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Intrepid2
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A family of hierarchical basis functions, constructed in a way that follows work by Fuentes et al. More...
#include <Intrepid2_HierarchicalBasisFamily.hpp>
A family of hierarchical basis functions, constructed in a way that follows work by Fuentes et al.
A family of hierarchical basis functions, constructed in a way that follows work by Fuentes et al., suitable for use in DG contexts.
This family is defined using the DerivedBasisFamily, which in turn templates the definitions on the H(grad) and H(vol) Lagrangian bases on the line.
At present, only hypercube topologies (line, quadrilateral, hexahedron) are supported, but other topologies will be supported in the future.
For mathematical details of the construction see: Federico Fuentes, Brendan Keith, Leszek Demkowicz, Sriram Nagaraj. "Orientation embedded high order shape functions for the exact sequence elements of all shapes." Computers & Mathematics with Applications, Volume 70, Issue 4, 2015, Pages 353-458, ISSN 0898-1221. https://doi.org/10.1016/j.camwa.2015.04.027.
Our implementation effectively differs from ESEAS only in the fact that we use only the default orientation on the cell, because Intrepid2 has other mechanisms for handling basis orientations. At present, we have implemented the basis functions on hypercube topologies. We plan to add support for simplices, wedges, and pyramids soon.
We have offline tests that verify agreement between our implementation and ESEAS. We hope to add these to the Trilinos continuous integration tests in the future.
This family is defined using the DerivedBasisFamily, which in turn templates the definitions on the H(grad) and H(vol) Lagrangian bases on the line.
The suitability of this family for DG contexts is primarily due to the fact that the H(grad) basis has a constant member. Note also that in this family, all members are associated with the cell interior; there are no basis functions associated with subcell topologies.
1.8.5