Improve Poisson tutorial with clearer explanations #198
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Improved Poisson tutorial with explanations and added clarity
Expanded explanations of weak form, FE spaces, mesh tags, transitions, and math-code mapping. Also improved visualization description.
JordiManyer
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JordiManyer
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Reviewed. I think some stuff is unnecessary, but I am happy to keep parts of it. Thank you for the contribution!
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| degree = 2 | ||
| Ω = Triangulation(model) | ||
| # dΩ represents integration over the 3D domain Ω (a volume integral), matching the dΩ notation in the weak form. |
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I don't think this makes sense. What does "represents integration mean"? I think the current explanation, a.k.a it's a quadrature of order degree the cells, is more precise.
| # In the strong form we have: | ||
| # -Δu = f in Ω, u = g on Γ_D, ∂u/∂n = h on Γ_N. | ||
| # | ||
| # To obtain the weak form, we multiply by a test function v (which vanishes on Γ_D) and integrate by parts, giving: |
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I don't think this is necessary. My point of view is that this is an implementation tutorial, not a math class. In the initial header, we state both the strong and weak formulations of the problem and give a reference so that people can have a look at the derivation. If you go to the given reference, you will find an explanation on exactly this, thus making it unnecessary.
| a(u,v) = ∫( ∇(v)⋅∇(u) )*dΩ | ||
| b(v) = ∫( v*f )*dΩ + ∫( v*h )*dΓ | ||
| # Math ⇔ Code mapping: | ||
| # a(u,v) = ∫( ∇(v)⋅∇(u) )*dΩ ↔ ∫_Ω ∇u⋅∇v dΩ |
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Again, I do not see the point of this. The API is expressive enough that this "translation" is unnecessary, I think. If you look at both sides, the changes are minimal. I do not think people struggle with making this translation themselves.
| # Summary so far: | ||
| # - V0 implements the test space V_h^0 (zero on Γ_D). | ||
| # - Ug implements the trial space U_h^g (Dirichlet value g). | ||
| # - a(u,v) and b(v) encode the variational problem. |
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Is the tutorial so long that we need a summary?
2 participants
This PR expands the Poisson tutorial with additional explanations to help beginners.
I added:
• Intro explanation of the weak form and how it connects to a(u,v) and b(v)
• Clarification on the mesh file (model.json) and boundary tags
• Explanation of test space (V0) and trial space (Ug)
• Small transition explanations between sections
• Math-to-code comments showing how the weak form maps to Gridap expressions
• Clearer visualization guidance to interpret results
Please let me know if anything should be changed, thank you.