Bringing Trimmed Serendipity Methods to Computational Practice in Firedrake
Author
Crum, JustinCheng, Cyrus
Ham, David A.
Mitchell, Lawrence
Kirby, Robert C.
Levine, Joshua A.
Gillette, Andrew
Affiliation
Department of Mathematics, University of ArizonaDepartment of Computer Science, University of Arizona
Issue Date
2022-03-31
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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.Rights
© 2022 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution International 4.0 License.Collection Information
This item from the UA Faculty Publications collection is made available by the University of Arizona with support from the University of Arizona Libraries. If you have questions, please contact us at repository@u.library.arizona.edu.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.Note
Open access articleISSN
0098-3500EISSN
1557-7295DOI
10.1145/3490485Version
Final published versionae974a485f413a2113503eed53cd6c53
10.1145/3490485
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Except where otherwise noted, this item's license is described as © 2022 Copyright held by the owner/author(s). This work is licensed under a Creative Commons Attribution International 4.0 License.