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PCPATCH: software for the topological construction of multigrid relaxation methods

Farrell, Patrick E.; Knepley, Matthew G.; Mitchell, Lawrence; Wechsung, Florian

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Authors

Patrick E. Farrell

Matthew G. Knepley

Lawrence Mitchell

Florian Wechsung



Abstract

Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this paper we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems.

Citation

Farrell, P. E., Knepley, M. G., Mitchell, L., & Wechsung, F. (2021). PCPATCH: software for the topological construction of multigrid relaxation methods. ACM Transactions on Mathematical Software, 47(3), 1-22. https://doi.org/10.1145/3445791

Journal Article Type Article
Acceptance Date Dec 21, 2020
Online Publication Date Jun 26, 2021
Publication Date 2021-06
Deposit Date Feb 17, 2020
Publicly Available Date Feb 4, 2021
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 47
Issue 3
Article Number 25
Pages 1-22
DOI https://doi.org/10.1145/3445791
Related Public URLs https://arxiv.org/pdf/1912.08516.pdf

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Copyright Statement
© Owner/Author | ACM 2021. 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://doi.org/10.1145/10.1145/3445791




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