Robert C. Kirby
Solver Composition Across the PDE/Linear Algebra Barrier
Kirby, Robert C.; Mitchell, Lawrence
Authors
Lawrence Mitchell
Abstract
The efficient solution of discretizations of coupled systems of partial differential equations (PDEs) is at the core of much of numerical simulation. Significant effort has been expended on scalable algorithms to precondition Krylov iterations for the linear systems that arise. With few exceptions, the reported numerical implementation of such solution strategies is specific to a particular model setup, and intimately ties the solver strategy to the discretization and PDE, especially when the preconditioner requires auxiliary operators. In this paper, we present recent improvements in the Firedrake finite element library that allow for straightforward development of the building blocks of extensible, composable preconditioners that decouple the solver from the model formulation. Our implementation extends the algebraic composability of linear solvers offered by the PETSc library by augmenting operators, and hence preconditioners, with the ability to provide any necessary auxiliary operators. Rather than specifying up front the full solver configuration tied to the model, solvers can be developed independently of model formulation and configured at runtime. We illustrate with examples from incompressible fluids and temperature-driven convection.
Citation
Kirby, R. C., & Mitchell, L. (2018). Solver Composition Across the PDE/Linear Algebra Barrier. SIAM Journal on Scientific Computing, 40(1), C76-C98. https://doi.org/10.1137/17m1133208
Journal Article Type | Article |
---|---|
Acceptance Date | Nov 7, 2017 |
Online Publication Date | Feb 15, 2018 |
Publication Date | Feb 15, 2018 |
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 | 40 |
Issue | 1 |
Pages | C76-C98 |
DOI | https://doi.org/10.1137/17m1133208 |
Related Public URLs | https://arxiv.org/pdf/1706.01346.pdf |
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Copyright Statement
© 2018 SIAM. Published by SIAM under the terms of the Creative Commons 4.0 license
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