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pbrubeck
commented
Mar 26, 2026
Co-authored-by: Pablo Brubeck <brubeck@protonmail.com>
pbrubeck
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Mar 27, 2026
| finat.JohnsonMercier, | ||
| finat.Morley, | ||
| ]) | ||
| def test_piola_manifold(ref_to_phys, element): |
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Suggested change
| def test_piola_manifold(ref_to_phys, element): | |
| def test_manifold(ref_to_phys, element): |
pbrubeck
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Mar 27, 2026
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| dim_x = len(xs[0]) | ||
| dim_y = len(ys[0]) |
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How does the old code handle different topological dimensions? It seems to work fine going from low dimension to a higher one, but I think you need least-squares in order to go the other way around. This code always builds a square matrix mat, but it might be singular.
The new code builds a possibly rectangular matrix DX if xs defines a simplex with tdim != gdim. If tdim == gdim, DX is square it inverts it with numpy.linalg.solve, and uses numpy.linalg.lstsq otherwise.
pbrubeck
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Mar 27, 2026
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| if len(xs) != len(ys): | ||
| raise Exception("") |
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Should this exception be considered in the new code?
pbrubeck
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Mar 27, 2026
| if DX.shape[0] == DX.shape[1]: | ||
| AT = numpy.linalg.solve(DX, DY) | ||
| else: | ||
| AT, *_ = numpy.linalg.lstsq(DX, DY) |
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Should we check for a small residual in the least-squares case?
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This PR enables FIAT to handle physical cells with higher codimension, and is by no means required to support manifolds in Firedrake (which we already do for some elements, including Johnson-Mercier). This is ONLY to allow testing the basis transformation in FIAT.