General changes for optimization and scalability

[TmsRC]

Summary

Implements a series of memory and compute optimizations to allow for larger grids and faster execution times. Depends on updated version of freegs4e (pull request #61).

• Optimizes the construction of the NKGSsolver Green's function and implements a new batched strategy for computing it; exposes an option to the user to avoid caching this structure in memory.
• Exposes options to the user for selecting type of solver, including the new, faster DST solver.
• Optimizes the way Myy is created, allows the user to avoid caching of Myy, as well as offering an FFT version of Myy.dot() that uses even less memory.
• Makes use of the updated freegs4e API in PR#61

Performance

Using example 02, at 513x1025, tolerance 1e-08

Caching?	Original time	Original RSS	New LU serial	DST serial	LU 64 threads	DST 64 threads	LU RSS	DST RSS
Yes	467s	30.5GB	334s	294s	95s	54s	19.3GB	16.0GB
No	---	---	test pending	test pending	276s	231s	8.0GB	5.4GB

Using example 05a, tolerance 1e-08, 40 steps, 64 threads, using DST solver, cached Green's function

Testcase	Original time	Original RSS	Cached Myy time	Cached Myy RSS	OTF Myy time	OTF Myy RSS
257x513	546s	350GB	311s	12GB	299s	4.3GB
513x1025	---	---	1133s	132GB	1033s	30GB

• Maximum resolution successfully tested for a static solve: 2049x4097, 1h56m, 163GB
• Maximum resolution successfully tested for an evolutive solve: 1025x2049, 1h36m, 286GB

Special considerations

A possible oversubscription issue was identified where multiprocessing is used for parallelism (currently only in nonlinear_solve.py) due to unmanaged contention with the threads from freegs4e.parallel. The issue should only show itself when cache_greens=False is set during NKGSsolver initialization and that solver is used for linearized evolution (this combination should be discouraged regardless). An issue will be opened for this bug once this pull request is merged.

Verification

Merge checks failing due to dependence on updated freegs4e. Verification stats below contingent on the corresponding freegs4e pull request.

• New tests added, new parametrizations added to existing tests, to evaluate new features
• Passing all tests save for the 2 mentioned below.
• The test for linearized growth rate (test_dynamics.py) fails for second order solvers, meaning it doesn't pass with DST: marked as xfail. It is recommended that the test is checked.
• The test test_static_solve() in test_static_solver.py fails when the second order multigrid solver is used. No attempt has been made at resolving the issue as support for multigrid solvers is planned to be abandoned: marked as xfail. Issue will be addressed at a later point.