Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes
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Authors
Scroggs, MW
Dokken, JS
Richardson, CN
Wells, GN
Publication Date
2022Journal Title
ACM Transactions on Mathematical Software
ISSN
0098-3500
Publisher
Association for Computing Machinery (ACM)
Type
Article
This Version
AM
Metadata
Show full item recordCitation
Scroggs, M., Dokken, J., Richardson, C., & Wells, G. (2022). Construction of Arbitrary Order Finite Element Degree-of-Freedom Maps on Polygonal and Polyhedral Cell Meshes. ACM Transactions on Mathematical Software https://doi.org/10.1145/3524456
Abstract
We develop a method for generating degree-of-freedom maps for arbitrary order
finite element spaces for any cell shape. The approach is based on the
composition of permutations and transformations by cell sub-entity. Current
approaches to generating degree-of-freedom maps for arbitrary order problems
typically rely on a consistent orientation of cell entities that permits the
definition of a common local coordinate system on shared edges and faces.
However, while orientation of a mesh is straightforward for simplex cells and
is a local operation, it is not a strictly local operation for quadrilateral
cells and in the case of hexahedral cells not all meshes are orientable. The
permutation and transformation approach is developed for a range of element
types, including Lagrange, and divergence- and curl-conforming elements, and
for a range of cell shapes. The approach is local and can be applied to cells
of any shape, including general polytopes and meshes with mixed cell types. A
number of examples are presented and the developed approach has been
implemented in an open-source finite element library.
Keywords
math.NA, math.NA, cs.NA
Identifiers
External DOI: https://doi.org/10.1145/3524456
This record's URL: https://www.repository.cam.ac.uk/handle/1810/335148
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