Efficient Mesh Management in Firedrake Using PETSc DMPlex

Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.

doi:10.1137/15m1026092

Efficient Mesh Management in Firedrake Using PETSc DMPlex

Lange, Michael; Mitchell, Lawrence; Knepley, Matthew G.; Gorman, Gerard J.

Authors

Michael Lange

Lawrence Mitchell

Matthew G. Knepley

Gerard J. Gorman

Abstract

The use of composable abstractions allows the application of new and established algorithms to a wide range of problems, while automatically inheriting the benefits of well-known performance optimizations. This work highlights the composition of the PETSc DMPlex domain topology abstraction with the Firedrake automated finite element system to create a PDE solving environment that combines expressiveness, flexibility, and high performance. We describe how Firedrake utilizes DMPlex to provide the indirection maps required for finite element assembly, while supporting various mesh input formats and runtime domain decomposition. In particular, we describe how DMPlex and its accompanying data structures allow the generic creation of user-defined discretizations, while utilizing data layout optimizations that improve cache coherency and ensure overlapped communication during assembly computation.

Citation

Lange, M., Mitchell, L., Knepley, M. G., & Gorman, G. J. (2016). Efficient Mesh Management in Firedrake Using PETSc DMPlex. SIAM Journal on Scientific Computing, 38(5), S143-S155. https://doi.org/10.1137/15m1026092

Journal Article Type	Article
Acceptance Date	Dec 21, 2015
Online Publication Date	Oct 27, 2016
Publication Date	Oct 27, 2016
Deposit Date	Aug 1, 2018
Publicly Available Date	Aug 2, 2018
Journal	SIAM Journal on Scientific Computing
Print ISSN	1064-8275
Electronic ISSN	1095-7197
Publisher	Society for Industrial and Applied Mathematics
Peer Reviewed	Peer Reviewed
Volume	38
Issue	5
Pages	S143-S155
DOI	https://doi.org/10.1137/15m1026092
Related Public URLs	https://arxiv.org/pdf/1506.07749.pdf