Algorithms for parallel generic hp-adaptive finite element software
| dc.contributor.author | Fehling, Marc, author | |
| dc.contributor.author | Bangerth, Wolfgang, author | |
| dc.contributor.author | ACM, publisher | |
| dc.date.accessioned | 2024-11-11T19:30:35Z | |
| dc.date.available | 2024-11-11T19:30:35Z | |
| dc.date.issued | 2023-09-19 | |
| dc.description.abstract | The hp-adaptive finite element method—where one independently chooses the mesh size (h) and polynomial degree (p) to be used on each cell—has long been known to have better theoretical convergence properties than either h- or p-adaptive methods alone. However, it is not widely used, owing at least in part to the difficulty of the underlying algorithms and the lack of widely usable implementations. This is particularly true when used with continuous finite elements. Herein, we discuss algorithms that are necessary for a comprehensive and generic implementation of hp-adaptive finite element methods on distributed-memory, parallel machines. In particular, we will present a multistage algorithm for the unique enumeration of degrees of freedom suitable for continuous finite element spaces, describe considerations for weighted load balancing, and discuss the transfer of variable size data between processes. We illustrate the performance of our algorithms with numerical examples and demonstrate that they scale reasonably up to at least 16,384 message passage interface processes. We provide a reference implementation of our algorithms as part of the open source library deal.II. | |
| dc.format.medium | born digital | |
| dc.format.medium | articles | |
| dc.identifier.bibliographicCitation | Marc Fehling and Wolfgang Bangerth. 2023. Algorithms for Parallel Generic hp-Adaptive Finite Element Software. ACM Trans. Math. Softw. 49, 3, Article 25 (September 2023), 26 pages. https://doi.org/10.1145/3603372 | |
| dc.identifier.doi | https://doi.org/10.1145/3603372 | |
| dc.identifier.uri | https://hdl.handle.net/10217/239513 | |
| dc.language | English | |
| dc.language.iso | eng | |
| dc.publisher | Colorado State University. Libraries | |
| dc.relation.ispartof | Publications | |
| dc.relation.ispartof | ACM DL Digital Library | |
| dc.rights | ©Marc Fehling, et al. ACM 2023. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in ACM Transactions on Mathematical Software, https://dx.doi.org/10.1145/3603372. | |
| dc.subject | parallel algorithms | |
| dc.subject | hp-adaptivity | |
| dc.subject | finite element methods | |
| dc.subject | high performance computing | |
| dc.title | Algorithms for parallel generic hp-adaptive finite element software | |
| dc.type | Text |
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