Justin Crum
Bringing trimmed Serendipity methods to computational practice in Firedrake
Crum, Justin; Cheng, Cyrus; Ham, David A.; Mitchell, Lawrence; Kirby, Robert C.; Levine, Joshua A.; Gillette, Andrew
Authors
Cyrus Cheng
David A. Ham
Lawrence Mitchell
Robert C. Kirby
Joshua A. Levine
Andrew Gillette
Abstract
We present an implementation of the trimmed serendipity finite element family, using the open-source finite element package Firedrake. The new elements can be used seamlessly within the software suite for problems requiring H1, H(curl), or H(div)-conforming elements on meshes of squares or cubes. To test how well trimmed serendipity elements perform in comparison to traditional tensor product elements, we perform a sequence of numerical experiments including the primal Poisson, mixed Poisson, and Maxwell cavity eigenvalue problems. Overall, we find that the trimmed serendipity elements converge, as expected, at the same rate as the respective tensor product elements, while being able to offer significant savings in the time or memory required to solve certain problems.
Citation
Crum, J., Cheng, C., Ham, D. A., Mitchell, L., Kirby, R. C., Levine, J. A., & Gillette, A. (2022). Bringing trimmed Serendipity methods to computational practice in Firedrake. ACM Transactions on Mathematical Software, 48(1), 1-19. https://doi.org/10.1145/3490485
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 1, 2021 |
Online Publication Date | Feb 16, 2022 |
Publication Date | 2022-03 |
Deposit Date | Oct 8, 2021 |
Publicly Available Date | Jun 20, 2022 |
Journal | ACM Transactions on Mathematical Software |
Print ISSN | 0098-3500 |
Electronic ISSN | 1557-7295 |
Publisher | Association for Computing Machinery (ACM) |
Peer Reviewed | Peer Reviewed |
Volume | 48 |
Issue | 1 |
Article Number | 8 |
Pages | 1-19 |
DOI | https://doi.org/10.1145/3490485 |
Public URL | https://durham-repository.worktribe.com/output/1231276 |
Related Public URLs | https://arxiv.org/pdf/2104.12986.pdf |
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Publisher Licence URL
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Copyright Statement
This work is licensed under a Creative Commons Attribution International 4.0 License.
© 2022 Copyright held by the owner/author(s).
0098-3500/2022/02-ART8.
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