Dear Peter,
> On 1 Feb 2019, at 09:35, Ham, David A <david.ham@imperial.ac.uk> wrote:
>
> Dear Peter,
>
> We don’t have nodal evaluation for arbitrary finite elements. The interpolation operator (both interpolate and Function.at) works for spaces with point evaluation nodes i.e. CG and DG so you can rig up a hack by interpolating the RT field into the spanning DG field (which is lossless), interpolating that into a spanning DG field on the new mesh (you can get the coordinates to interpolate at by interpolating the coordinate field into the corresponding vector DG space), and then finally projecting from the DG space down to RT. This is effectively a variant on: https://www.firedrakeproject.org/interpolation.html#interpolation-from-external-data
In addition to doing this, if you have a mesh hierarchy, then the interpolation between meshes in the mesh hierarchy is supported for all elements. For those that are not point-evaluation, it is a little ugly right now: we hope to make it simpler in the future. But you can do this:
Hi Lawrence,
Is there something wrong with the way I do interpolation? Namely, I point locate the quadrature points for the dual basis vectors from the target mesh in the source mesh. I admit that this is not conservative like supermesh, but it should work for every element and be first order accurate (I think). I cannot see why its any harder to do this than the DG route since they both require point location between meshes. I know LibMesh does this hierarchical-in-dimension thing from Leszek, but I can never remember exactly why.
Thanks,
Matt
mesh = ...
mh = MeshHierarchy(mesh, ...)
Vc = FunctionSpace(mh[0], "RT", 1)
Vf = FunctionSpace(mh[1], "RT", 1)
interpolator = EmbeddedDGTransfer(Vc.ufl_element())
c = Function(Vc)
f = Function(Vf)
# Move primal field from coarse to fine
interpolator.prolong(c, f)
# Move primal field from fine to coarse
interpolator.inject(f, c)
# Move dual field (a residual) from fine to coarse
interpolator.restrict(f, c)
> However a nicer approach is probably to use Patrick Farrell’s pefarrell/supermesh-mixed-mass-matrix branch which makes project work between different meshes of the same domain.
Note right now this is restricted to different meshes where you can provide an oracle that relates the cells on the coarse mesh to potentially overlapping cells on the fine mesh (A trivial, although not efficient, such oracle is that every coarse cell potentially overlaps with every fine cell).
Thanks,
Lawrence
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