Clement interpolant #4244
Clement interpolant #4244
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| For arguments, see :class:`.Interpolator`. | ||
| """ | ||
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| def __new__(cls, expr, V, **kwargs): |
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Should this check go to __init__ ?
| if rank != len(self.V.value_shape): | ||
| raise ValueError(f"Rank-{rank} input inconsistent with target space.") | ||
| mesh = self.V.mesh() | ||
| dim = mesh.topological_dimension() |
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This dim should be the number of copies of the element V.block_size. I think a VectorFunctionSpace and TensorFunctionSpace could be indexed with a double index (flat_dof_id, component_id). So rank could possibly be unrestricted and there wouldn't have to be special cases if you treat the rank-0 as the general case.
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| @pytest.mark.parametrize("rank", range(3)) | ||
| @pytest.mark.parametrize("dim", range(1, 4)) | ||
| def test_clement_interpolator_simplex(dim, rank): |
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We should test a vector with 3 components in a 2D mesh.
| domain = "{[i]: 0 <= i < patch.dofs}" | ||
| instructions = "patch[i] = patch[i] + vol[0]" | ||
| keys = {"vol": (volume, op2.READ), "patch": (patch_volume, op2.RW)} | ||
| parloops.par_loop((domain, instructions), dX, keys) |
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The patch volume here could become a cached_property so it is not recomputed every time. Maybe we could attach this property to the mesh, so it can be reused more widely across different Interpolators.
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Good idea. I've addressed this in 34ceb67, using the cell_sizes cached property as a template.
I've been meaning to upstream some functionality from Animate that might be useful for the wider Firedrake community, so am starting with this. Let me know if it's of interest!
This PR adds functionality for the Clément interpolant, which transfers fields from P1 space to P0 space via local volume averaging. We've found this particularly useful for gradient/Hessian recovery in P1 space (can upstream those later).
I've included tests on simplices in 1D, 2D, and 3D, and for scalar-, vector-, and matrix-valued functions.
A limitation of the approach is that the local averaging breaks down on the boundary, but it does a good job in the domain interior. I also have an implementation of local facet averaging on the boundary that I can provide, if it'd be of use.
http://www.numdam.org/item/M2AN_1975__9_2_77_0.pdf