CeedElemRestriction for H(curl) #1265
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@jeremylt, do you have any last comments or is this ready to merge from your POV? |
…ore general orientation transformations
Adds CeedElemRestrictionCreateCurlOriented which takes a tridiagonal element-wise transformation matrix, typically with entries {-1, 0, 1}.
…striction types (default, oriented, strided)
Also update oriented restriction test to also test transpose.
… including use of int8_t for tridiagonal matrix
…ictions (RT or ND elements)
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Thank you @jedbrown @jeremylt @nbeams @rezgarshakeri for all your help with this feature and PR! Now onto GPU backends for H(div) and H(curl)... 🚀 |
Thank you for this nice feature. |
This was referenced Aug 7, 2023
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Reopening #1168 from within CEED/libCEED for GitLab CI tests.
From #1168:
High-order H(curl) spaces (p > 1) in 3D involve pairs of element face dofs which must be treated specially in the L-vector to E-vector transformation. These transformations are more complicated than the simple sign flip accounted for in #889. In general, the pairs of dofs are transfomed by 2x2 blocks with entries {-1, 0, 1} to write the transformed E-vector dofs as linear combinations of the L-vector dofs. Thus, if each pair of face dofs are arranged to be consecutive in the element dof ordering, we can represent the transformation required as a tridiagonal matrix with entries {-1, 0, 1} applied to the E-vector. Note this is a (more expensive) generalization of the simple orientation flip case where the transformation matrix is just diagonal with entries {-1, 1}. Note that an alternative approach is to apply some global ordering of the nodes of the mesh as a preprocessing step after which a simple signed restriction suffices (like in https://epubs.siam.org/doi/10.1137/08073901X). However this strategy has its own shortcomings in particular when doing things like AMR.
More information can be found in this paper: https://dl.acm.org/doi/pdf/10.1145/3524456 (section 4.1.4, for example). See also mfem/mfem#1046 and https://github.com/mfem/mfem/blob/master/fem/doftrans.hpp for examples of how this transformation is handled in MFEM.
This PR adds CeedElemRestrictionCreateCurlOriented, which is similar to the CeedElemRestrictionCreateOriented constructor introduced in #889. Currently only implemented for CPU backends, with the main change coming in CeedElemRestrictionApply_Ref_Core.
Also adds some missing methods which should make blocked and opt backends work for oriented restrictions.