Functional feature: Computes matrix entries for H1/Hcurl

[jonwong12]

This PR adds a gradient_matrix_kernel to functional which will compute the element tangent entries of the residual in the form of a continuous vector K_e of size (test_ndof * test_dim * trial_ndof * trial_dim * num_elem). It should work for H1, Hcurl, and L2 spaces. However L2 is not tested specifically in this PR.

Afterwards an serac::mfem_ext::AssembledSparseMatrix is constructed. This holds the mapping from K_e to a rank-local assembled CSR-matrix. Calling AssembledSparseMatrix.FillData(K_e) will maintain the same sparsity pattern but change matrix entries. AssembledSparseMatrix is derived from mfem::SparseMatrix; however FillData() and ParallelAssemble() methods were added.

Note:
Currently AssembledSparseMatrix uses some "forbidden C++ calls" to get at protected information in mfem::ElementRestriction. Ideally this information would be public in mfem. Additionally there is an mfem issue with L2 when using LEXICOGRAPHIC ordering which a follow-up PR will try to address. For NATIVE ordering, see this branch for a working H1-L2 matrix assembly.

TODO:

• Add validation checks for hcurl and elasticity
• Add second method in functional.hpp to update an AssembledSparseMatrix directly

[codecov-commenter]

Codecov Report

Merging #484 (bb88b6a) into develop (fb35d7b) will increase coverage by 0.34%.
The diff coverage is 100.00%.

@@             Coverage Diff             @@
##           develop     #484      +/-   ##
===========================================
+ Coverage    94.72%   95.06%   +0.34%     
===========================================
  Files           68       70       +2     
  Lines         3678     3934     +256     
===========================================
+ Hits          3484     3740     +256     
  Misses         194      194              

Impacted Files	Coverage Δ
src/serac/numerics/assembled_sparse_matrix.cpp	100.00% <100.00%> (ø)
src/serac/numerics/assembled_sparse_matrix.hpp	100.00% <100.00%> (ø)
...cs/utilities/functional/detail/metaprogramming.hpp	100.00% <100.00%> (ø)
.../serac/physics/utilities/functional/functional.hpp	97.36% <100.00%> (+0.70%)	⬆️
...rc/serac/physics/utilities/functional/integral.hpp	100.00% <100.00%> (ø)
src/serac/physics/utilities/functional/tensor.hpp	99.58% <100.00%> (+0.01%)	⬆️
...lities/functional/tests/functional_comparisons.cpp	96.31% <100.00%> (+0.41%)	⬆️

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[jonwong12]

@joshessman-llnl I have a issue/branch in MFEM to do this matrix assembly, but I don't know what the timeline for that is. I think they are interested in seeing some benchmarks. In that branch, I just friend AssembledSparseMatrix in mfem::ElementRestriction, so I agree this is a temporary solution.

One point of contention is that MFEM seems more concerned with higher order elements where assembling a matrix may have declining payoffs, whereas for the problems we solve, matrices are useful.

Alternatively this PR doesn't support L2 (LEXICOGRAPHIC ordering, but NATIVE ordering is fine?), because mfem::ElementRestriction and mfem::L2ElementRestriction are not derived from each other. We could re-implement or use variants (and get at protected arrays). @jamiebramwell What are your thoughts on this?

[samuelpmishLLNL]

This all looks very promising to me!

I want to apologize again for not providing a rich enough set of tools to make the implementation of gradient_matrix_kernel straightforward. I am hopeful that we can significantly simplify gradient_matrix_kernel by adding some additional features to the tensor class. In the meantime, having this working example will be incredibly useful when we eventually pursue that refactor.

[jamiebramwell]

@samuelpmishLLNL @samuelpmishLLNL , any open issues in this PR?

[samuelpmishLLNL]

I think it looks good, approving now

[joshessman-llnl]

Just some minor style comments; otherwise, looks good to me!