Numerical solution u', hide_plot=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "44ab3744", + "metadata": {}, + "outputs": [], + "source": [ + "plot_field(stencil_coeffs=uex, Vh=V1h, space_kind='hcurl', domain=domain, title='Exact solution u_ex', hide_plot=False)" + ] + }, + { + "cell_type": "markdown", + "id": "c89c62c3", + "metadata": {}, + "source": [ + "### Test the notebook" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "81370f97", + "metadata": {}, + "outputs": [], + "source": [ + "import ipytest\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "e47d2bb5", + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_l2error():\n", + " assert l2_error < 8e-03" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} From 6770814c1600cd8d3025f7cd3f7d74dc65e303ca Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 5 Dec 2025 21:09:30 +0100 Subject: [PATCH 43/63] update notebook --- examples/feec/README.md | 4 ++-- .../feec_time_harmonic_Maxwell.ipynb | 22 ++++++++++++------- 2 files changed, 16 insertions(+), 10 deletions(-) diff --git a/examples/feec/README.md b/examples/feec/README.md index 433ca27f6..ed13f9a56 100644 --- a/examples/feec/README.md +++ b/examples/feec/README.md @@ -1,7 +1,7 @@ In this directory, we present the following examples arising within the FEEC framework: * Poisson problem * General curl-curl eigenvalue problem (with DG and FEEC) -* Time-Harmonic Maxwell problem +* Time-harmonic Maxwell problem * Time-dependent Maxwell problem -All provide visualizing using the vtk plotting utilities of PSYDAC. \ No newline at end of file +All provide visualizing using the VTK plotting utilities of PSYDAC. \ No newline at end of file diff --git a/examples/notebooks/feec_time_harmonic_Maxwell.ipynb b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb index 2f683dd09..6d89a4322 100644 --- a/examples/notebooks/feec_time_harmonic_Maxwell.ipynb +++ b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb @@ -84,7 +84,7 @@ "V0h, V1h, V2h = derham_h.spaces\n", "\n", "# Geometric global projectors\n", - "nquads = [10 * (d + 1) for d in degree]\n", + "nquads = [(d + 1) for d in degree]\n", "P0, P1, P2 = derham_h.projectors(nquads=nquads)\n", "\n", "# Identity operator\n", @@ -157,13 +157,10 @@ "\n", "\n", " from sympy import lambdify\n", - " f_vect_x = lambdify(domain.coordinates, f_vect[0])\n", - " f_vect_y = lambdify(domain.coordinates, f_vect[1])\n", - "\n", " u_ex_x = lambdify(domain.coordinates, u_ex[0])\n", " u_ex_y = lambdify(domain.coordinates, u_ex[1])\n", "\n", - " return f_vect, [f_vect_x, f_vect_y], [u_ex_x, u_ex_y]" + " return f_vect, [u_ex_x, u_ex_y]" ] }, { @@ -181,13 +178,14 @@ "metadata": {}, "outputs": [], "source": [ - "from psydac.fem.projectors import get_dual_dofs\n", - "tilde_f = get_dual_dofs(Vh=V1h, f=f_vect_l2, domain_h=domain_h)\n", + "f_vect, u_ex = get_source_and_solution_hcurl(eta=-omega**2, domain=domain)\n", "\n", + "from psydac.fem.projectors import get_dual_dofs\n", + "tilde_f = get_dual_dofs(Vh=V1h, f=f_vect, domain_h=domain_h)\n", "f = dH1.dot(tilde_f)\n", "\n", "# filtering the discrete source \n", - "tilde_f = cP1.T @ tilde_f\n" + "tilde_f = cP1.T @ tilde_f" ] }, { @@ -248,6 +246,14 @@ "u += ubc" ] }, + { + "cell_type": "markdown", + "id": "90124e42", + "metadata": {}, + "source": [ + "## Step 8: Look at the exact solution and compute the error" + ] + }, { "cell_type": "code", "execution_count": null, From dd955d21b78670b2e483dd019f09e0a746b8c99c Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Fri, 5 Dec 2025 21:37:01 +0100 Subject: [PATCH 44/63] update typos --- docs/source/examples.rst | 6 ++++++ docs/source/index.rst | 8 +------- docs/source/output.rst | 11 ----------- examples/notebooks/feec_curlcurl_eigenvalue.ipynb | 6 +++--- examples/notebooks/feec_time_harmonic_Maxwell.ipynb | 6 +++--- 5 files changed, 13 insertions(+), 24 deletions(-) diff --git a/docs/source/examples.rst b/docs/source/examples.rst index dd1fa95aa..e3b10553d 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -9,6 +9,10 @@ Examples .. The notebooks should have all output cleared before being committed to the repository. Notebooks --------- +For the documentation, we provide several Jupyter notebooks that illustrate how to use PSYDAC to solve different types of problems. +They can be found in the `notebooks directory `_, +but are also generated as part of the documentation and can be accessed here: + .. toctree:: :maxdepth: 1 @@ -29,6 +33,8 @@ FEEC Examples In the `FEEC examples directory `_, you will find several examples of how to use Psydac to solve problems arising within the Finite Element Exterior Calculus (FEEC) framework. These examples include: + + * Poisson problems * General curl-curl eigenvalue problems * Time-harmonic Maxwell equations with source terms diff --git a/docs/source/index.rst b/docs/source/index.rst index d34b1e063..070566f3f 100644 --- a/docs/source/index.rst +++ b/docs/source/index.rst @@ -7,12 +7,6 @@ Welcome to PSYDAC's documentation! ================================== -.. _note: -.. note:: - - This documentation is still under construction. - For the time being, its purpose is to assist the developers. - .. include:: ../../README.md :parser: myst_parser.sphinx_ @@ -22,8 +16,8 @@ Welcome to PSYDAC's documentation! :hidden: installation - output examples + output modules psydac-mesh maintenance diff --git a/docs/source/output.rst b/docs/source/output.rst index 20ccc54e0..ec92d56b8 100644 --- a/docs/source/output.rst +++ b/docs/source/output.rst @@ -171,14 +171,3 @@ Here is a usage example: # See PostProcessManager.export_to_vtk's and TensorFemSpace.eval_fields' docstrings for more information post.export_to_vtk('filename_vtk', grid=grid, npts_per_cell=npts_per_cell, snapshots='all', fields = ('u0', 'u1')) - -Further Examples ----------------- - -Further examples are present in the following files: - - -* ``examples/poisson_3d_target_torus.py`` -* ``examples/sample_multipatch_parallel.py`` -* ``examples/notebooks/Poisson_non_periodic.ipynb`` -* ``psydac/api/tests/test_postprocessing.py`` diff --git a/examples/notebooks/feec_curlcurl_eigenvalue.ipynb b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb index d5338b66d..48091254c 100644 --- a/examples/notebooks/feec_curlcurl_eigenvalue.ipynb +++ b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb @@ -10,9 +10,9 @@ "In this notebook we show how to compute approximate eigenvalues for the curl-curl eigenvalue problem using the FEEC (Finite Element Exterior Calculus) API of PSYDAC. The problem reads as follows:\n", "\n", "\n", - "Let $\\Omega=[0, \\pi] \\times [0, \\pi]$. We want to find $\\lambda >0$ and $\\bm{E} \\in H_0(\\mathrm{curl}, \\Omega)$ such that\n", + "Let $\\Omega=[0, \\pi] \\times [0, \\pi]$. We want to find $\\lambda >0$ and $\\boldsymbol{E} \\in H_0(\\mathrm{curl}, \\Omega)$ such that\n", "\n", - "$$ \\mathbf{curl} \\ \\mathrm{curl} \\ \\bm{E} = \\lambda \\bm{E}. $$\n", + "$$ \\mathbf{curl} \\ \\mathrm{curl} \\ \\boldsymbol{E} = \\lambda \\boldsymbol{E}. $$\n", "\n", "\n", "\n", @@ -138,7 +138,7 @@ "\n", "The $\\mathrm{curl}$ operators are discretized by the conforming curl operator $D^1 P^1$ and its transpose. The right-hand-side is given by the conforming mass matrix $(P^1)^T H^1 P^1$ where we also have to add a penalization term corresponding to the discontinuous jumps in the broken spaces: $(I - P^1)^T H^1 (I - P^1)$. In total, the discrete equation reads: \n", "\n", - "$$ \\left( D^1 P^1 \\right)^T H^2 D^1 P^1 \\bm{E}_h = \\lambda \\left((P^1)^T H^1 P^1 + (I - P^1)^T H^1 (I - P^1)\\right) \\bm{E}_h$$" + "$$ \\left( D^1 P^1 \\right)^T H^2 D^1 P^1 \\boldsymbol{E}_h = \\lambda \\left((P^1)^T H^1 P^1 + (I - P^1)^T H^1 (I - P^1)\\right) \\boldsymbol{E}_h$$" ] }, { diff --git a/examples/notebooks/feec_time_harmonic_Maxwell.ipynb b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb index 6d89a4322..cd4913bd9 100644 --- a/examples/notebooks/feec_time_harmonic_Maxwell.ipynb +++ b/examples/notebooks/feec_time_harmonic_Maxwell.ipynb @@ -7,9 +7,9 @@ "source": [ "# Solving the time-harmonic Maxwells equations on a multipatch domain\n", "\n", - "For $\\omega \\in \\mathbb{R}$ and $\\bm{J} \\in L^2(\\Omega)$, we solve\n", - "$$- \\omega^2 \\bm{E} + \\mathbf{curl} \\mathrm{curl} \\bm{E} = \\bm{J}, $$\n", - "where $\\bm{E} \\in H(\\mathrm{curl}, \\Omega).$" + "For $\\omega \\in \\mathbb{R}$ and $\\boldsymbol{J} \\in L^2(\\Omega)$, we solve\n", + "$$- \\omega^2 \\boldsymbol{E} + \\mathbf{curl} \\mathrm{curl} \\boldsymbol{E} = \\boldsymbol{J}, $$\n", + "where $\\boldsymbol{E} \\in H(\\mathrm{curl}, \\Omega).$" ] }, { From fc698badd7a2572876ad5f57854175d4fd9cb384 Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Thu, 11 Dec 2025 11:43:43 +0100 Subject: [PATCH 45/63] update fem L2 proj example notebook --- examples/notebooks/fem_L2_projection.ipynb | 301 +++++++++++++-------- 1 file changed, 194 insertions(+), 107 deletions(-) diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb index 27d3d1d19..16e90f04c 100644 --- a/examples/notebooks/fem_L2_projection.ipynb +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -5,13 +5,23 @@ "id": "2443e734", "metadata": {}, "source": [ - "# Projecting a function onto a finite element space\n", + "# Finite element projections of scalar and vector-valued functions\n", "\n", - "In this notebook we show how to define a scalar FEM space over a given (discretized) domain, how to plot some basis functions, assemble a mass matrix and compute the L2 projection of a given function \n", + "*Warning: this notebook is a draft, meant to discuss which interfaces should be exposed to users*\n", "\n", - "## Step 1 : define the domain and discretize it\n", - "\n", - "This is similar to what is done in other examples" + "In this notebook we show how to: \n", + "- define FEM spaces over a given domain, \n", + "- plot some FEM functions with a simple 2D plotting function,\n", + "- apply H1 and Hcurl conforming projections to discrete multipatch fields,\n", + "- assemble mass matrices and compute the L2 projections of some given functions." + ] + }, + { + "cell_type": "markdown", + "id": "455febb2", + "metadata": {}, + "source": [ + "## Step 1 : define a domain with sympde" ] }, { @@ -22,38 +32,34 @@ "outputs": [], "source": [ "import numpy as np\n", - "\n", "from sympde.topology import Square, PolarMapping\n", - "from sympde.utilities.utils import plot_domain\n", "\n", - "from psydac.api.tests.build_domain import build_pretzel\n", - "\n", - "# Define the topological geometry for each patch\n", + "# Define each patch as a mapped subdomain\n", "rmin, rmax = 0.3, 1.\n", "\n", - "# First quarter annulus\n", "domain_log_1 = Square('A_1', bounds1=(0., 1.), bounds2=(0., np.pi/2))\n", "F_1 = PolarMapping('F_1', dim=2, c1=0., c2=0., rmin=rmin, rmax=rmax)\n", "Omega_1 = F_1(domain_log_1)\n", "\n", - "# Second quarter annulus\n", - "domain_log_2 = Square('A_2', bounds1=(0., 1.), bounds2=(np.pi, 3/2 * np.pi))\n", + "domain_log_2 = Square('A_2', bounds1=(0., 1.), bounds2=(np.pi, 2 * np.pi))\n", "F_2 = PolarMapping('F_2', dim=2, c1=rmin+rmax, c2=0., rmin=rmax, rmax=rmin)\n", "Omega_2 = F_2(domain_log_2)\n", "\n", - "# Join the patches\n", + "domain_log_3 = Square('A_3', bounds1=(0., 1.), bounds2=(np.pi/2, np.pi))\n", + "F_3 = PolarMapping('F_3', dim=2, c1=2*(rmin+rmax), c2=0., rmin=rmin, rmax=rmax)\n", + "Omega_3 = F_3(domain_log_3)\n", "\n", - "# [remark] this could be an opportunity to describe how the interfaces of a domain are numbered\n", + "# Join the patches with the Domain.join function from sympde\n", "from sympde import Domain\n", - "connectivity = [((0,1,-1),(1,1,-1), 1)]\n", - "patches = [Omega_1, Omega_2]\n", - "Omega = Domain.join(patches, connectivity, 'domain')\n", - "\n", - "# Example of a complex multi-patch domain\n", - "# Omega = build_pretzel()\n", + "connectivity = [((Omega_1,1,-1), (Omega_2,1,-1), 1), ((Omega_2,1,1), (Omega_3,1,1), 1)]\n", + "patches = [Omega_1, Omega_2, Omega_3]\n", + "Omega = Domain.join(patches, connectivity, 'Omega')\n", "\n", - "# Simple visualization of the topological domain\n", - "plot_domain(Omega, draw=False, isolines=True)" + "# Simple visualization of the domain\n", + "from sympde.utilities.utils import plot_domain\n", + "npatches = len(Omega.subdomains)\n", + "print(f'A domain named {Omega}, with {npatches} patches:')\n", + "plot_domain(Omega, isolines=True)\n" ] }, { @@ -61,16 +67,8 @@ "id": "b1f65c13", "metadata": {}, "source": [ - "## Step 2 : define a FEM space and plot some basis functions\n", + "## Step 2 : define scalar and vector FEM spaces, plot some basis functions\n", "\n", - "[this could actually be a good opportunity to present how the indices work in psydac arrays]" - ] - }, - { - "cell_type": "markdown", - "id": "a8ea7ee6", - "metadata": {}, - "source": [ "We first define a scalar-valued FEM space V" ] }, @@ -83,38 +81,55 @@ "source": [ "from sympde.topology import ScalarFunctionSpace, VectorFunctionSpace\n", "\n", - "from psydac.linalg.utilities import array_to_psydac\n", - "from psydac.api.discretization import discretize\n", - "from psydac.fem.basic import FemField\n", - "from psydac.fem.plotting_utilities import plot_field_2d as plot_field\n", - "\n", - "# the kind argument also specifies the pushforward defining the FEM space on the physical domain\n", - "# kind=None results in a (scalar, vector?) space defined by a simple change of variable (0-form pushforward)\n", - "V = ScalarFunctionSpace('V', Omega, kind=None)\n", + "# the kind argument specifies the pushforward defining the FEM space on the physical domain\n", + "# kind=None results in a space defined by a simple change of variable\n", + "V = ScalarFunctionSpace('V', Omega, kind=None)\n", "\n", "ncells = [10, 10]\n", "degree = [2, 2]\n", "\n", - "# [remark] for multipatch domains the periodic flag is a priori unrelevant, should raise an error / warning \n", - "# periodic = [ False, True]\n", - "periodic = [False, False] \n", - "\n", - "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic)\n", + "from psydac.api.discretization import discretize\n", + "Omega_h = discretize(Omega, ncells=ncells)\n", "Vh = discretize(V, Omega_h, degree=degree)\n", + "print(f\"we have defined a FEM space of type {type(Vh)}, with dimension {Vh.nbasis}\")\n", "\n", - "npatches = len(Vh.patch_spaces)\n", - "for k in range(npatches):\n", - " knots = Vh.patch_spaces[k].knots[0]\n", - " print(f'Spline knots (logical coords) along axis 0 in patch {k}: \\n {knots}')\n", + "# plot some basis function from the FEM space, using a simple wrapper for matplotlib\n", + "from psydac.fem.basic import FemField\n", + "from psydac.linalg.utilities import array_to_psydac\n", "\n", - "# plot some basis function from the space \n", - "# [remark] here I'm using numpy arrays, but one could illustrate the psydac indexing\n", + "# here we set the coefficients by hand using numpy arrays\n", "bf_c = np.zeros(Vh.nbasis)\n", - "bf_c[Vh.nbasis//4] = 1\n", - "bf_c[Vh.nbasis//4+6] = 1\n", + "i0 = 108\n", + "bf_c[i0] = 1\n", + "i1 = 211\n", + "bf_c[i1] = 1\n", + "i2 = 215\n", + "bf_c[i2] = 1\n", "bf = FemField(Vh, coeffs=array_to_psydac(bf_c, Vh.coeff_space))\n", "\n", - "plot_field(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, title='two basis functions', hide_plot=False)" + "from psydac.fem.plotting_utilities import plot_field_2d\n", + "plot_field_2d(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, cmap='viridis', title=fr'three scalar-valued basis functions: $\\phi_{ {i0} }$, $\\phi_{ {i1} }$, $\\phi_{ {i2} }$', filename='')\n" + ] + }, + { + "cell_type": "markdown", + "id": "79eb29ab", + "metadata": {}, + "source": [ + "Note: the multipatch space Vh is made of discontinuous functions. A conforming projection may be used to map them to continuous functions" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "76d8fa2a", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.feec.conforming_projectors import construct_h1_conforming_projection\n", + "cP = construct_h1_conforming_projection(Vh, hom_bc=False)\n", + "Pbf = FemField(Vh, coeffs=array_to_psydac(cP@bf_c, Vh.coeff_space))\n", + "plot_field_2d(fem_field=Pbf, Vh=Vh, space_kind=None, domain=Omega, cmap='viridis', title='H1-conforming projection of the above basis functions', filename='')" ] }, { @@ -132,21 +147,49 @@ "metadata": {}, "outputs": [], "source": [ - "\n", - "W = VectorFunctionSpace('W', Omega, kind=None) # a priori 2d vectors\n", + "# again, kind=None will result in a FEM space defined by a simple change of variable on the physical domain\n", + "W = VectorFunctionSpace('W', Omega, kind=None) \n", "Wh = discretize(W, Omega_h, degree=degree)\n", + "print(f\"we have defined a FEM space of type {type(Wh)}, with dimension {Wh.nbasis}\")\n", "\n", "# plot some basis function from the space \n", "# [remark] here I'm using numpy arrays, but one could illustrate the psydac indexing\n", "dim_Wh = Wh.nbasis\n", "bf2_c = np.zeros(dim_Wh)\n", - "bf2_c[dim_Wh//4+5] = 1\n", - "bf2_c[dim_Wh//4+42] = 1\n", - "bf2_c[dim_Wh//4+102] = 1\n", + "i0 = 108; bf2_c[i0] = 1\n", + "i1 = 314; bf2_c[i1] = 1\n", + "i2 = 479; bf2_c[i2] = 1\n", "bf2 = FemField(Wh, coeffs=array_to_psydac(bf2_c, Wh.coeff_space))\n", "\n", - "plot_field(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", - " plot_type='components', title='three basis vector functions', hide_plot=False)\n" + "plot_field_2d(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", + " plot_type='components', cmap='viridis', title=fr'three vector-valued basis functions: $\\Phi_{ {i0} }$, $\\Phi_{ {i1} }$, $\\Phi_{ {i2} }$', filename='')\n" + ] + }, + { + "cell_type": "markdown", + "id": "e2793980", + "metadata": {}, + "source": [ + "A stream plot of these basis functions is also possible, to better vizualise the vector fields" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "5249428d", + "metadata": {}, + "outputs": [], + "source": [ + "plot_field_2d(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", + " plot_type='vector_field', vf_skip=1, title=fr'three vector-valued basis functions: $\\Phi_{ {i0} }$, $\\Phi_{ {i1} }$, $\\Phi_{ {i2} }$', filename='')" + ] + }, + { + "cell_type": "markdown", + "id": "21ca10a3", + "metadata": {}, + "source": [ + "Note: again, the multipatch space Wh is made of discontinuous functions. A conforming projection could be used, but continuity is harder to impose for vector-valued functions: this will be discussed in a further example." ] }, { @@ -154,9 +197,9 @@ "id": "36a9632b", "metadata": {}, "source": [ - "## Step 3 : compute the mass matrix\n", + "## Step 3 : compute the mass matrices for Vh and Wh\n", "\n", - "We assemble the mass matrix and visualize it. Again we start with the scalar-valued FEM space" + "We assemble the mass matrices and visualize them. Again we start with the scalar-valued FEM space" ] }, { @@ -176,28 +219,25 @@ "from psydac.api.settings import PSYDAC_BACKENDS\n", "\n", "backend_language = 'python'\n", - "backend = PSYDAC_BACKENDS[backend_language]\n", "\n", "u, v = elements_of(V, names='u, v')\n", "a = BilinearForm((u, v), integral(Omega, u * v))\n", - "ah = discretize(a, Omega_h, [Vh, Vh], backend=backend)\n", + "ah = discretize(a, Omega_h, [Vh, Vh], backend=PSYDAC_BACKENDS[backend_language])\n", "\n", - "M = ah.assemble() # Mass matrix in stencil format (linear operator)\n", + "# Mass matrix in Psydac 'stencil' (linear operator) format \n", + "M_V = ah.assemble() \n", "\n", "# visualize the mass matrix by plotting its numpy conversion\n", - "mat = M.toarray()\n", - "\n", - "#----------------\n", + "mat = M_V.toarray()\n", "fig,ax = plt.subplots(1,1)\n", - "ax.set_title(f\"Mass matrix M on the domain with {npatches} patch(es)\")\n", + "ax.set_title(f\"Mass matrix of Vh, with {npatches} blocks (1 per patch)\")\n", "im = ax.matshow(mat, norm=colors.LogNorm(), cmap='hot_r')\n", - "cb = fig.colorbar(im, ax=ax)\n", - "fig.show()\n" + "cb = fig.colorbar(im, ax=ax)\n" ] }, { "cell_type": "markdown", - "id": "57f85041", + "id": "3a3db420", "metadata": {}, "source": [ "We next assemble the mass matrix of the vector-valued FEM space" @@ -210,25 +250,21 @@ "metadata": {}, "outputs": [], "source": [ - "## and we do the same for the vector-valued space W\n", - "\n", "from sympde.calculus import dot\n", "\n", "u, v = elements_of(W, names='u, v')\n", "a = BilinearForm((u, v), integral(Omega, dot(u,v)))\n", - "ah_W = discretize(a, Omega_h, [Wh, Wh], backend=backend)\n", + "ah_W = discretize(a, Omega_h, [Wh, Wh], backend=PSYDAC_BACKENDS[backend_language])\n", "\n", - "M_W = ah_W.assemble() # Mass matrix in stencil format (linear operator)\n", + "# Mass matrix in Psydac 'stencil' (linear operator) format \n", + "M_W = ah_W.assemble() \n", "\n", "# visualize the mass matrix by plotting its numpy conversion\n", "mat_W = M_W.toarray()\n", - "\n", - "#----------------\n", "fig,ax = plt.subplots(1,1)\n", - "ax.set_title(f\"Mass matrix M on the domain with {npatches} patch(es)\")\n", + "ax.set_title(f\"Mass matrix of Wh, with {2*npatches} blocks (2 per patch)\")\n", "im = ax.matshow(mat_W, norm=colors.LogNorm(), cmap='hot_r')\n", - "cb = fig.colorbar(im, ax=ax)\n", - "fig.show()" + "cb = fig.colorbar(im, ax=ax)" ] }, { @@ -236,9 +272,45 @@ "id": "dae32f1c", "metadata": {}, "source": [ - "## Step 4 : compute the moments of a given target function and its L2 projection\n", + "## Step 4 : compute the moments of some given target function, and their L2 projections\n", "\n", - "we invert the mass matrix on the moments of a given function f: first for the scalar-valued space" + "we first define a scalar function f and visualize it on the domain" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "de936090", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import cos, exp\n", + "x,y = Omega.coordinates\n", + "ref_f = exp(-(y-0.7*cos(3*x))**2 / (2 * 0.15**2))\n", + "\n", + "from sympy import lambdify\n", + "f_call = lambdify(Omega.coordinates, ref_f) # make the expression a callable function\n", + "\n", + "from psydac.fem.plotting_utilities import get_plotting_grid, my_small_plot\n", + "etas, xx, yy = get_plotting_grid(Omega.mappings, N=100)\n", + "ref_f_vals = [f_call(xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)]\n", + "\n", + "my_small_plot(\n", + " title=r'a reference function $f$ (scalar valued)',\n", + " vals=[ref_f_vals],\n", + " xx=xx,\n", + " yy=yy,\n", + " save_fig='',\n", + " cmap='viridis',\n", + ")\n" + ] + }, + { + "cell_type": "markdown", + "id": "75014e6a", + "metadata": {}, + "source": [ + "we next compute the moments of f in Vh and invert the mass matrix to get the L2 projection" ] }, { @@ -251,15 +323,17 @@ "from psydac.linalg.solvers import inverse\n", "from psydac.fem.projectors import get_dual_dofs\n", "\n", - "x,y = Omega.coordinates\n", - "ref_f = (x-1/2)**2 + y**2\n", + "# the dual dofs are the moments, i.e. the products _{L2(Omega)}\n", "tilde_f = get_dual_dofs(Vh=Vh, f=ref_f, domain_h=Omega_h, backend_language=backend_language)\n", "\n", - "inv_M = inverse(M, solver='cg')\n", - "\n", + "inv_M = inverse(M_V, solver='cg')\n", "f_h = inv_M @ tilde_f\n", "\n", - "plot_field(stencil_coeffs=f_h, Vh=Vh, space_kind='h1', domain=Omega, title='f_h: L2 projection of f', hide_plot=False)" + "plot_field_2d(\n", + " stencil_coeffs=f_h, Vh=Vh, space_kind='h1', \n", + " domain=Omega, title=r'$f_h$: L2 projection of $f$ in Vh', cmap='viridis', filename='')\n", + "\n", + "print('note the lower accuracy in the regions where the grid is not aligned with the anisotropic smoothness')\n" ] }, { @@ -267,48 +341,61 @@ "id": "8258971a", "metadata": {}, "source": [ - "next for the vector-valued space" + "we then repeat the above steps for the vector-valued space Wh" ] }, { "cell_type": "code", "execution_count": null, - "id": "1f0f103d", + "id": "772df7b3", "metadata": {}, "outputs": [], "source": [ - "from sympy import pi, cos, sin, Tuple, exp, atan\n", + "from sympy import pi, cos, Tuple\n", "\n", - "envelope = exp(-(x-.6)**2 / (2 * 0.15**2))\n", - "ref_gx = envelope * cos(2*pi*y)\n", - "ref_gy = envelope * 1\n", + "ref_g_x = ref_f * cos(2*pi*y)\n", + "ref_g_y = ref_f * 1\n", "\n", - "ref_g = Tuple(ref_gx, ref_gy)\n", + "ref_g = Tuple(ref_g_x, ref_g_y)\n", "\n", - "tilde_g = get_dual_dofs(Vh=Wh, f=ref_g, domain_h=Omega_h, backend_language=backend_language)\n", + "# make the expression a callable function\n", + "g_vect = [lambdify(Omega.coordinates, ref_g[d]) for d in [0,1]]\n", "\n", - "inv_M_W = inverse(M_W, solver='cg')\n", + "ref_vals_g = [[g_vect[d](xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)] for d in [0,1]]\n", + "# g_y = [g_vect[1](xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)]\n", "\n", - "g_h = inv_M_W @ tilde_g\n", + "# ref_f_vals = [f_call(xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)]\n", "\n", - "# plot_field(fem_field=, Vh=Wh, space_kind=None, domain=Omega, \n", - "# plot_type='components', title='two basis vector functions', hide_plot=False)\n", + "from psydac.fem.plotting_utilities import my_small_streamplot\n", "\n", - "plot_field(stencil_coeffs=g_h, Vh=Wh, space_kind='h1', domain=Omega, \n", - " plot_type='vector_field', title='g_h: L2 projection of g', hide_plot=False)" + "my_small_streamplot(\n", + " title=r'a reference function $g$ (vector valued)',\n", + " vals_x=ref_vals_g[0],\n", + " vals_y=ref_vals_g[1],\n", + " xx=xx,\n", + " yy=yy,\n", + " skip=8,\n", + " amp_factor=1,\n", + " hide_plot=False,\n", + " dpi=200,\n", + ")" ] }, { "cell_type": "code", "execution_count": null, - "id": "6c77d25a", + "id": "1f0f103d", "metadata": {}, "outputs": [], "source": [ - "# note: specifying a different space_kind is possible but will a priori result in inconsistent pushforward\n", + "# again, the dual dofs are the moments relative to the basis of Wh, i.e. the products _{L2(Omega)}\n", + "tilde_g = get_dual_dofs(Vh=Wh, f=ref_g, domain_h=Omega_h, backend_language=backend_language)\n", + "\n", + "inv_M_W = inverse(M_W, solver='cg')\n", + "g_h = inv_M_W @ tilde_g\n", "\n", - "plot_field(stencil_coeffs=g_h, Vh=Wh, space_kind='hcurl', domain=Omega, \n", - " plot_type='vector_field', title='g_h: L2 projection of g with inconsistent pushforward', hide_plot=False)" + "plot_field_2d(stencil_coeffs=g_h, Vh=Wh, space_kind='h1', domain=Omega, \n", + " plot_type='vector_field', title='g_h: L2 projection of g', filename='')" ] } ], From d0bbcecd8e7c90cb4ee7eb24d994e6b4cc21512c Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Thu, 11 Dec 2025 13:42:16 +0100 Subject: [PATCH 46/63] Update PETSc version in installation docs --- docs/source/installation.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/source/installation.rst b/docs/source/installation.rst index de9c01e31..2c3975eca 100644 --- a/docs/source/installation.rst +++ b/docs/source/installation.rst @@ -203,7 +203,7 @@ First, we download the latest release of PETSc from its `official Git repository .. code-block:: sh - git clone --depth 1 --branch v3.21.4 https://gitlab.com/petsc/petsc.git + git clone --depth 1 --branch v3.23.2 https://gitlab.com/petsc/petsc.git Next, we specify a configuration for complex numbers, and install PETSc in a local directory: From 02a0ddb7457595017b93b17c440f6ecd7ebc431c Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Thu, 11 Dec 2025 13:44:33 +0100 Subject: [PATCH 47/63] update fem L2 proj notebook --- examples/notebooks/fem_L2_projection.ipynb | 122 ++++++++++++++++++--- 1 file changed, 109 insertions(+), 13 deletions(-) diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb index 16e90f04c..4da3539ec 100644 --- a/examples/notebooks/fem_L2_projection.ipynb +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -252,8 +252,8 @@ "source": [ "from sympde.calculus import dot\n", "\n", - "u, v = elements_of(W, names='u, v')\n", - "a = BilinearForm((u, v), integral(Omega, dot(u,v)))\n", + "uu, vv = elements_of(W, names='uu, vv')\n", + "a = BilinearForm((uu, vv), integral(Omega, dot(uu,vv)))\n", "ah_W = discretize(a, Omega_h, [Wh, Wh], backend=PSYDAC_BACKENDS[backend_language])\n", "\n", "# Mass matrix in Psydac 'stencil' (linear operator) format \n", @@ -327,15 +327,45 @@ "tilde_f = get_dual_dofs(Vh=Vh, f=ref_f, domain_h=Omega_h, backend_language=backend_language)\n", "\n", "inv_M = inverse(M_V, solver='cg')\n", - "f_h = inv_M @ tilde_f\n", + "f_coeffs = inv_M @ tilde_f\n", + "fh = FemField(Vh, f_coeffs)\n", "\n", - "plot_field_2d(\n", - " stencil_coeffs=f_h, Vh=Vh, space_kind='h1', \n", - " domain=Omega, title=r'$f_h$: L2 projection of $f$ in Vh', cmap='viridis', filename='')\n", + "plot_field_2d(fem_field=fh, domain=Omega, title=r'$f_h$: L2 projection of $f$ in Vh', cmap='viridis', filename='')\n", "\n", "print('note the lower accuracy in the regions where the grid is not aligned with the anisotropic smoothness')\n" ] }, + { + "cell_type": "markdown", + "id": "0de90ef8", + "metadata": {}, + "source": [ + "compute the norm and the error" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a23c225a", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.expr.expr import Norm \n", + "error = ref_f - u\n", + "err_l2norm = Norm(error, Omega, kind='l2')\n", + "nquads = [p + 1 for p in degree]\n", + "err_l2norm_h = discretize(err_l2norm, Omega_h, Vh, nquads=nquads, backend=PSYDAC_BACKENDS[backend_language])\n", + "err_l2 = err_l2norm_h.assemble(u=fh)\n", + "print(f'> L2 projection error : {err_l2}')\n", + "\n", + "zero_h = FemField(Vh, coeffs=array_to_psydac(np.zeros(Vh.nbasis), Vh.coeff_space))\n", + "f_l2 = err_l2norm_h.assemble(u=zero_h)\n", + "print(f'> L2 norm of f : {f_l2}')\n", + "\n", + "rel_err_f = err_l2 / f_l2\n", + "print(f'> L2 relative error : {rel_err_f}')" + ] + }, { "cell_type": "markdown", "id": "8258971a", @@ -358,16 +388,14 @@ "\n", "ref_g = Tuple(ref_g_x, ref_g_y)\n", "\n", + "print(type(ref_g))\n", + "\n", "# make the expression a callable function\n", "g_vect = [lambdify(Omega.coordinates, ref_g[d]) for d in [0,1]]\n", "\n", "ref_vals_g = [[g_vect[d](xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)] for d in [0,1]]\n", - "# g_y = [g_vect[1](xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)]\n", - "\n", - "# ref_f_vals = [f_call(xx_k, yy_k) for xx_k, yy_k in zip(xx, yy)]\n", "\n", "from psydac.fem.plotting_utilities import my_small_streamplot\n", - "\n", "my_small_streamplot(\n", " title=r'a reference function $g$ (vector valued)',\n", " vals_x=ref_vals_g[0],\n", @@ -392,10 +420,78 @@ "tilde_g = get_dual_dofs(Vh=Wh, f=ref_g, domain_h=Omega_h, backend_language=backend_language)\n", "\n", "inv_M_W = inverse(M_W, solver='cg')\n", - "g_h = inv_M_W @ tilde_g\n", + "g_coeffs = inv_M_W @ tilde_g\n", + "\n", + "gh = FemField(Wh, g_coeffs)\n", + "\n", + "plot_field_2d(fem_field=gh, domain=Omega, plot_type='vector_field', title='g_h: L2 projection of g', filename='')" + ] + }, + { + "cell_type": "markdown", + "id": "3f9d6e2b", + "metadata": {}, + "source": [ + "compute the norm and the error" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d6e6b7b4", + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import Matrix \n", + "\n", + "error = Matrix([ref_g[0]-uu[0], ref_g[1]-uu[1]])\n", + "err_l2norm = Norm(error, Omega, kind='l2')\n", + "nquads = [p + 1 for p in degree]\n", + "err_l2norm_h = discretize(err_l2norm, Omega_h, Wh, nquads=nquads, backend=PSYDAC_BACKENDS[backend_language])\n", + "err_l2 = err_l2norm_h.assemble(uu=gh)\n", + "print(f'> L2 projection error : {err_l2}')\n", + "\n", + "zero_h = FemField(Wh, coeffs=array_to_psydac(np.zeros(Wh.nbasis), Wh.coeff_space))\n", + "g_l2 = err_l2norm_h.assemble(uu=zero_h)\n", + "print(f'> L2 norm of g : {g_l2}')\n", + "\n", + "rel_err_g = err_l2 / g_l2\n", + "print(f'> L2 relative error : {rel_err_g}')" + ] + }, + { + "cell_type": "markdown", + "id": "a5b15eef", + "metadata": {}, + "source": [ + "### Testing the notebook" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "2a7634d4", + "metadata": {}, + "outputs": [], + "source": [ + "import ipytest\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "caa039a8", + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_l2error_f():\n", + " assert rel_err_f < 5e-02\n", "\n", - "plot_field_2d(stencil_coeffs=g_h, Vh=Wh, space_kind='h1', domain=Omega, \n", - " plot_type='vector_field', title='g_h: L2 projection of g', filename='')" + "def test_l2error_g():\n", + " assert rel_err_g < 5e-02" ] } ], From 931bed5e06c01f8f12191b40ea49effbe924c52f Mon Sep 17 00:00:00 2001 From: Martin Campos Pinto Date: Thu, 11 Dec 2025 15:15:42 +0100 Subject: [PATCH 48/63] minor cleaning on fem L2 proj notebook --- examples/notebooks/fem_L2_projection.ipynb | 11 ++++------- 1 file changed, 4 insertions(+), 7 deletions(-) diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb index 4da3539ec..85044413c 100644 --- a/examples/notebooks/fem_L2_projection.ipynb +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -108,7 +108,7 @@ "bf = FemField(Vh, coeffs=array_to_psydac(bf_c, Vh.coeff_space))\n", "\n", "from psydac.fem.plotting_utilities import plot_field_2d\n", - "plot_field_2d(fem_field=bf, Vh=Vh, space_kind=None, domain=Omega, cmap='viridis', title=fr'three scalar-valued basis functions: $\\phi_{ {i0} }$, $\\phi_{ {i1} }$, $\\phi_{ {i2} }$', filename='')\n" + "plot_field_2d(fem_field=bf, Vh=Vh, domain=Omega, cmap='viridis', title=fr'three scalar-valued basis functions: $\\phi_{ {i0} }$, $\\phi_{ {i1} }$, $\\phi_{ {i2} }$', filename='')\n" ] }, { @@ -129,7 +129,7 @@ "from psydac.feec.conforming_projectors import construct_h1_conforming_projection\n", "cP = construct_h1_conforming_projection(Vh, hom_bc=False)\n", "Pbf = FemField(Vh, coeffs=array_to_psydac(cP@bf_c, Vh.coeff_space))\n", - "plot_field_2d(fem_field=Pbf, Vh=Vh, space_kind=None, domain=Omega, cmap='viridis', title='H1-conforming projection of the above basis functions', filename='')" + "plot_field_2d(fem_field=Pbf, Vh=Vh, domain=Omega, cmap='viridis', title='H1-conforming projection of the above basis functions', filename='')" ] }, { @@ -161,7 +161,7 @@ "i2 = 479; bf2_c[i2] = 1\n", "bf2 = FemField(Wh, coeffs=array_to_psydac(bf2_c, Wh.coeff_space))\n", "\n", - "plot_field_2d(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", + "plot_field_2d(fem_field=bf2, Vh=Wh, domain=Omega, \n", " plot_type='components', cmap='viridis', title=fr'three vector-valued basis functions: $\\Phi_{ {i0} }$, $\\Phi_{ {i1} }$, $\\Phi_{ {i2} }$', filename='')\n" ] }, @@ -180,7 +180,7 @@ "metadata": {}, "outputs": [], "source": [ - "plot_field_2d(fem_field=bf2, Vh=Wh, space_kind=None, domain=Omega, \n", + "plot_field_2d(fem_field=bf2, Vh=Wh, domain=Omega, \n", " plot_type='vector_field', vf_skip=1, title=fr'three vector-valued basis functions: $\\Phi_{ {i0} }$, $\\Phi_{ {i1} }$, $\\Phi_{ {i2} }$', filename='')" ] }, @@ -385,11 +385,8 @@ "\n", "ref_g_x = ref_f * cos(2*pi*y)\n", "ref_g_y = ref_f * 1\n", - "\n", "ref_g = Tuple(ref_g_x, ref_g_y)\n", "\n", - "print(type(ref_g))\n", - "\n", "# make the expression a callable function\n", "g_vect = [lambdify(Omega.coordinates, ref_g[d]) for d in [0,1]]\n", "\n", From 2c65add921645cbb0fe241197745f51d00ffd121 Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 12 Dec 2025 11:45:41 +0100 Subject: [PATCH 49/63] delete plt.show --- .../notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb | 8 +++++--- 1 file changed, 5 insertions(+), 3 deletions(-) diff --git a/examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb b/examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb index cb8cdcea7..449293000 100644 --- a/examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb +++ b/examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb @@ -206,8 +206,6 @@ " ax.set_title(f\"Eigenvalues estimated with CG {iterative_solver.getIterationNumber()} iterations\")\n", " im = ax.scatter(np.arange(eigenvalues_approx.size), eigenvalues_approx)\n", " plt.xlabel('index')\n", - " fig.show()\n", - " plt.pause(20)\n", " \n", "if comm is not None:\n", " comm.Barrier()" @@ -279,7 +277,11 @@ ] } ], - "metadata": {}, + "metadata": { + "language_info": { + "name": "python" + } + }, "nbformat": 4, "nbformat_minor": 5 } From 8100732e415e617338e749e0ec061cbcaad91ca3 Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 12 Dec 2025 11:48:57 +0100 Subject: [PATCH 50/63] rephrase sentence for callable source --- examples/notebooks/positive_Helmholtz_3D_VTK.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb index 23acf0be9..acffc71c2 100644 --- a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb +++ b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb @@ -15,7 +15,7 @@ "\n", "$$ \\mathrm{curl} \\mathrm{curl} u + \\mu u = f, $$\n", "\n", - "where $\\mu = \\pi$, and $f$ is a callable function in terms of the domain coordinates, the expression of which is a priori not known. \n", + "where $\\mu = \\pi$, and $f$ is a callable function (of the domain coordinates) for which we may not have a symbolic expression. \n", "\n", "Only for illustration here we use the callable function\n", "$$f(x,y,z) = (10e^{-0.5(x-4)^2 - 1.5z^2 - 0.1y^2}, 0, \\cos(y)\\sin(\\pi x / 5)),$$\n", From eb19a237c5aa7fd48a90a6af182817c7b4099bf2 Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 12 Dec 2025 14:14:35 +0100 Subject: [PATCH 51/63] rename examples, remark mu positive --- .../regularized_curlcurl_3D_fx.png | Bin 0 -> 1973988 bytes .../regularized_curlcurl_3D_fy.png | Bin 0 -> 1973988 bytes .../regularized_curlcurl_3D_fz.png | Bin 0 -> 1973988 bytes .../regularized_curlcurl_3D_ux.png | Bin 0 -> 1973988 bytes .../regularized_curlcurl_3D_uy.png | Bin 0 -> 1973988 bytes .../regularized_curlcurl_3D_uz.png | Bin 0 -> 1973988 bytes ...regularized_curlcurl_eigenvalues_PETSc.png | Bin 0 -> 18778 bytes ...tsc_eigenvalues_regularized_curlcurl.ipynb | 284 ++++++++++++++++++ .../regularized_curlcurl_3D_VTK.ipynb | 276 +++++++++++++++++ 9 files changed, 560 insertions(+) create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_fx.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_fy.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_fz.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_ux.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_uy.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_3D_uz.png create mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_eigenvalues_PETSc.png create mode 100644 examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb create mode 100644 examples/notebooks/regularized_curlcurl_3D_VTK.ipynb diff --git a/examples/notebooks/paraview_images/regularized_curlcurl_3D_fx.png b/examples/notebooks/paraview_images/regularized_curlcurl_3D_fx.png new file mode 100644 index 0000000000000000000000000000000000000000..00d948219f177a26418846e1a6c0854d6a4025cb GIT binary patch literal 1973988 zcmeEv2bfmH_5M<%!!AvcW;;4Whz(4lMx$snighs> zV~nv27)1rdf-PbLv7iVFQWWXz{@>lp&Ntt!b9;NgXCIh5bLPxB?|kfiIdf*_h9Sou z*}O^nCM6{$%?BMda9Bx6-DM>u^)75w7d6Y?saJ--+KfH?H)9XI=%Vw+j6QAbmN_H$6H1N<9F0WHkKCxnaovNxTbm4~x5CI}U1c(3;AOa~u zpqlvbLj;Hb5g-CYfCvzQbRj?nldk!qwM2jj5CI}U1c*R20%S1!9uNT{Km<~QK$~li zc&j!SAT>tQP$CdM0%SAcW6TkV01+SpM1TkofuIo}g9#c@>LUU~fCvx)B0vPfM}Q0_ ze2h5)5g-CYfCvx)A`mnJWH3P^N_`w4MkM z0U|&Ih(JCOAcM*0ywhtUKm>>Y5g-ETMt}?^-SbE5i2xBG0z`laBo=`oyG{Q?B)I@& zGl~5U&@duE1c(3;AOb|d5&<$8OK8|Y1c(3;AOb{y2qYE(GML0p4Gkj#M1Tko0U|&I zED<1sv4n;VM1Tko0q+Q0+H8m8BgqBuZX$aUfeax~KCxmvDNTkZl&%l~B0vO)01?Oy z0%S0`nQA&p1c(3;AOb`nLkN(;WN0$!3K1XzM1Tkof!rWK29ukqj>OUWmws>+a{(fO znu8DlB0vO)fIxt3MnJ&=5g-CYfCvx)B9Iyc$Y4@4RWy_c5CI}U1c(3;5D1XL2q;(} z0z`la5CI~PLj*bu{p`oI=K_$;?D>JcD=N&OVk0U|&IJR|VKF|+qhdoF-y=h=}6WC#JWnG8)P zT_FNQfCvx)B9I#d$Y63a)pV2y5CI}U1c*R}5Fmre&}7mTB0vO)01+Spxj}#oCO1>9 zb9CaOH@0UkfDRNs5&gRudJ zO+y}=)`Dd-Q4Q>Uo#gV(Njd@hyW2F0z@Ew1juIMp95Mz1c(3; zAOb{y2)IRn48|>DlqUj2fCvx)B0vP>Y5g-CVAW%NBVmxU~5J*x75g-CYfCvx)A`mSCWH8a<&C!Se5g-CY zfCvzQAP^vf2?9mxAOb{S#F{Z@G8cf~10p~K;z6K(Ji~HSB0vP9LSXIMwXfHF-hTV- zx^?UJ>C>lg-@ZM1^k~wgNmM3q93nsjh(PcN)Tyef3SKKU5&eZVwXU^u$n}-h{K5W=95SnC|Nh^o|5g-Dt5nv3)HDv5S1X6^+>eZ_k zE?n5HTeoA5IcBfD_JZZ$F;71EB;qkg9C1X87A;cb3r!^gM1Tm$2=ISkG8*2>_y6Df z-!T`!8+Pm!B?7Z&&tATKdH3$!4?OU|#xRW18#Y|CW{q6QG7%sGL?B%Vkin#DzGy8GaEHLpKmWYVHrupo z*G}$+7z`MUT*ERE$Q=T0%jfRQT!8FMJ2QN_i=2-z;X>>?ca?z`_cZrmsySs(&LfC!`!0Wz30 z&KhkF3xN(bA5A+Bh?_TW-fg$tcFHNIbnV(TtRX|z3#I}`K*eMRgGbPsva+&}2d8=> zKm>?DhzKwzCPZ+lI@JguYvl3AA4d!WOGrp7NvSW$=fzg)#fuk9_OIxC;Nc<{0E=bV zbgkRCBnh)f1c(3;NC5(5GbxxPnivZLScSn>lZC20z`lakiqafKm<$>c;ST?X3Us@ zD~4LOY-!RQXchPbB0jIa`YQHCfh`?!$RQXP89ISn(TFRO4nO?x($Z2Whf}yuX}|sU z+k5Z5QCX)>ok0DdG9o|(h(M$Wk&hzxsPvgA08*jW3mju{!WD^k}0z@F^2rwR#^DhA1H$h;^ zlquNCbJ9sCg-u^DHZ~05gqqf^TaOww3g^*)&2oQl< z1en@eiv<5B0yPNWwA+_oei=7F4<9}}0!ZF}|9u?Y0@l*Ickf1x8sU=0Hf`D*eDJ|9 zzWCynEn6ZmfI|=gB0vOEiU1i*N+*tHhk^i7MsB|OW?b+*X3Usq4(P`wZY0SNMH83{kk7ey=`~lBTmnY%Oe3&-`SNF;d1l0j5!-FI z-7mlV0zy;2ez^ZekZ+5R3@T1?fej!uEn2jY>sclOM1Tko0U3dCe>=+~u}lP#kHA0v z@eiC5_tjTlAtj}A=gxvdU~@7y4Mku-4%%I~aN)9L%dkxe+lwL?kwXvxB0vOEiU1i* zN+*tHhk^jsclz|{^Vw&gz5DLFD^{#PvTdtYt#;jYS0tBE7kqaq?e1c*R<2;^p$b$k$WWFjCCz_pSqSFRL~phvjgKzqbS z?oU4X3xF#DKmap;#vn)Z<4VeFRllDMK76D4o

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\n", + "We can see that the eigenavalues corresponding to the kernel of the curlcurl operator are shifted thanks to the regularization.\n", + "\n", + "\n", + "## Step 6 : Save and export solution\n", + "This step is similar to what is explained in other tests." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c77d25a", + "metadata": {}, + "outputs": [], + "source": [ + "# Save the results using OutputManager\n", + "from psydac.api.postprocessing import OutputManager\n", + "import os\n", + "\n", + "os.makedirs('results_eigenvalues_positive_Helmholtz', exist_ok=True)\n", + "\n", + "Om = OutputManager(\n", + " f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm,\n", + " save_mpi_rank=True, \n", + " mode = 'w' \n", + ")\n", + "\n", + "Om.add_spaces(V=Wh)\n", + "Om.export_space_info()\n", + "\n", + "Om.set_static() # the fields do not depend on time\n", + "\n", + "Om.export_fields(u=uh) # saves the coefficients of the solution\n", + "\n", + "Om.close()\n", + "\n", + "# Export the results to VTK using PostProcessManager\n", + "from psydac.api.postprocessing import PostProcessManager\n", + "\n", + "Pm = PostProcessManager(\n", + " domain=Omega,\n", + " space_file=f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm\n", + ")\n", + "\n", + "Pm.export_to_vtk(\n", + " f'results_eigenvalues_positive_Helmholtz/visu_{Omega.name}',\n", + " grid=None,\n", + " npts_per_cell=[4,2,4],\n", + " fields='u'\n", + ")\n", + "\n", + "Pm.close()" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb new file mode 100644 index 000000000..0e9653f5f --- /dev/null +++ b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb @@ -0,0 +1,276 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "2443e734", + "metadata": {}, + "source": [ + "# 3D example with VTK and ParaView \n", + "\n", + "In this notebook we show how to solve a 3D problem in parallel, save the solution in HDF5 format and export it to VTK. \n", + "\n", + "We solve the regularized curl-curl problem in 3D with a callable function for the source. In practice, the source could be the interpolation of some experimental data. Besides, we impose periodic boundary conditions everywhere in the boundary.\n", + "\n", + "Let $\\Omega=[0, 10] \\times [-2\\pi, 2\\pi]\\times [-3, 1]$. We want to find $u\\in H(\\mathrm{curl}, \\Omega)$ such that\n", + "\n", + "$$ \\mathrm{curl} \\mathrm{curl} u + \\mu u = f, $$\n", + "\n", + "where $\\mu = \\pi$, and $f$ is a callable function (of the domain coordinates) for which we may not have a symbolic expression. \n", + "\n", + "Since $\\mu>0$ the resulting operator is positive definite and we can use conjugate gradient to solve the system. In the case of the time-harmonic Maxwell problem we have that $\\mu<0$, which yields an indefinite operator and conjugate gradient is no longer guaranteed to converge.\n", + "\n", + "Only for illustration here we use the callable function\n", + "$$f(x,y,z) = (10e^{-0.5(x-4)^2 - 1.5z^2 - 0.1y^2}, 0, \\cos(y)\\sin(\\pi x / 5)),$$\n", + "\n", + "and project it from $H(\\mathrm{curl}, \\Omega)$ to the corresponding discretized space. This process is analogous with any callable vectorial function.\n", + "\n", + "\n", + "\n", + "## Step 1 : define the domain and spaces and discretize them\n", + "\n", + "This is similar to what is done in other examples" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "39c21151", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "from mpi4py import MPI\n", + "from sympde.topology import Cube\n", + "from sympde.topology import VectorFunctionSpace\n", + "from psydac.api.discretization import discretize\n", + "\n", + "comm = MPI.COMM_WORLD # MPI communicator\n", + "\n", + "Omega = Cube('Omega', bounds1=(0, 10), bounds2=(-2*np.pi, 2*np.pi), bounds3=(-3, 1)) # 3D cubic domain\n", + "\n", + "W = VectorFunctionSpace('W', Omega, kind='hcurl') # Hcurl space\n", + "\n", + "ncells = [25, 30, 11] # number of cells in each direction\n", + "degree = [3, 2, 2] # B-spline degree in each direction\n", + "\n", + "periodic = [True, True, True] # set periodic BC in every direction\n", + "\n", + "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic, comm=comm)\n", + "Wh = discretize(W, Omega_h, degree=degree)" + ] + }, + { + "cell_type": "markdown", + "id": "36a9632b", + "metadata": {}, + "source": [ + "## Step 2 : compute the matrix\n", + "\n", + "We assemble the mass and curl curl matrices." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "091d4560", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.topology import elements_of, element_of\n", + "from sympde.expr.expr import BilinearForm, LinearForm, integral\n", + "from sympde.calculus import dot, curl\n", + "from psydac.api.settings import PSYDAC_BACKENDS\n", + "from psydac.fem.basic import FemField\n", + "\n", + "backend_language = 'python'\n", + "backend = PSYDAC_BACKENDS[backend_language]\n", + "\n", + "u, v = elements_of(W, names='u, v') #trial and test functions\n", + "\n", + "m = BilinearForm((u, v), integral(Omega, dot(u, v)))\n", + "mh = discretize(m, Omega_h, [Wh, Wh], backend=backend)\n", + "M = mh.assemble() # Mass matrix\n", + "\n", + "k = BilinearForm((u, v), integral(Omega, dot(curl(u), curl(v))))\n", + "kh = discretize(k, Omega_h, [Wh, Wh], backend=backend)\n", + "K = kh.assemble() # Curl curl matrix\n", + "\n", + "mu = np.pi\n", + "\n", + "A = K + mu*M # system matrix, positive-definite" + ] + }, + { + "cell_type": "markdown", + "id": "8927f88c", + "metadata": {}, + "source": [ + "## Step 3 : compute the right-hand size\n", + "\n", + "We project a callable function to the vector space and use it to assemble the right-hand side of the system." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a13044fa", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl\n", + "f_callable = [lambda x, y, z: 10*np.exp(-0.5*(x-4)**2 - 1.5*z**2 - 1e-1*y**2),\n", + " lambda x, y, z: 0,\n", + " lambda x, y, z: np.cos(y)*np.sin(x*np.pi/5)]\n", + "\n", + "proj_Wh = GlobalGeometricProjectorHcurl(Wh, nquads=[p+1 for p in degree]) # get Hcurl projector, nquads is the number of points for the Gauss quadrature.\n", + "fh = proj_Wh(f_callable) # project callable to field in Wh\n", + "\n", + "f = element_of(W, name='f') # free variable for the FemField\n", + "\n", + "l = LinearForm(v, integral(Omega, dot(f,v)))\n", + "lh = discretize(l, Omega_h, Wh, backend=backend)\n", + "rhs = lh.assemble(f=fh) # assmble RHS, f is a free parameter" + ] + }, + { + "cell_type": "markdown", + "id": "8258971a", + "metadata": {}, + "source": [ + "## Step 4 : solve the system\n", + "Solve the system using Conjugate Gradient. Notice that since $\\mu>0$, the matrix is positive definite." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "1f0f103d", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.linalg.solvers import inverse\n", + "\n", + "inv_A = inverse(A, solver='cg', tol=1e-2, maxiter=100) # invert using Conjugate Gradient\n", + "\n", + "u = inv_A @ rhs # array of coefficients\n", + "\n", + "uh = FemField(Wh, coeffs=u) # finite element field, callable" + ] + }, + { + "cell_type": "markdown", + "id": "e0c73790", + "metadata": {}, + "source": [ + "## Step 5 : Save results to HDF5 format\n", + "We save the coefficients of the solution and the field used in the right-hand size. This step generates a YAML file containing the space information, and a HDF5 file that stores the coefficients. The fields are saved in parallel. This step does not include an evaluation of the fields on a grid." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "6c77d25a", + "metadata": {}, + "outputs": [], + "source": [ + "# Save the results using OutputManager\n", + "from psydac.api.postprocessing import OutputManager\n", + "import os\n", + "\n", + "os.makedirs('results_positive_Helmholtz', exist_ok=True)\n", + "\n", + "Om = OutputManager(\n", + " f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm,\n", + " save_mpi_rank=True, \n", + " mode = 'w' \n", + ")\n", + "\n", + "Om.add_spaces(V=Wh)\n", + "Om.export_space_info()\n", + "\n", + "Om.set_static() # the fields do not depend on time\n", + "\n", + "save_fields = {\n", + " 'u': uh,\n", + " 'f': fh\n", + "}\n", + "\n", + "Om.export_fields(**save_fields) # saves the coefficients of the fields\n", + "\n", + "Om.close()\n", + "\n", + "# This generates a YAML file containing the space information, and a HDF5 file that stores the solution coefficients. \n", + "# At this point the solution has not been evaluated on any grid." + ] + }, + { + "cell_type": "markdown", + "id": "a619a838", + "metadata": {}, + "source": [ + "## Step 6 : Evaluate fields on a grid and export to VTK\n", + "Evaluate the saved fields on a grid and export the result to VTK format." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "86a1c531", + "metadata": {}, + "outputs": [], + "source": [ + "# Export the results to VTK using PostProcessManager\n", + "from psydac.api.postprocessing import PostProcessManager\n", + "\n", + "Pm = PostProcessManager(\n", + " domain=Omega,\n", + " space_file=f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " comm=comm\n", + ")\n", + "\n", + "Pm.export_to_vtk(\n", + " f'results_regularized_curlcurl/visu_{Omega.name}',\n", + " grid=None,\n", + " npts_per_cell=[4,2,4],\n", + " fields=save_fields.keys() # evaluate all the fields that were saved\n", + ")\n", + "\n", + "Pm.close()\n", + "# If this file is run in sequential, then this step will generate a single .vtu file that can be opened with ParaView.\n", + "# If it is run in parallel, it generates a .vtu file per process (containing the local grid) and a .pvtu file. To visualize it in ParaView, open the .pvtu file." + ] + }, + { + "cell_type": "markdown", + "id": "af41d09b", + "metadata": {}, + "source": [ + "## Visualization of the solution in ParaView\n", + "

\n", + " \n", + " \n", + " \n", + "

" + ] + }, + { + "cell_type": "markdown", + "id": "0bb786a7", + "metadata": {}, + "source": [ + "## Visualization of the source in ParaView\n", + "

\n", + " \n", + " \n", + " \n", + "

" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} From 71dcf108804b7057f9f3b8eab65d55c266a39f05 Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 12 Dec 2025 14:16:59 +0100 Subject: [PATCH 52/63] forgot update list names --- docs/source/examples.rst | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/source/examples.rst b/docs/source/examples.rst index e3b10553d..50c096f3d 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -21,8 +21,8 @@ but are also generated as part of the documentation and can be accessed here: examples/Poisson_non_periodic examples/Helmholtz_non_periodic examples/fem_L2_projection - examples/positive_Helmholtz_3D_VTK - examples/petsc_eigenvalues_positive_Helmholtz + examples/regularized_curlcurl_3D_VTK + examples/petsc_eigenvalues_regularized_curlcurl examples/feec_curlcurl_eigenvalue examples/feec_time_harmonic_Maxwell From 68a75ca620e9f38c3ec9db9728b3c4db126e0d43 Mon Sep 17 00:00:00 2001 From: elmosa Date: Fri, 12 Dec 2025 17:50:43 +0100 Subject: [PATCH 53/63] delete unneeded files, fix rename vtk files --- .../positive_Helmholtz_3D_fx.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_3D_fy.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_3D_fz.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_3D_ux.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_3D_uy.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_3D_uz.png | Bin 1973988 -> 0 bytes .../positive_Helmholtz_eigenvalues_PETSc.png | Bin 18778 -> 0 bytes ...petsc_eigenvalues_positive_Helmholtz.ipynb | 287 ------------------ ...tsc_eigenvalues_regularized_curlcurl.ipynb | 12 +- .../notebooks/positive_Helmholtz_3D_VTK.ipynb | 274 ----------------- .../regularized_curlcurl_3D_VTK.ipynb | 10 +- 11 files changed, 11 insertions(+), 572 deletions(-) delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fy.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_fz.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_ux.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_uy.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_3D_uz.png delete mode 100644 examples/notebooks/paraview_images/positive_Helmholtz_eigenvalues_PETSc.png delete mode 100644 examples/notebooks/petsc_eigenvalues_positive_Helmholtz.ipynb delete mode 100644 examples/notebooks/positive_Helmholtz_3D_VTK.ipynb diff --git a/examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png b/examples/notebooks/paraview_images/positive_Helmholtz_3D_fx.png deleted file mode 100644 index 00d948219f177a26418846e1a6c0854d6a4025cb..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 1973988 zcmeEv2bfmH_5M<%!!AvcW;;4Whz(4lMx$snighs> zV~nv27)1rdf-PbLv7iVFQWWXz{@>lp&Ntt!b9;NgXCIh5bLPxB?|kfiIdf*_h9Sou z*}O^nCM6{$%?BMda9Bx6-DM>u^)75w7d6Y?saJ--+KfH?H)9XI=%Vw+j6QAbmN_H$6H1N<9F0WHkKCxnaovNxTbm4~x5CI}U1c(3;AOa~u zpqlvbLj;Hb5g-CYfCvzQbRj?nldk!qwM2jj5CI}U1c*R20%S1!9uNT{Km<~QK$~li zc&j!SAT>tQP$CdM0%SAcW6TkV01+SpM1TkofuIo}g9#c@>LUU~fCvx)B0vPfM}Q0_ ze2h5)5g-CYfCvx)A`mnJWH3P^N_`w4MkM z0U|&Ih(JCOAcM*0ywhtUKm>>Y5g-ETMt}?^-SbE5i2xBG0z`laBo=`oyG{Q?B)I@& zGl~5U&@duE1c(3;AOb|d5&<$8OK8|Y1c(3;AOb{y2qYE(GML0p4Gkj#M1Tko0U|&I zED<1sv4n;VM1Tko0q+Q0+H8m8BgqBuZX$aUfeax~KCxmvDNTkZl&%l~B0vO)01?Oy z0%S0`nQA&p1c(3;AOb`nLkN(;WN0$!3K1XzM1Tkof!rWK29ukqj>OUWmws>+a{(fO znu8DlB0vO)fIxt3MnJ&=5g-CYfCvx)B9Iyc$Y4@4RWy_c5CI}U1c(3;5D1XL2q;(} z0z`la5CI~PLj*bu{p`oI=K_$;?D>JcD=N&OVk0U|&IJR|VKF|+qhdoF-y=h=}6WC#JWnG8)P zT_FNQfCvx)B9I#d$Y63a)pV2y5CI}U1c*R}5Fmre&}7mTB0vO)01+Spxj}#oCO1>9 zb9CaOH@0UkfDRNs5&gRudJ zO+y}=)`Dd-Q4Q>Uo#gV(Njd@hyW2F0z@Ew1juIMp95Mz1c(3; 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zNI7$k@Lx%<(Sepk;9V^8-~(|?ls++)B;l7|GP|Mfd4kL~8X-UpekVVmVbqeXfqvoy zL7V;`W*qc(DCSm>Kt&q0G4Z7JG?sB64G~vp&eo$tdno@Eboh{f|M;w;2-MSkXhRJ=jtNUJ?*78}T!(`7oBRLlr+nr_SKbj=vybW\n", - " \n", - "

\n", - "\n", - "\n", - "\n", - "## Step 6 : Save and export solution\n", - "This step is similar to what is explained in other tests." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6c77d25a", - "metadata": {}, - "outputs": [], - "source": [ - "# Save the results using OutputManager\n", - "from psydac.api.postprocessing import OutputManager\n", - "import os\n", - "\n", - "os.makedirs('results_eigenvalues_positive_Helmholtz', exist_ok=True)\n", - "\n", - "Om = OutputManager(\n", - " f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", - " comm=comm,\n", - " save_mpi_rank=True, \n", - " mode = 'w' \n", - ")\n", - "\n", - "Om.add_spaces(V=Wh)\n", - "Om.export_space_info()\n", - "\n", - "Om.set_static() # the fields do not depend on time\n", - "\n", - "Om.export_fields(u=uh) # saves the coefficients of the solution\n", - "\n", - "Om.close()\n", - "\n", - "# Export the results to VTK using PostProcessManager\n", - "from psydac.api.postprocessing import PostProcessManager\n", - "\n", - "Pm = PostProcessManager(\n", - " domain=Omega,\n", - " space_file=f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " fields_file=f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", - " comm=comm\n", - ")\n", - "\n", - "Pm.export_to_vtk(\n", - " f'results_eigenvalues_positive_Helmholtz/visu_{Omega.name}',\n", - " grid=None,\n", - " npts_per_cell=[4,2,4],\n", - " fields='u'\n", - ")\n", - "\n", - "Pm.close()" - ] - } - ], - "metadata": { - "language_info": { - "name": "python" - } - }, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb b/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb index c954276f3..9f34466d9 100644 --- a/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb +++ b/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb @@ -238,11 +238,11 @@ "from psydac.api.postprocessing import OutputManager\n", "import os\n", "\n", - "os.makedirs('results_eigenvalues_positive_Helmholtz', exist_ok=True)\n", + "os.makedirs('results_eigenvalues_regularized_curlcurl', exist_ok=True)\n", "\n", "Om = OutputManager(\n", - " f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " f'results_eigenvalues_regularized_curlcurl/space_info_{Omega.name}.yml',\n", + " f'results_eigenvalues_regularized_curlcurl/field_info_{Omega.name}.h5',\n", " comm=comm,\n", " save_mpi_rank=True, \n", " mode = 'w' \n", @@ -262,13 +262,13 @@ "\n", "Pm = PostProcessManager(\n", " domain=Omega,\n", - " space_file=f'results_eigenvalues_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " fields_file=f'results_eigenvalues_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " space_file=f'results_eigenvalues_regularized_curlcurl/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_eigenvalues_regularized_curlcurl/field_info_{Omega.name}.h5',\n", " comm=comm\n", ")\n", "\n", "Pm.export_to_vtk(\n", - " f'results_eigenvalues_positive_Helmholtz/visu_{Omega.name}',\n", + " f'results_eigenvalues_regularized_curlcurl/visu_{Omega.name}',\n", " grid=None,\n", " npts_per_cell=[4,2,4],\n", " fields='u'\n", diff --git a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb b/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb deleted file mode 100644 index acffc71c2..000000000 --- a/examples/notebooks/positive_Helmholtz_3D_VTK.ipynb +++ /dev/null @@ -1,274 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "id": "2443e734", - "metadata": {}, - "source": [ - "# 3D example with VTK and ParaView \n", - "\n", - "In this notebook we show how to solve a 3D problem in parallel, save the solution in HDF5 format and export it to VTK. \n", - "\n", - "We solve the positive Helmholtz equation in 3D with a callable function for the source. In practice, the source could be the interpolation of some experimental data. Besides, we impose periodic boundary conditions everywhere in the boundary.\n", - "\n", - "Let $\\Omega=[0, 10] \\times [-2\\pi, 2\\pi]\\times [-3, 1]$. We want to find $u\\in H(\\mathrm{curl}, \\Omega)$ such that\n", - "\n", - "$$ \\mathrm{curl} \\mathrm{curl} u + \\mu u = f, $$\n", - "\n", - "where $\\mu = \\pi$, and $f$ is a callable function (of the domain coordinates) for which we may not have a symbolic expression. \n", - "\n", - "Only for illustration here we use the callable function\n", - "$$f(x,y,z) = (10e^{-0.5(x-4)^2 - 1.5z^2 - 0.1y^2}, 0, \\cos(y)\\sin(\\pi x / 5)),$$\n", - "\n", - "and project it from $H(\\mathrm{curl}, \\Omega)$ to the corresponding discretized space. This process is analogous with any callable vectorial function.\n", - "\n", - "\n", - "\n", - "## Step 1 : define the domain and spaces and discretize them\n", - "\n", - "This is similar to what is done in other examples" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "39c21151", - "metadata": {}, - "outputs": [], - "source": [ - "import numpy as np\n", - "from mpi4py import MPI\n", - "from sympde.topology import Cube\n", - "from sympde.topology import VectorFunctionSpace\n", - "from psydac.api.discretization import discretize\n", - "\n", - "comm = MPI.COMM_WORLD # MPI communicator\n", - "\n", - "Omega = Cube('Omega', bounds1=(0, 10), bounds2=(-2*np.pi, 2*np.pi), bounds3=(-3, 1)) # 3D cubic domain\n", - "\n", - "W = VectorFunctionSpace('W', Omega, kind='hcurl') # Hcurl space\n", - "\n", - "ncells = [25, 30, 11] # number of cells in each direction\n", - "degree = [3, 2, 2] # B-spline degree in each direction\n", - "\n", - "periodic = [True, True, True] # set periodic BC in every direction\n", - "\n", - "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic, comm=comm)\n", - "Wh = discretize(W, Omega_h, degree=degree)" - ] - }, - { - "cell_type": "markdown", - "id": "36a9632b", - "metadata": {}, - "source": [ - "## Step 2 : compute the matrix\n", - "\n", - "We assemble the mass and curl curl matrices." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "091d4560", - "metadata": {}, - "outputs": [], - "source": [ - "from sympde.topology import elements_of, element_of\n", - "from sympde.expr.expr import BilinearForm, LinearForm, integral\n", - "from sympde.calculus import dot, curl\n", - "from psydac.api.settings import PSYDAC_BACKENDS\n", - "from psydac.fem.basic import FemField\n", - "\n", - "backend_language = 'python'\n", - "backend = PSYDAC_BACKENDS[backend_language]\n", - "\n", - "u, v = elements_of(W, names='u, v') #trial and test functions\n", - "\n", - "m = BilinearForm((u, v), integral(Omega, dot(u, v)))\n", - "mh = discretize(m, Omega_h, [Wh, Wh], backend=backend)\n", - "M = mh.assemble() # Mass matrix\n", - "\n", - "k = BilinearForm((u, v), integral(Omega, dot(curl(u), curl(v))))\n", - "kh = discretize(k, Omega_h, [Wh, Wh], backend=backend)\n", - "K = kh.assemble() # Curl curl matrix\n", - "\n", - "mu = np.pi\n", - "\n", - "A = K + mu*M # system matrix, positive-definite" - ] - }, - { - "cell_type": "markdown", - "id": "8927f88c", - "metadata": {}, - "source": [ - "## Step 3 : compute the right-hand size\n", - "\n", - "We project a callable function to the vector space and use it to assemble the right-hand side of the system." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "a13044fa", - "metadata": {}, - "outputs": [], - "source": [ - "from psydac.feec.global_geometric_projectors import GlobalGeometricProjectorHcurl\n", - "f_callable = [lambda x, y, z: 10*np.exp(-0.5*(x-4)**2 - 1.5*z**2 - 1e-1*y**2),\n", - " lambda x, y, z: 0,\n", - " lambda x, y, z: np.cos(y)*np.sin(x*np.pi/5)]\n", - "\n", - "proj_Wh = GlobalGeometricProjectorHcurl(Wh, nquads=[p+1 for p in degree]) # get Hcurl projector, nquads is the number of points for the Gauss quadrature.\n", - "fh = proj_Wh(f_callable) # project callable to field in Wh\n", - "\n", - "f = element_of(W, name='f') # free variable for the FemField\n", - "\n", - "l = LinearForm(v, integral(Omega, dot(f,v)))\n", - "lh = discretize(l, Omega_h, Wh, backend=backend)\n", - "rhs = lh.assemble(f=fh) # assmble RHS, f is a free parameter" - ] - }, - { - "cell_type": "markdown", - "id": "8258971a", - "metadata": {}, - "source": [ - "## Step 4 : solve the system\n", - "Solve the system using Conjugate Gradient" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "1f0f103d", - "metadata": {}, - "outputs": [], - "source": [ - "from psydac.linalg.solvers import inverse\n", - "\n", - "inv_A = inverse(A, solver='cg', tol=1e-2, maxiter=100) # invert using Conjugate Gradient\n", - "\n", - "u = inv_A @ rhs # array of coefficients\n", - "\n", - "uh = FemField(Wh, coeffs=u) # finite element field, callable" - ] - }, - { - "cell_type": "markdown", - "id": "e0c73790", - "metadata": {}, - "source": [ - "## Step 5 : Save results to HDF5 format\n", - "We save the coefficients of the solution and the field used in the right-hand size. This step generates a YAML file containing the space information, and a HDF5 file that stores the coefficients. The fields are saved in parallel. This step does not include an evaluation of the fields on a grid." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "6c77d25a", - "metadata": {}, - "outputs": [], - "source": [ - "# Save the results using OutputManager\n", - "from psydac.api.postprocessing import OutputManager\n", - "import os\n", - "\n", - "os.makedirs('results_positive_Helmholtz', exist_ok=True)\n", - "\n", - "Om = OutputManager(\n", - " f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", - " comm=comm,\n", - " save_mpi_rank=True, \n", - " mode = 'w' \n", - ")\n", - "\n", - "Om.add_spaces(V=Wh)\n", - "Om.export_space_info()\n", - "\n", - "Om.set_static() # the fields do not depend on time\n", - "\n", - "save_fields = {\n", - " 'u': uh,\n", - " 'f': fh\n", - "}\n", - "\n", - "Om.export_fields(**save_fields) # saves the coefficients of the fields\n", - "\n", - "Om.close()\n", - "\n", - "# This generates a YAML file containing the space information, and a HDF5 file that stores the solution coefficients. \n", - "# At this point the solution has not been evaluated on any grid." - ] - }, - { - "cell_type": "markdown", - "id": "a619a838", - "metadata": {}, - "source": [ - "## Step 6 : Evaluate fields on a grid and export to VTK\n", - "Evaluate the saved fields on a grid and export the result to VTK format." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "86a1c531", - "metadata": {}, - "outputs": [], - "source": [ - "# Export the results to VTK using PostProcessManager\n", - "from psydac.api.postprocessing import PostProcessManager\n", - "\n", - "Pm = PostProcessManager(\n", - " domain=Omega,\n", - " space_file=f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " fields_file=f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", - " comm=comm\n", - ")\n", - "\n", - "Pm.export_to_vtk(\n", - " f'results_positive_Helmholtz/visu_{Omega.name}',\n", - " grid=None,\n", - " npts_per_cell=[4,2,4],\n", - " fields=save_fields.keys() # evaluate all the fields that were saved\n", - ")\n", - "\n", - "Pm.close()\n", - "# If this file is run in sequential, then this step will generate a single .vtu file that can be opened with ParaView.\n", - "# If it is run in parallel, it generates a .vtu file per process (containing the local grid) and a .pvtu file. To visualize it in ParaView, open the .pvtu file." - ] - }, - { - "cell_type": "markdown", - "id": "af41d09b", - "metadata": {}, - "source": [ - "## Visualization of the solution in ParaView\n", - "

\n", - " \n", - " \n", - " \n", - "

" - ] - }, - { - "cell_type": "markdown", - "id": "0bb786a7", - "metadata": {}, - "source": [ - "## Visualization of the source in ParaView\n", - "

\n", - " \n", - " \n", - " \n", - "

" - ] - } - ], - "metadata": {}, - "nbformat": 4, - "nbformat_minor": 5 -} diff --git a/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb index 0e9653f5f..b458a2835 100644 --- a/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb +++ b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb @@ -177,11 +177,11 @@ "from psydac.api.postprocessing import OutputManager\n", "import os\n", "\n", - "os.makedirs('results_positive_Helmholtz', exist_ok=True)\n", + "os.makedirs('results_regularized_curlcurl', exist_ok=True)\n", "\n", "Om = OutputManager(\n", - " f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " f'results_regularized_curlcurl/space_info_{Omega.name}.yml',\n", + " f'results_regularized_curlcurl/field_info_{Omega.name}.h5',\n", " comm=comm,\n", " save_mpi_rank=True, \n", " mode = 'w' \n", @@ -226,8 +226,8 @@ "\n", "Pm = PostProcessManager(\n", " domain=Omega,\n", - " space_file=f'results_positive_Helmholtz/space_info_{Omega.name}.yml',\n", - " fields_file=f'results_positive_Helmholtz/field_info_{Omega.name}.h5',\n", + " space_file=f'results_regularized_curlcurl/space_info_{Omega.name}.yml',\n", + " fields_file=f'results_regularized_curlcurl/field_info_{Omega.name}.h5',\n", " comm=comm\n", ")\n", "\n", From cfa5c195d37d81504bab02406d210f69df6c0d05 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Sat, 13 Dec 2025 11:08:59 +0100 Subject: [PATCH 54/63] Use docs/requirements.txt for pip caching --- .github/workflows/documentation.yml | 3 +-- 1 file changed, 1 insertion(+), 2 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index 98e669c69..fb29afe1a 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -38,8 +38,7 @@ jobs: cache: 'pip' cache-dependency-path: | pyproject.toml - requirements.txt - requirements_extra.txt + docs/requirements.txt - name: Install non-Python dependencies on Ubuntu uses: awalsh128/cache-apt-pkgs-action@latest From c41fce0d07fb25fac529665ef1bd13e2fb156352 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 16 Dec 2025 15:44:52 +0100 Subject: [PATCH 55/63] update curlcurl title and remove static plot, but plot it for docs --- .../notebooks/feec_curlcurl_eigenvalue.ipynb | 2 +- .../regularized_curlcurl_eigenvalues_PETSc.png | Bin 18778 -> 0 bytes ...petsc_eigenvalues_regularized_curlcurl.ipynb | 6 ++---- 3 files changed, 3 insertions(+), 5 deletions(-) delete mode 100644 examples/notebooks/paraview_images/regularized_curlcurl_eigenvalues_PETSc.png diff --git a/examples/notebooks/feec_curlcurl_eigenvalue.ipynb b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb index 48091254c..d77f7ef9e 100644 --- a/examples/notebooks/feec_curlcurl_eigenvalue.ipynb +++ b/examples/notebooks/feec_curlcurl_eigenvalue.ipynb @@ -5,7 +5,7 @@ "id": "6be9f483", "metadata": {}, "source": [ - "# Example of solving the $\\mathbf{curl}-\\mathrm{curl}$ eigenvalue problem\n", + "# Example of solving the curl-curl eigenvalue problem\n", "\n", "In this notebook we show how to compute approximate eigenvalues for the curl-curl eigenvalue problem using the FEEC (Finite Element Exterior Calculus) API of PSYDAC. The problem reads as follows:\n", "\n", diff --git a/examples/notebooks/paraview_images/regularized_curlcurl_eigenvalues_PETSc.png b/examples/notebooks/paraview_images/regularized_curlcurl_eigenvalues_PETSc.png deleted file mode 100644 index 62c2b46fe90ba2dc318927d42ef4472a749241a1..0000000000000000000000000000000000000000 GIT binary patch literal 0 HcmV?d00001 literal 18778 zcmd74c{r8(+cthHl~QR^QqhhE6e&?MHIXuADq|&Op69tyDJc;`lzCRBP$)$iGLxBv zkfF@;dw#U{cX+=0Iga-^-rw(d-#>PHS?gZ+@EOkQyw2;q)*U$+i51J3mr)e8Lh|JC zGZeMJm7-``=@#Ri1Lck1@IOJz6K5?IOfFm6Trk(6q%T;S8k$%d>RsGwtz&MXXJWjc zn|Cia@9wR-mX@X#f;>D%|2Tr%#QX}6g~@CO&a%|>CDc}b-BK?b(L3SlH#j6vwBGE*(H`V#l4}8GWrHj>hAnFUw@$~{&w0$ zwb~Tv5BjG?buO#wiK^ulr^K0-R4IoQFHiP5W=C0_Q0ttWY4iQGS}ynMRXfrC^oBiHCS)6UU~UH2Aget;QYgX3MQzg#U*aucm15=PinkqR#Wuis8Mxe^3i3>g;lw zRTPzbktDGosGVFl{6*VyBJ-Z=3x_e|Iz#?FXOnVk z!^ev=t$Hsd*QFRY32OO%RT5~jeDqm(tWh;%pvTd;aB_BLz$MW~l{xd)_=H;0`KyNf z0oDV}eZ6PSAE6Zs^m!?I-baJq@Jnm&nl>GauFvr{M+A26l<*WD_0yVukf5INQhDx~ 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\n", + "The estimated eigenvalues are shown above.\n", "We can see that the eigenavalues corresponding to the kernel of the curlcurl operator are shifted thanks to the regularization.\n", "\n", "\n", From 2416ce6e63c6cd5ed70026ff9e1729a5b1d82a36 Mon Sep 17 00:00:00 2001 From: jowezarek Date: Tue, 23 Dec 2025 18:41:04 +0100 Subject: [PATCH 56/63] add vector_potential notebook, delete old example --- .../feec_vector_potential_torus.ipynb | 534 ++++++++++++++++++ .../paraview_images/vector_potential_A.png | Bin 0 -> 465916 bytes .../paraview_images/vector_potential_A_0.png | Bin 0 -> 224741 bytes .../paraview_images/vector_potential_A_H.png | Bin 0 -> 456923 bytes .../vector_potential_A_H_b.png | Bin 0 -> 45685 bytes .../vector_potential_A_H_b_lines.png | Bin 0 -> 43000 bytes .../paraview_images/vector_potential_B.png | Bin 0 -> 546115 bytes .../paraview_images/vector_potential_B_0.png | Bin 0 -> 27496 bytes .../paraview_images/vector_potential_B_H.png | Bin 0 -> 68349 bytes .../vector_potential_curlA.png | Bin 0 -> 546191 bytes examples/vector_potential_3d.py | 287 ---------- 11 files changed, 534 insertions(+), 287 deletions(-) create mode 100644 examples/notebooks/feec_vector_potential_torus.ipynb create mode 100644 examples/notebooks/paraview_images/vector_potential_A.png create mode 100644 examples/notebooks/paraview_images/vector_potential_A_0.png create mode 100644 examples/notebooks/paraview_images/vector_potential_A_H.png create mode 100644 examples/notebooks/paraview_images/vector_potential_A_H_b.png create mode 100644 examples/notebooks/paraview_images/vector_potential_A_H_b_lines.png create mode 100644 examples/notebooks/paraview_images/vector_potential_B.png create mode 100644 examples/notebooks/paraview_images/vector_potential_B_0.png create mode 100644 examples/notebooks/paraview_images/vector_potential_B_H.png create mode 100644 examples/notebooks/paraview_images/vector_potential_curlA.png delete mode 100644 examples/vector_potential_3d.py diff --git a/examples/notebooks/feec_vector_potential_torus.ipynb b/examples/notebooks/feec_vector_potential_torus.ipynb new file mode 100644 index 000000000..9cf5e26a2 --- /dev/null +++ b/examples/notebooks/feec_vector_potential_torus.ipynb @@ -0,0 +1,534 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "0c5b846b", + "metadata": {}, + "source": [ + "# Computing the vector potential of a solenoidal field on a Torus\n", + "A torus is a 3D domain with zero cavities and one tunnel. \n", + "\n", + "As such, on a Torus, there exists only the trivial normal harmonic field, but a one-dimensional space of tangential harmonic fields.\n", + "\n", + "Hence, any solenoidal field $B\\in H_0(div0)$ on a torus can be decomposed (Helmholtz decomposition) as\n", + "\n", + "$B = curl(A_0) + \\lambda B_H$\n", + "\n", + "where $B_H$ is a tangential harmonic field, and $A_0\\in H_0(curl)$ is the vector potential of the \"harmonic-free\" solenoidal field $B - \\lambda B_H$.\n", + "\n", + "In this notebook, we compute a vector potential of the solenoidal magnetic field\n", + "\n", + "$B(x, y, z) = \\left(\\begin{matrix} \n", + "(1/(x^2 + y^2)) \\cdot ( (-C_0 y) + x(2z-1)(\\sqrt{x^2 + y^2}-r)(\\sqrt{x^2 + y^2}-R) ) \\\\ \n", + "(1/(x^2 + y^2)) \\cdot ( ( C_0 x) + y(2z-1)(\\sqrt{x^2 + y^2}-r)(\\sqrt{x^2 + y^2}-R) ) \\\\ \n", + "(1/(x^2 + y^2)) \\cdot ( \\sqrt{x^2 + y^2}((r+R)-2\\sqrt{x^2 + y^2})z(z-1) ) \n", + "\\end{matrix}\\right),\\quad\\quad C_0=-10,\\ r=0.5,\\ R=1.$\n", + "\n", + "where $r$ is the inner and $R$ is the outer radius. We use this magnetic field as initial guess for a relaxation method for the computation of an MHD equilibrium.\n", + "\n", + "We compute $A_0$ and a vector potential of the tangential harmonic field $B_H$ separately." + ] + }, + { + "cell_type": "markdown", + "id": "6c5d3a3e", + "metadata": {}, + "source": [ + "## Step 1 : Computation of the \"harmonic-free\" vector potential $A_0$\n", + "S.th. $curl(A_0) = B - \\lambda B_H$.\n", + "\n", + "A (weak-divergence-free) vector potential $A_0\\in H_0(curl)$ of the \"harmonic-free\" part of $B$ can be computed as the solution of the Hodge-Laplace problem\n", + "\n", + "$\\left( \\widetilde{curl}_h\\ curl\\ - grad\\ \\widetilde{div}_h \\right) A_0 = \\widetilde{curl}_h\\ B.$\n", + "\n", + "### Define and discretize the domain and the de Rham sequence" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "9a7d4d77", + "metadata": {}, + "outputs": [], + "source": [ + "from mpi4py import MPI\n", + "import numpy as np\n", + "\n", + "from sympde.topology import Cube, Mapping, Derham\n", + "\n", + "from psydac.api.discretization import discretize\n", + "\n", + "comm = MPI.COMM_WORLD # MPI communicator\n", + "ncells = [16, 16, 16] # number of cells in each direction\n", + "degree = [3, 3, 3] # B-spline degree in each direction\n", + "periodic = [False, True, False] # periodicity of the domain\n", + "\n", + "r = 0.5 # inner radius of the torus\n", + "R = 1. # outer radius of the torus\n", + "\n", + "logical_domain = Cube('C', bounds1=(0.5,1), bounds2=(0,2*np.pi), bounds3=(0,1)) # 3D cubic domain - to be mapped to a toroidal domain (with square cross section)\n", + "\n", + "class SquareTorus(Mapping):\n", + "\n", + " _expressions = {'x': 'x1 * cos(x2)',\n", + " 'y': 'x1 * sin(x2)',\n", + " 'z': 'x3'}\n", + " \n", + " _ldim = 3\n", + " _pdim = 3\n", + "\n", + "mapping = SquareTorus('ST')\n", + "\n", + "domain = mapping(logical_domain) # the mapped domain\n", + "derham = Derham(domain)\n", + "domain_h = discretize(domain, ncells=ncells, periodic=periodic, comm=comm)\n", + "derham_h = discretize(derham, domain_h, degree=degree)\n", + "\n", + "V0, V1, V2, V3 = derham.spaces\n", + "V0h, V1h, V2h, V3h = derham_h.spaces\n", + "V0cs, V1cs, V2cs, V3cs = [Vh.coeff_space for Vh in derham_h.spaces]" + ] + }, + { + "cell_type": "markdown", + "id": "d3cd1ca2", + "metadata": {}, + "source": [ + "### Assembly of the system matrix\n", + "\n", + "corresponding to the bilinear form, and additionally taking care of homogeneous boundary conditions,\n", + "\n", + "$V^1_h\\times V^1_h \\ni (u, v) \\mapsto \\int curl(u)\\cdot curl(v) + \\widetilde{div}_h(u) \\widetilde{div}_h(v)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "ef34b831", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.calculus import inner\n", + "from sympde.expr import integral, BilinearForm\n", + "from sympde.topology import elements_of\n", + "\n", + "from psydac.api.settings import PSYDAC_BACKEND_GPYCCEL\n", + "from psydac.linalg.basic import IdentityOperator\n", + "from psydac.linalg.solvers import inverse\n", + "\n", + "backend = PSYDAC_BACKEND_GPYCCEL\n", + "\n", + "G, C, D = derham_h.derivatives(kind='linop') # gradient, curl and divergence as psydac.linalg.basic.LinearOperator objects\n", + "\n", + "# symbolic functions of the symbolic function spaces - to be used as trial and test functions\n", + "u0, v0 = elements_of(V0, names='u0, v0')\n", + "u1, v1 = elements_of(V1, names='u1, v1')\n", + "u2, v2 = elements_of(V2, names='u2, v2')\n", + "u3, v3 = elements_of(V3, names='u3, v3')\n", + "\n", + "# Bilinear Forms corresponding to mass matrices of all four function spaces\n", + "m0 = BilinearForm((u0, v0), integral(domain, u0*v0))\n", + "m1 = BilinearForm((u1, v1), integral(domain, inner(u1, v1)))\n", + "m2 = BilinearForm((u2, v2), integral(domain, inner(u2, v2)))\n", + "m3 = BilinearForm((u3, v3), integral(domain, u3*v3))\n", + "\n", + "# Discretization of the mass-matrix bilinear forms\n", + "m0h = discretize(m0, domain_h, (V0h, V0h), backend=backend)\n", + "m1h = discretize(m1, domain_h, (V1h, V1h), backend=backend)\n", + "m2h = discretize(m2, domain_h, (V2h, V2h), backend=backend)\n", + "m3h = discretize(m3, domain_h, (V3h, V3h), backend=backend)\n", + "\n", + "# Assembly of the mass matrices\n", + "M0 = m0h.assemble()\n", + "M1 = m1h.assemble()\n", + "M2 = m2h.assemble()\n", + "M3 = m3h.assemble()\n", + "\n", + "# Dirichlet projectors in order to apply the projection method\n", + "DP0, DP1, _, _ = derham_h.dirichlet_projectors(kind='linop')\n", + "I0 = IdentityOperator(V0cs)\n", + "\n", + "# Modified mass matrix for the proper computation of the weak divergence\n", + "M0_0 = DP0 @ M0 @ DP0 + (I0 - DP0)\n", + "\n", + "# Conjugate Gradient inverse of M0_0, preconditioned using an LST (Loli, Sangalli, Tani) preconditioner\n", + "M0_0_pc, = derham_h.LST_preconditioners(M0=M0, hom_bc=True)\n", + "M0_0_inv = inverse(M0_0, 'CG', pc=M0_0_pc, maxiter=1000, tol=1e-15)\n", + "\n", + "# System matrix\n", + "S = C.T @ M2 @ C + M1 @ G @ M0_0_inv @ DP0 @ G.T @ M1" + ] + }, + { + "cell_type": "markdown", + "id": "1dec8028", + "metadata": {}, + "source": [ + "### Assembly of the right-hand-side\n", + "\n", + "corresponding to the linear form\n", + "\n", + "$V^1_h \\ni v \\mapsto \\int v\\cdot\\widetilde{curl}_h B$.\n", + "\n", + "We also check whether\n", + "\n", + "$div(B) = 0\\text{ in }\\Omega\\quad\\quad\\text{ and }\\quad\\quad n\\cdot B=0\\text{ on }\\partial\\Omega$\n", + "\n", + "hold." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7cf36d2f", + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.topology import Union, NormalVector\n", + "\n", + "# Define callable function corresponding to B\n", + "def get_B(r, R, C0=-10):\n", + " rad = lambda x, y : np.sqrt(x**2 + y**2)\n", + "\n", + " B1 = lambda x, y, z : (1/rad(x, y)**2) * ( (-C0 * y) + x * (2*z-1) * (rad(x, y)-r) * (rad(x, y)-R) )\n", + " B2 = lambda x, y, z : (1/rad(x, y)**2) * ( ( C0 * x) + y * (2*z-1) * (rad(x, y)-r) * (rad(x, y)-R) )\n", + " B3 = lambda x, y, z : (1/rad(x, y)**2) * ( rad(x, y) * ((r+R)-2*rad(x, y)) * z * (z-1) )\n", + "\n", + " B = (B1, B2, B3)\n", + " return B\n", + "\n", + "# Project B into V2h\n", + "_, _, P2, _ = derham_h.projectors()\n", + "r, R = domain.logical_domain.bounds1\n", + "\n", + "B = P2(get_B(r, R))\n", + "b = B.coeffs\n", + "\n", + "# Check whether B is indead divergence free\n", + "div_b = D @ b\n", + "div_b_norm = np.sqrt( M3.dot_inner(div_b, div_b) )\n", + "print(f'|| div(B) ||_L2(domain) = {div_b_norm:.3g}')\n", + "\n", + "# Check whether B is indead tangential to the boundary\n", + "def get_boundaries(*args):\n", + "\n", + " if not args:\n", + " return ()\n", + " else:\n", + " assert all(1 <= a <= 6 for a in args)\n", + " assert len(set(args)) == len(args)\n", + "\n", + " boundaries = {1: {'axis': 0, 'ext': -1},\n", + " 2: {'axis': 0, 'ext': 1},\n", + " 3: {'axis': 1, 'ext': -1},\n", + " 4: {'axis': 1, 'ext': 1},\n", + " 5: {'axis': 2, 'ext': -1},\n", + " 6: {'axis': 2, 'ext': 1}}\n", + "\n", + " return tuple(boundaries[i] for i in args)\n", + "\n", + "dir_zero_boundary = get_boundaries(1, 2, 5, 6) # we exclude the \"periodic boundary\" in y-direction as it is not technically a boundary anymore\n", + "boundary = Union(*[domain.get_boundary(**kw) for kw in dir_zero_boundary])\n", + "\n", + "# Assembly of \"tangential trace mass matrix\"\n", + "nn = NormalVector('nn')\n", + "m2_bd = BilinearForm((u2, v2), integral(boundary, inner(nn, u2) * inner(nn, v2)))\n", + "m2_bd_h = discretize(m2_bd, domain_h, (V2h, V2h), backend=backend, sum_factorization=False)\n", + "M2_bd = m2_bd_h.assemble()\n", + "\n", + "dirichlet_boundary_norm = np.sqrt( M2_bd.dot_inner(b, b) )\n", + "print(f'|| n \\\\cdot B ||_L2(boundary) = {dirichlet_boundary_norm:.3g}')\n", + "\n", + "# Assembly of the right-hand-side\n", + "rhs = C.T @ M2 @ b" + ] + }, + { + "cell_type": "markdown", + "id": "890ee988", + "metadata": {}, + "source": [ + "### Employ the projection method and solve for $A_0$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7b3b6552", + "metadata": {}, + "outputs": [], + "source": [ + "I1 = IdentityOperator(V1cs)\n", + "\n", + "# Modify system matrix and right-hand-side in order to take care of boundary conditions\n", + "S_0 = DP1 @ S @ DP1 + (I1 - DP1)\n", + "rhs_0 = DP1 @ rhs\n", + "\n", + "# Solve for A_0\n", + "maxiter = 1000\n", + "tol = 1e-10\n", + "\n", + "S_0_inv = inverse(S_0, 'cg', maxiter=maxiter, tol=tol)\n", + "\n", + "a_0 = S_0_inv @ rhs_0" + ] + }, + { + "cell_type": "markdown", + "id": "48eb3ff5", + "metadata": {}, + "source": [ + "## Step 2 : Computation of the vector potential $A_H$ of $B_H$\n", + "S.th. $curl(A_H) = B_H$ and $\\|curl(A_H)\\| = 1$.\n", + "\n", + "The theoretical background for the computation of vector potentials of tangential harmonic fields has been recently published\n", + "by Martin Campos Pinto and Julian Owezarek (https://arxiv.org/abs/2508.16822).\n", + "\n", + "The potential is decomposed into $A_H = A_H^b + A_H^0$. We call $A_H^b\\in H(curl)$ the lifting potential and $A_H^0\\in H_0(curl)$ the correction potential.\n", + "\n", + "### Construct a suitable choice of $A^b_H$ for the torus" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "83d2264e", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.fem.basic import FemField\n", + "from psydac.linalg.utilities import array_to_psydac\n", + "\n", + "def get_lifting_field():\n", + " dim = V1cs.dimension\n", + " array = np.zeros(dim)\n", + "\n", + " nx, ny, nz = ncells\n", + " px, py, pz = degree\n", + "\n", + " i3 = int(np.floor((nz+pz-1)/2))\n", + " Nz = nz + pz\n", + "\n", + " start = (nx+px-1)*ny*(nz+pz) + (nx+px)*ny*(nz+pz)\n", + "\n", + " for i2 in range(ny):\n", + " index = i2*(Nz-1) + i3\n", + " array[start + index] = 1\n", + " \n", + " coeffs = array_to_psydac(array, V1cs)\n", + " return coeffs\n", + "\n", + "a_H_b = get_lifting_field()" + ] + }, + { + "cell_type": "markdown", + "id": "45008c1a", + "metadata": {}, + "source": [ + "### Visualization of the lifting field\n", + "\n", + "

\n", + " \n", + " \n", + "

" + ] + }, + { + "cell_type": "markdown", + "id": "60cf5046", + "metadata": {}, + "source": [ + "### Compute the correction potential $A^0_H$\n", + "\n", + "It's yet again a solution to the previously introduced Hodge-Laplace problem, but now with a different right-hand-side\n", + "\n", + "$\\left( \\widetilde{curl}_h\\ curl\\ - grad\\ \\widetilde{div}_h \\right) A^0_H = - \\widetilde{curl}_h\\ curl A^b_H.$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7a862b0d", + "metadata": {}, + "outputs": [], + "source": [ + "rhs_aH0 = - C.T @ M2 @ C @ a_H_b\n", + "rhs_aH0_0 = DP1 @ rhs_aH0\n", + "\n", + "a_H_0 = S_0_inv @ rhs_aH0_0" + ] + }, + { + "cell_type": "markdown", + "id": "d5fc3b98", + "metadata": {}, + "source": [ + "### Assemble the (normalized) harmonic potential $A_H$ and compute $\\lambda$\n", + "\n", + "s.th. $B_H = curl(\\lambda\\ A_H)$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "eefee648", + "metadata": {}, + "outputs": [], + "source": [ + "a_H = a_H_0 + a_H_b\n", + "a_H /= np.sqrt( M2.dot_inner(C @ a_H, C @ a_H) )\n", + "\n", + "b_H = C @ a_H\n", + "lam = M2.dot_inner(b, b_H)" + ] + }, + { + "cell_type": "markdown", + "id": "3030f8ef", + "metadata": {}, + "source": [ + "## Step 3 : Assemble the entire vector potential and verify the solution\n", + "\n", + "$A = A_0 + \\lambda A_H$\n", + "\n", + "$\\epsilon := \\| curl(A) - B \\|_{L^2}$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d27f99d5", + "metadata": {}, + "outputs": [], + "source": [ + "a = a_0 + lam * a_H\n", + "\n", + "diff = C @ a - b\n", + "err_l2 = np.sqrt( M2.dot_inner(diff, diff) )\n", + "print(f'|| curl(A) - B ||_L2 = {err_l2:.3g}')" + ] + }, + { + "cell_type": "markdown", + "id": "701a6557", + "metadata": {}, + "source": [ + "## Step 4 : Save results" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "8e573154", + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.postprocessing import OutputManager\n", + "from psydac.api.postprocessing import PostProcessManager\n", + "import os\n", + "\n", + "# B = curl(A_0) + curl(lam * A_H) =: B_0 + B_H = curl(A_0 + lam * A_H) =: curl(A)\n", + "B_H = FemField(V2h, C @ (lam * a_H))\n", + "B_0 = FemField(V2h, b - C @ (lam * a_H))\n", + "curlA = FemField(V2h, C @ a)\n", + "\n", + "# A = A_0 + lam * A_H, here as above we write A_H and mean lam * A_H\n", + "A = FemField(V1h, a)\n", + "A_H = FemField(V1h, lam * a_H)\n", + "A_0 = FemField(V1h, a_0)\n", + "\n", + "# lifting field A_H_b\n", + "A_H_b = FemField(V1h, a_H_b)\n", + "\n", + "# Save the results using OutputManager\n", + "# Export the results to VTK using PostProcessManager\n", + "\n", + "os.makedirs('results_vector_potential', exist_ok=True)\n", + "\n", + "Om = OutputManager(\n", + " 'results_vector_potential/space_info.yml',\n", + " 'results_vector_potential/field_info.h5',\n", + " comm=comm,\n", + " save_mpi_rank=True, \n", + " mode = 'w' \n", + ")\n", + "\n", + "Om.add_spaces(V1=V1h)\n", + "Om.add_spaces(V2=V2h)\n", + "Om.export_space_info()\n", + "\n", + "Om.set_static() # the fields do not depend on time\n", + "\n", + "save_fields = {\n", + " 'B' : B,\n", + " 'B_H' : B_H,\n", + " 'B_0' : B_0,\n", + " 'curlA' : curlA,\n", + " 'A' : A,\n", + " 'A_H' : A_H,\n", + " 'A_0' : A_0,\n", + " 'A_H_b' : A_H_b\n", + "}\n", + "\n", + "Om.export_fields(**save_fields) # saves the coefficients of the fields\n", + "\n", + "Om.close()\n", + "\n", + "# This generates a YAML file containing the space information, and a HDF5 file that stores coefficients. \n", + "# At this point the solution has not been evaluated on any grid.\n", + "\n", + "Pm = PostProcessManager(\n", + " domain=domain,\n", + " space_file=f'results_vector_potential/space_info.yml',\n", + " fields_file=f'results_vector_potential/field_info.h5',\n", + " comm=comm\n", + ")\n", + "\n", + "Pm.export_to_vtk(\n", + " f'results_vector_potential/visu',\n", + " grid=None,\n", + " npts_per_cell=[6,6,6],\n", + " fields=save_fields.keys() # evaluate all the fields that were saved\n", + ")\n", + "\n", + "Pm.close()\n", + "# If this file is run in sequential, then this step will generate a single .vtu file that can be opened with ParaView.\n", + "# If it is run in parallel, it generates a .vtu file per process (containing the local grid) and a .pvtu file. To visualize it in ParaView, open the .pvtu file." + ] + }, + { + "cell_type": "markdown", + "id": "83437c67", + "metadata": {}, + "source": [ + "## Visualization in ParaView\n", + "\n", + "### Compare $B$ and $curl(A)$\n", + "\n", + "

\n", + " \n", + " \n", + "

\n", + "\n", + "### Inverstigate decomposition of $B$ into $B_0$, the harmonic-free part, and $B_H$, the harmonic part\n", + "\n", + "

\n", + " \n", + " \n", + "

\n", + "\n", + "### Invetsigate decomposition of $A$ into $A_0$, the potential of $B_0$, and $A_H$, the potential of $B_H$\n", + "\n", + "

\n", + " \n", + " \n", + " \n", + "

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z!PI#dmE5sH`)H(}h8o|k31K;JyEdh#r!Orn#m2_!LM$6+WYm6nyuFe+-(NsX+g0A4 zz$BFY?b7?dTRniy{9~ntSm&_Kn|q{%vtplM02dc4aXRJte163C1_o3^$6$U3Dk>@m z2M1hdK1V{Du1kSEq#`5%OE7)~hO2I0Zjlp}r@@hxb zU+?b%3Lbvo36@wf0w?{U+`TddO`7iYtnss(Rb~mWnk;r$Cz!SWb_v)2^Mt=X(olcD zH<(`FwZ8uMrGpPB=&e^{mERc_uErZdZ$xZq@g!wT$ wD = - (M0)^-1 G^T M1. - - Thus, not taking into account boundary conditions, the full system of equations reads - - v^T C^T M2 C A + v^T M1 G (M0)^-1 M0 (M0)^-1 G^T M1 A = v^T C^T M2 B for all v in V1h - - <=> ( C^T M2 C + M1 G (M0)^-1 G^T M1 ) A = C^T M2 B. - - Note: (M0)^-1 here is the inverse "mass matrix of functions satisfying hom. DBCs", - not the inverse of the entire M0 "mass matrix of all functions". - - This example highlights the importance of choosing the correct inverse, - choosing the correct preconditioner for this correct inverse, - and applying the projection method using `DirichletProjector`s to solve this discrete problem. - """ - - assert b.space is derham_h.spaces[2].coeff_space - - # ----- Obtain standard objects: domain, domain_h, derham, function spaces, mass matrices, derivative operators, ... - - domain_h = derham_h.domain_h - domain = domain_h.domain - derham = Derham(domain) - - V0, V1, V2, V3 = derham.spaces - V0h, V1h, V2h, V3h = derham_h.spaces - V0cs, V1cs, V2cs, V3cs = [Vh.coeff_space for Vh in derham_h.spaces] - - u0, v0 = elements_of(V0, names='u0, v0') - u1, v1 = elements_of(V1, names='u1, v1') - u2, v2 = elements_of(V2, names='u2, v2') - u3, v3 = elements_of(V3, names='u3, v3') - - G, C, D = derham_h.derivatives(kind='linop') - - a0 = BilinearForm((u0, v0), integral(domain, u0*v0)) - a1 = BilinearForm((u1, v1), integral(domain, inner(u1, v1))) - a2 = BilinearForm((u2, v2), integral(domain, inner(u2, v2))) - a3 = BilinearForm((u3, v3), integral(domain, u3*v3)) - - t0 = time.time() - a0h = discretize(a0, domain_h, (V0h, V0h), backend=backend) - a1h = discretize(a1, domain_h, (V1h, V1h), backend=backend) - a2h = discretize(a2, domain_h, (V2h, V2h), backend=backend) - a3h = discretize(a3, domain_h, (V3h, V3h), backend=backend) - t1 = time.time() - print() - print(f'Mass matrix bilinear forms discretized in {t1-t0:.3g}') - - t0 = time.time() - M0 = a0h.assemble() - M1 = a1h.assemble() - M2 = a2h.assemble() - M3 = a3h.assemble() - t1 = time.time() - print(f'Mass matrices assembled in {t1-t0:.3g}') - - # ----- Sanity check: b should be divergence-free. The method will convergence even if it is not, - # but b = curl(a) won't hold. - divB = D @ b - l2norm_divB = np.sqrt(M3.dot_inner(divB, divB)) - assert l2norm_divB < 1e-10, 'The coefficient vector passed to this function should belong to a divergence-free function.' - - # ----- We need to obtain an inverse M0 object in order to assemble the system matrix - DP0, DP1, _, _ = derham_h.dirichlet_projectors(kind='linop') # <- Dirichlet boundary projectors for the projection method - I0 = IdentityOperator(V0cs) - - # Option1: Modified mass matrix of functions satisfying hom. DBCs - M0_0 = DP0 @ M0 @ DP0 + (I0 - DP0) - t0 = time.time() - M0_0_pc, = derham_h.LST_preconditioners(M0=M0, hom_bc=True) - t1 = time.time() - M0_0_inv = inverse(M0_0, 'pcg', pc=M0_0_pc, maxiter=1000, tol=1e-15) - - # Option2: Inverse of entire mass matrix - t2 = time.time() - M0_pc, = derham_h.LST_preconditioners(M0=M0, hom_bc=False) - t3 = time.time() - M0_inv = inverse(M0, 'pcg', pc=M0_pc, maxiter=1000, tol=1e-15) - - print(f'M0 and M0_0 preconditioner obtained in {((t3-t2)+(t1-t0)):.3g}') - print() - - # ----- There are now (at least) three ways to assemble the system matrix - - # Option1: The correct option. Using M0_0_inv and a projection operator immediately before M0_0_inv - S1 = C.T @ M2 @ C + M1 @ G @ M0_0_inv @ DP0 @ G.T @ M1 - # Note that not including the projector here, i.e., using the following stiffness matrix - #S1 = C.T @ M2 @ C + M1 @ G @ M0_0_inv @ G.T @ M1 - # results in a wrong solution (and is super slow) - - # Option2: The entirely wrong option. Using M0_inv and no additional projector - S2 = C.T @ M2 @ C + M1 @ G @ M0_inv @ G.T @ M1 - - # Option3: The better of the wrong options. Using M0_inv, but an additional projector - S3 = C.T @ M2 @ C + M1 @ G @ M0_inv @ DP0 @ G.T @ M1 - - # ----- We assemble the rhs vector - rhs = C.T @ M2 @ b - - # ----- We can now solve the three resulting systems - I1 = IdentityOperator(V1cs) - - maxiter = 5000 - tol = 1e-10 - - vector_potential_list = [] - timings_list = [] - info_list = [] - - for S in [S1, S2, S3]: - # Apply the projection method - S_bc = DP1 @ S @ DP1 + (I1 - DP1) - rhs_bc = DP1 @ rhs - - # Obtain a solver for the system matrix - S_bc_inv = inverse(S_bc, 'cg', maxiter=maxiter, tol=tol) - - # Solve the system - t0 = time.time() - a = S_bc_inv @ rhs_bc - t1 = time.time() - info = S_bc_inv.get_info() - - vector_potential_list.append(a) - timings_list.append(t1-t0) - info_list.append(info) - - # ----- Analyse the results - - # Option1 is the fastest, and accurate. - a1 = vector_potential_list[0] - info1 = info_list[0] - diff = b - C @ a1 - l2norm_diff = np.sqrt(M2.dot_inner(diff, diff)) - print(f' ----- Option1: C.T @ M2 @ C + M1 @ G @ M0_0_inv @ DP0 @ G.T @ M1 -----') - print() - print(f' || B - curl(A) || = {l2norm_diff:.3g}') - print(f' Time : {timings_list[0]:.3g}') - print(f' Niter : {info1["niter"]}') - print(f' Convergence : {info1["success"]}') - print(f' Res. Norm : {info1["res_norm"]:.3g}') - print() - - # Option2 is not much slower, but delivers an entirely wrong solution - a2 = vector_potential_list[1] - info2 = info_list[1] - diff = b - C @ a2 - l2norm_diff = np.sqrt(M2.dot_inner(diff, diff)) - print(f' ----- Option2: C.T @ M2 @ C + M1 @ G @ M0_inv @ G.T @ M1 -----') - print() - print(f' || B - curl(A) || = {l2norm_diff:.3g}') - print(f' Time : {timings_list[1]:.3g}') - print(f' Niter : {info2["niter"]}') - print(f' Convergence : {info2["success"]}') - print(f' Res. Norm : {info2["res_norm"]:.3g}') - print() - - # Option3 is takes forever to converge, but delivers an accurate solution - a3 = vector_potential_list[2] - info3 = info_list[2] - diff = b - C @ a3 - l2norm_diff = np.sqrt(M2.dot_inner(diff, diff)) - print(f' ----- Option3: C.T @ M2 @ C + M1 @ G @ M0_inv @ DP0 @ G.T @ M1 -----') - print() - print(f' || B - curl(A) || = {l2norm_diff:.3g}') - print(f' Time : {timings_list[2]:.3g}') - print(f' Niter : {info3["niter"]}') - print(f' Convergence : {info3["success"]}') - print(f' Res. Norm : {info3["res_norm"]:.3g}') - print() - print(f'Note that increasing the problem size, or decreasing the tolerance, renders Option3 unafforadable.') - - return a1 - -#============================================================================== -if __name__ == '__main__': - - ncells = [16, 16, 16] - degree = [3, 3, 3] - periodic = [False, False, False] - - comm = None - backend = PSYDAC_BACKEND_GPYCCEL - - logical_domain = Cube('C', bounds1=(0,1), bounds2=(0,1), bounds3=(0,1)) - - class CollelaMap3D(Mapping): - _expressions = {'x': 'x1 + (a/2)*sin(2.*pi*(x1-0.5))*sin(2.*pi*(x2-0.5))', - 'y': 'x2 + (a/2)*sin(2.*pi*(x1-0.5))*sin(2.*pi*(x2-0.5))', - 'z': 'x3'} - - _ldim = 3 - _pdim = 3 - - mapping = CollelaMap3D('C', a=0.1) - - domain = mapping(logical_domain) - derham = Derham(domain) - - domain_h = discretize(domain, ncells=ncells, periodic=periodic, comm=comm) - derham_h = discretize(derham, domain_h, degree=degree) - - G, C, D = derham_h.derivatives(kind='linop') - P0, P1, P2, P3 = derham_h.projectors() - - from sympde.utilities.utils import plot_domain - #plot_domain(domain, draw=True, isolines=True) - - A1 = lambda x, y, z: np.sin(2*np.pi*y) * np.sin(2*np.pi*z) - A2 = lambda x, y, z: np.sin(2*np.pi*z) * np.sin(2*np.pi*x) - A3 = lambda x, y, z: np.sin(2*np.pi*x) * np.sin(2*np.pi*y) - A = (A1, A2, A3) - - a_ex = P1(A).coeffs - # a should already satisfy hom. DBCs (n \times a = 0 on the boundary) - # But we can make sure that this holds exactly by projecting it - _, DP1, _, _ = derham_h.dirichlet_projectors(kind='linop') - a_ex = DP1 @ a_ex - - # Now b belongs to H_0(div0) as required - b = C @ a_ex - - a = compute_vector_potential_3d(b, derham_h) From 849dd0dbf802fb9beccdc87538bd5eed66d3d29b Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 23 Dec 2025 20:13:56 +0100 Subject: [PATCH 57/63] move cp from CI to makefile --- .github/workflows/documentation.yml | 5 ----- docs/Makefile | 4 ++++ 2 files changed, 4 insertions(+), 5 deletions(-) diff --git a/.github/workflows/documentation.yml b/.github/workflows/documentation.yml index fb29afe1a..8a0190504 100644 --- a/.github/workflows/documentation.yml +++ b/.github/workflows/documentation.yml @@ -138,11 +138,6 @@ jobs: run: | python -m pip install -r docs/requirements.txt - - name: Copy Notebooks - run: | - mkdir docs/source/examples - cp -r examples/notebooks/* docs/source/examples/ - - name: Make the sphinx doc run: | rm -rf docs/source/modules/STUBDIR diff --git a/docs/Makefile b/docs/Makefile index cabd2762a..f58006da2 100644 --- a/docs/Makefile +++ b/docs/Makefile @@ -17,4 +17,8 @@ help: # Catch-all target: route all unknown targets to Sphinx using the new # "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS). %: Makefile + @mkdir -p source/examples + @cp -r ../examples/notebooks/* source/examples/ + @cp *.md source/ + @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O) From 1334c301131ab39349838611539da9934838ca4d Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 23 Dec 2025 21:57:35 +0100 Subject: [PATCH 58/63] change backend to pyccel --- examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb b/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb index 3f02365bb..119a01872 100644 --- a/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb +++ b/examples/notebooks/petsc_eigenvalues_regularized_curlcurl.ipynb @@ -80,7 +80,7 @@ "from psydac.api.settings import PSYDAC_BACKENDS\n", "from psydac.fem.basic import FemField\n", "\n", - "backend_language = 'python'\n", + "backend_language = 'pyccel-gcc'\n", "backend = PSYDAC_BACKENDS[backend_language]\n", "\n", "u, v = elements_of(W, names='u, v') #trial and test functions\n", From 9054f1fddcc59116c51e46aa766a2a6b4b5ca377 Mon Sep 17 00:00:00 2001 From: Frederik Schnack Date: Tue, 23 Dec 2025 22:21:05 +0100 Subject: [PATCH 59/63] change backend to pyccel --- examples/notebooks/regularized_curlcurl_3D_VTK.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb index b458a2835..e8ef51c29 100644 --- a/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb +++ b/examples/notebooks/regularized_curlcurl_3D_VTK.ipynb @@ -82,7 +82,7 @@ "from psydac.api.settings import PSYDAC_BACKENDS\n", "from psydac.fem.basic import FemField\n", "\n", - "backend_language = 'python'\n", + "backend_language = 'pyccel-gcc'\n", "backend = PSYDAC_BACKENDS[backend_language]\n", "\n", "u, v = elements_of(W, names='u, v') #trial and test functions\n", From a439c06d5a381e3ee6144c993604a840ca98d1aa Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 24 Dec 2025 17:49:14 +0100 Subject: [PATCH 60/63] Make 'success' entry of linear solvers 'info' dict a Python bool --- psydac/linalg/solvers.py | 29 +++++++++++++++++++---------- 1 file changed, 19 insertions(+), 10 deletions(-) diff --git a/psydac/linalg/solvers.py b/psydac/linalg/solvers.py index 871e5090e..fc3cce3cc 100644 --- a/psydac/linalg/solvers.py +++ b/psydac/linalg/solvers.py @@ -261,7 +261,7 @@ def solve_without_pc(self, b, out=None): print( "+---------+---------------------+") # Convergence information - self._info = {'niter': m, 'success': am < tol_sqr, 'res_norm': sqrt(am) } + self._info = {'niter': m, 'success': bool(am < tol_sqr), 'res_norm': sqrt(am) } if recycle: x.copy(out=self._options["x0"]) @@ -370,7 +370,9 @@ def solve_with_pc(self, b, out=None): print( "+---------+---------------------+") # Convergence information - self._info = {'niter': k, 'success': nrmr_sqr < tol_sqr, 'res_norm': sqrt(nrmr_sqr) } + self._info = {'niter': k, + 'success': bool(nrmr_sqr < tol_sqr), + 'res_norm': sqrt(nrmr_sqr)} if recycle: x.copy(out=self._options["x0"]) @@ -560,7 +562,9 @@ def solve(self, b, out=None): print( "+---------+---------------------+") # Convergence information - self._info = {'niter': m, 'success': res_sqr < tol_sqr, 'res_norm': sqrt(res_sqr)} + self._info = {'niter': m, + 'success': bool(res_sqr < tol_sqr), + 'res_norm': sqrt(res_sqr)} if recycle: x.copy(out=self._options["x0"]) @@ -773,7 +777,9 @@ def solve_without_pc(self, b, out=None): print("+---------+---------------------+") # Convergence information - self._info = {'niter': m, 'success': res_sqr < tol_sqr, 'res_norm': sqrt(res_sqr)} + self._info = {'niter': m, + 'success': bool(res_sqr < tol_sqr), + 'res_norm': sqrt(res_sqr)} if recycle: x.copy(out=self._options["x0"]) @@ -959,8 +965,9 @@ def solve_with_pc(self, b, out=None): print("+---------+---------------------+") # convergence information - self._info = {'niter': niter, 'success': res_sqr < - tol_sqr, 'res_norm': sqrt(res_sqr)} + self._info = {'niter': niter, + 'success': bool(res_sqr < tol_sqr), + 'res_norm': sqrt(res_sqr)} # Recycle solution as next initial guess, if enabled if recycle: @@ -1248,7 +1255,9 @@ def solve(self, b, out=None): print( "+---------+---------------------+") # Convergence information - self._info = {'niter': itn, 'success': rnorm tol. self._successful = istop in [1,2,3] @@ -1747,7 +1756,7 @@ def solve(self, b, out=None): am = sqrt(r.inner(r).real) if am < tol: - self._info = {'niter': 1, 'success': am < tol, 'res_norm': am } + self._info = {'niter': 1, 'success': bool(am < tol), 'res_norm': am } return x beta.append(am) @@ -1794,7 +1803,7 @@ def solve(self, b, out=None): x.mul_iadd(y[i], self._Q[i]) # Convergence information - self._info = {'niter': k+1, 'success': am < tol, 'res_norm': am } + self._info = {'niter': k+1, 'success': bool(am < tol), 'res_norm': am} if recycle: x.copy(out=self._options["x0"]) From 4b95e7a786376db059009f5bcb8ad85b2b3601b7 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 24 Dec 2025 18:31:43 +0100 Subject: [PATCH 61/63] Plot grid in plot_field_2d for the single-patch case --- psydac/fem/plotting_utilities.py | 16 ++++++++++++++-- 1 file changed, 14 insertions(+), 2 deletions(-) diff --git a/psydac/fem/plotting_utilities.py b/psydac/fem/plotting_utilities.py index b3943f53e..07f87bb86 100644 --- a/psydac/fem/plotting_utilities.py +++ b/psydac/fem/plotting_utilities.py @@ -363,12 +363,23 @@ def grid_vals(v): return get_grid_vals( else: raise ValueError(plot_type) + # If there is just one patch, also plot the grid + if not vh.space.is_multipatch: + ncells = min(vh.space.component_spaces[0].axis_spaces[i].ncells for i in [0, 1]) + N = N_vis // ncells + gridlines_x1, gridlines_x2 = get_patch_knots_gridlines(vh.space, N, mappings, 0) + else: + gridlines_x1 = None + gridlines_x2 = None + my_small_plot( title=title, vals=plot_vals_list, titles=subtitles, xx=xx, yy=yy, + gridlines_x1 = gridlines_x1, + gridlines_x2 = gridlines_x2, surface_plot=surface_plot, cb_min=cb_min, cb_max=cb_max, @@ -472,8 +483,9 @@ def my_small_plot( ax=ax, pad=0.05) if gridlines_x1 is not None: - ax.plot(*gridlines_x1, color='k') - ax.plot(*gridlines_x2, color='k') + ax.plot(*gridlines_x1, color='k', linewidth=1) + if gridlines_x2 is not None: + ax.plot(*gridlines_x2, color='k', linewidth=1) if show_xylabel: ax.set_xlabel(r'$x$', rotation='horizontal') ax.set_ylabel(r'$y$', rotation='horizontal') From 6a7e6813937dc53f14aa406301bf283d5e94f116 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 24 Dec 2025 18:52:41 +0100 Subject: [PATCH 62/63] Add notebook w/ 2D Poisson's eqn. on single-patch domain --- docs/source/examples.rst | 1 + examples/notebooks/poisson_2d_square.ipynb | 333 +++++++++++++++++++++ 2 files changed, 334 insertions(+) create mode 100644 examples/notebooks/poisson_2d_square.ipynb diff --git a/docs/source/examples.rst b/docs/source/examples.rst index bc590276f..e1f3d0858 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -18,6 +18,7 @@ but are also generated as part of the documentation and can be accessed here: :maxdepth: 1 :caption: Notebooks: + examples/poisson_2d_square examples/Poisson_non_periodic examples/Helmholtz_non_periodic examples/fem_L2_projection diff --git a/examples/notebooks/poisson_2d_square.ipynb b/examples/notebooks/poisson_2d_square.ipynb new file mode 100644 index 000000000..8a2e6f3e0 --- /dev/null +++ b/examples/notebooks/poisson_2d_square.ipynb @@ -0,0 +1,333 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Solving Poisson's equation on a square domain with a mapped grid\n", + "\n", + "In this notebook, we will show how to solve Poisson's equation on a single-patch square domain.\n", + "Thanks to the simple geometry, will use the method of manufactured solution to build a test case where the exact solution is known a priori.\n", + "As we are running this in a notebook, everything will be run in serial and hence we are limiting ourselves to a fairly coarse discretization to avoid taking too much time.\n", + "However, PSYDAC allows for hybrid MPI + OpenMP parallelization with barely any changes to the code.\n", + "The lines that are impacted by that will be preceeded by their MPI equivalent." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Problem definition with SymPDE\n", + "\n", + "PSYDAC uses the powerful topological tools of SymPDE to build a large variety of domains.\n", + "Here we use SymPDE to map a square domain $\\widehat{\\Omega}$ to another square $\\Omega := F(\\widehat{\\Omega})$ with non-orthogonal coordinates.\n", + "On such a simple domain, we define an exact solution $u$ which satisfies homogeneous Dirichlet boundary conditions, and we compute the right-hand side $f$ of the equation.\n", + "The strong form of Poisson's equation reads simply\n", + "\n", + "$$\n", + "\\left\\{\n", + "\\begin{aligned}\n", + " -\\nabla^2 u &= f && \\text{in $\\Omega$}, \\\\\n", + " u &= 0 && \\text{on $\\partial\\Omega$}.\n", + "\\end{aligned}\n", + "\\right.\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sympy import sin, pi\n", + "\n", + "from sympde.topology import Square, CollelaMapping2D\n", + "from sympde.calculus import laplace\n", + "from sympde.utilities.utils import plot_domain\n", + "\n", + "# Problem definition\n", + "OmegaP = Square('Omega') # parametric domain\n", + "F = CollelaMapping2D('F', eps=0.1, k1=1, k2=1) # mapping\n", + "Omega = F(OmegaP) # physical domain\n", + "x, y = Omega.coordinates # physical coordinates\n", + "u_ex = sin(pi * x) * sin(pi * y) # manufactured solution\n", + "f = -laplace(u_ex) # right-hand side\n", + "\n", + "# Simple visualization of the domain\n", + "plot_domain(Omega, isolines=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Abstract weak formulation with SymPDE\n", + "\n", + "The weak formulation of Poisson's equation reads:\n", + "\n", + "$$\n", + "\\text{Given $f \\in L^2(\\Omega)$},\n", + "\\quad\n", + "\\text{find $u \\in H^1_0(\\Omega)$ s.t.}\n", + "\\quad\n", + "\\underbrace{\\int_{\\Omega} \\nabla u \\cdot \\nabla v\\,\\mathrm{d}\\Omega}_{a(u, v)} =\n", + "\\underbrace{\\int_{\\Omega} f\\,v \\,\\mathrm{d}\\Omega}_{l(v)}\n", + "\\quad\n", + "\\forall v \\in H^1_0(\\Omega).\n", + "$$\n", + "\n", + "Here $H^1_0(\\Omega)$ satisfies homogeneous Dirichlet boundary conditions.\n", + "Currently, SymPDE does not allow attaching this information to the function space.\n", + "(This is consistent with the fact that the FEM fields in PSYDAC are in general non-zero at the boundary.)\n", + "Instead, an additional constraint is attached to the weak formulation explicitly, in the form of an `EssentialBC` object.\n", + "\n", + "Since we are using the method of manufactured solutions, we can compute the $L^2$ and $H^1$ norms of the error.\n", + "The norms are defined symbolically in SymPDE using `Norm` objects.\n", + "The error is $u-u_{ex}$, where the trial function $u$ is a SymPDE `ScalarFunction` object, while the exact solution $u_{ex}$ is a SymPy expression of the physical coordinates.\n", + "Since $u$ represents a free parameter, it will have to be replaced by a PSYDAC FEM field when assemblying the norm." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from sympde.topology import ScalarFunctionSpace\n", + "from sympde.topology import elements_of\n", + "from sympde.topology import NormalVector\n", + "from sympde.calculus import grad, inner\n", + "from sympde.expr import LinearForm, BilinearForm, Norm\n", + "from sympde.expr import integral\n", + "from sympde.expr import find, EssentialBC\n", + "\n", + "# Space, trial function u, and test function v\n", + "V = ScalarFunctionSpace('V', Omega)\n", + "u, v = elements_of(V, names='u, v')\n", + "\n", + "# Bilinear form a(u, v) and linear form l(v)\n", + "a = BilinearForm((u, v), integral(Omega, inner(grad(u), grad(v))))\n", + "l = LinearForm(v, integral(Omega, f * v))\n", + "\n", + "# Homogeneous Dirichlet boundary conditions: u=0 on ∂Ω\n", + "bc = EssentialBC(u, 0, Omega.boundary)\n", + "\n", + "# Weak formulation of Poisson's eqn. with boundary conditions as constraint\n", + "equation = find(u, forall=v, lhs=a(u, v), rhs=l(v), bc=bc)\n", + "\n", + "# L^2 and H^1 norms of the error\n", + "l2norm = Norm(u - u_ex, Omega, kind='l2')\n", + "h1norm = Norm(u - u_ex, Omega, kind='h1')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Galerkin method with PSYDAC\n", + "\n", + "Starting from the weak formulation of Poisson's equation, a Galerkin method of solution can be formulated as follows:\n", + "\n", + "- Let $u_h \\approx u$ in a finite dimensional subspace $V_h \\subset H^1_0$\n", + "- Choose a basis for $V_h = span(\\phi_1, \\phi_2, \\dots \\phi_N)$\n", + "- Search for $u_h(x,y) := \\sum_{j=1}^N w_j\\, \\phi_j(x,y)$\n", + "- Choose test functions $v = \\phi_i$\n", + "- A linear PDE yields the linear system $\\mathbb{A}~\\mathsf{w} = \\mathsf{b}$\n", + "\n", + "$$\n", + "\\text{Given $f \\in L^2(\\Omega)$},\n", + "\\quad\n", + "\\text{find $\\mathsf{w}\\in\\mathbb{R}^N$ s.t.}\n", + "\\quad\n", + "\\sum_{j=1}^N \\underbrace{\\left(\\int_{\\Omega_h} \\nabla\\phi_i \\cdot \\nabla\\phi_j\\,\\mathrm{d}\\Omega \\right)}_{A_{ij}} w_j\n", + "= \\underbrace{\\int_{\\Omega_h} f\\,\\phi_i\\,\\mathrm{d}\\Omega}_{b_i},\n", + "\\quad\n", + "\\text{for $i = 1, \\dots, N$}.\n", + "$$\n", + "\n", + "PSYDAC provides the function `discretize` which maps SymPDE abstract objects to their discrete PSYDAC counterpart.\n", + "For a Poisson problem over a single-patch domain, this means:\n", + "\n", + "| SymPDE | PSYDAC |\n", + "| --------------------- | ---------------------- |\n", + "| `Domain` | `Geometry` |\n", + "| `ScalarFunctionSpace` | `TensorFemSpace` |\n", + "| `Equation` | `DiscreteEquation` |\n", + "| `Functional` (including `Norm` and `SemiNorm`) | `DiscreteFunctional` |\n", + "| `LinearForm` | `DiscreteLinearForm` |\n", + "| `BilinearForm` | `DiscreteBilinearForm` |\n", + "\n", + "In addition, SymPDE's `ScalarFunction` objects correspond to PSYDAC's `FemField` objects.\n", + "\n", + "When discretizing an object of type `Functional`, `LinearForm`, or `BilinearForm`, PSYDAC automatically generates Python code for the corresponding assembly functions.\n", + "This Python code can be accelerated to Fortran or C, and even include OpenMP instructions, depending on the \"backend\" chosen by the user.\n", + "The available backends can be accessed through the `PSYDAC_BACKENDS` dictionary defined in the module `psydac.api.settings`, where the dictionary key is one the following strings: `['python', 'pyccel-gcc', 'pyccel-intel', 'pyccel-pgi', 'pyccel-nvidia']`.\n", + "Each of the dictionary values is itself a dictionary containing various options which can be modified by the user.\n", + "\n", + "`PSYDAC_BACKENDS['python']` defines a pure Python backend; this means that the generated Python assembly files will be used as they are.\n", + "The other options are based on accelerating the Python assembly files using the Pyccel transpiler and one of the compilers: GCC, Intel, PGI, or NVIDIA.\n", + "For all but the Python backend, OpenMP parallelization can be activated by setting `backend['omp'] = True`, and compilation flags can be accessed and changed using `backend['flags']`." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "from psydac.api.discretization import discretize\n", + "from psydac.api.settings import PSYDAC_BACKENDS\n", + "\n", + "# Modify to use MPI and/or OpenMP\n", + "use_mpi = False\n", + "use_openmp = False\n", + "\n", + "# MPI communicator, if any\n", + "if use_mpi:\n", + " from mpi4py import MPI\n", + " comm = MPI.COMM_WORLD\n", + "else:\n", + " comm = None\n", + "\n", + "# Choose backend\n", + "backend = PSYDAC_BACKENDS['pyccel-gcc']\n", + "if use_openmp:\n", + " import os\n", + " os.environ['OMP_NUM_THREADS'] = \"4\"\n", + " backend['omp'] = True \n", + "\n", + "# Discretization parameters\n", + "ncells = [9, 9]\n", + "degree = [3, 3]\n", + "periodic = [False, False]\n", + "nquads = [p + 1 for p in degree]\n", + "\n", + "# Discretize domain and function space\n", + "Omega_h = discretize(Omega, ncells=ncells, periodic=periodic)\n", + "V_h = discretize(V, Omega_h, degree=degree)\n", + "\n", + "# Discretize weak formulation and error norms.\n", + "# Python code is generated for the assembly kernels.\n", + "# The number of quadrature points should be provided.\n", + "# If a Pyccel backend is chosen, the Python code is translated to Fortran.\n", + "equation_h = discretize(equation, Omega_h, [V_h, V_h], nquads=nquads, backend=backend)\n", + "l2norm_h = discretize(l2norm, Omega_h, V_h, nquads=nquads, backend=backend)\n", + "h1norm_h = discretize(h1norm, Omega_h, V_h, nquads=nquads, backend=backend)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Solve the equation and compute the error norms\n", + "\n", + "When calling the `assemble` method of a `DiscreteBilinearForm`, `DiscreteLinearForm`, or `DiscreteFunctional`, PSYDAC assembles a matrix, vector, or scalar quantity, respectively.\n", + "Objects of type `DiscreteEquation` do not have an `assemble` method, but they have the methods `set_solver` and `solve` instead:\n", + "- The `set_solver` method specifies the iterative algorithm (and its parameters) for solving the linear system $\\mathbb{A} \\mathrm{w} = \\mathrm{b}$ to obtain the spline coefficients $\\mathrm{w}$ of the Galerkin solution $u_h$.\n", + "- The `solve` methods performs a few steps.\n", + " First, it assembles both the left-hand-side matrix $\\mathbb{A}$ and right-hand-side vector $\\mathrm{b}$.\n", + " Then, it solves the linear system $\\mathbb{A} \\mathrm{w} = \\mathrm{b}$ with the chosen iterative algorithm.\n", + " Finally, it creates a callable `FemField` with spline coefficients $\\mathrm{w}$." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import time\n", + "from psydac.fem.plotting_utilities import plot_field_2d\n", + "\n", + "# Set the solver parameters (CG = Conjugate Gradient)\n", + "equation_h.set_solver('CG', info=True, tol=1e-14)\n", + "\n", + "# Compute the numerical solution u_h:\n", + "# 1. assemble (distributed) sparse matrix A\n", + "# 2. assemble (distributed) dense vector b\n", + "# 3. solve linear system A w = b\n", + "# 4. create callable field u_h(x,y)\n", + "t0_s = time.time()\n", + "u_h, info = equation_h.solve()\n", + "t1_s = time.time()\n", + "\n", + "# Compute the L^2 and H^1 error norms\n", + "t0_d = time.time()\n", + "l2_error = l2norm_h.assemble(u=u_h)\n", + "h1_error = h1norm_h.assemble(u=u_h)\n", + "t1_d = time.time()\n", + "\n", + "# Print convergence information, error norms, and timings\n", + "print('> CG info :: ',info )\n", + "print('> L2 error :: {:.2e}'.format(l2_error))\n", + "print('> H1 error :: {:.2e}'.format(h1_error))\n", + "print('> Solution time :: {:.2e} s'.format(t1_s - t0_s))\n", + "print('> Evaluat. time :: {:.2e} s'.format(t1_d - t0_d))\n", + "\n", + "# Plot the results\n", + "plot_field_2d(u_h,\n", + " domain = Omega,\n", + " title = '$u_h(x,y)$: computed FEM solution',\n", + " plot_type = 'components',\n", + " N_vis = 50,\n", + " hide_plot = False,\n", + " filename = None,\n", + " cmap = 'jet',\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Testing the notebook" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "import ipytest\n", + "ipytest.autoconfig(raise_on_error=True)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "%%ipytest\n", + "\n", + "def test_l2error():\n", + " assert l2_error < 8.68e-03\n", + "\n", + "def test_h1error():\n", + " assert h1_error < 1.35e-01" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} From f64b62ba464b85e4dc76fdc7bf10e2fb8f42a783 Mon Sep 17 00:00:00 2001 From: =?UTF-8?q?Yaman=20G=C3=BC=C3=A7l=C3=BC?= Date: Wed, 24 Dec 2025 18:53:02 +0100 Subject: [PATCH 63/63] Write PSYDAC in all caps --- docs/source/examples.rst | 2 +- examples/notebooks/fem_L2_projection.ipynb | 4 ++-- 2 files changed, 3 insertions(+), 3 deletions(-) diff --git a/docs/source/examples.rst b/docs/source/examples.rst index e1f3d0858..26c4139b7 100644 --- a/docs/source/examples.rst +++ b/docs/source/examples.rst @@ -32,7 +32,7 @@ FEEC Examples ------------- In the `FEEC examples directory `_, -you will find several examples of how to use Psydac to solve problems arising within the Finite Element Exterior Calculus (FEEC) framework. +you will find several examples of how to use PSYDAC to solve problems arising within the Finite Element Exterior Calculus (FEEC) framework. These examples include: diff --git a/examples/notebooks/fem_L2_projection.ipynb b/examples/notebooks/fem_L2_projection.ipynb index 85044413c..96b0d585b 100644 --- a/examples/notebooks/fem_L2_projection.ipynb +++ b/examples/notebooks/fem_L2_projection.ipynb @@ -224,7 +224,7 @@ "a = BilinearForm((u, v), integral(Omega, u * v))\n", "ah = discretize(a, Omega_h, [Vh, Vh], backend=PSYDAC_BACKENDS[backend_language])\n", "\n", - "# Mass matrix in Psydac 'stencil' (linear operator) format \n", + "# Mass matrix in PSYDAC 'stencil' (linear operator) format \n", "M_V = ah.assemble() \n", "\n", "# visualize the mass matrix by plotting its numpy conversion\n", @@ -256,7 +256,7 @@ "a = BilinearForm((uu, vv), integral(Omega, dot(uu,vv)))\n", "ah_W = discretize(a, Omega_h, [Wh, Wh], backend=PSYDAC_BACKENDS[backend_language])\n", "\n", - "# Mass matrix in Psydac 'stencil' (linear operator) format \n", + "# Mass matrix in PSYDAC 'stencil' (linear operator) format \n", "M_W = ah_W.assemble() \n", "\n", "# visualize the mass matrix by plotting its numpy conversion\n",

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