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Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond

Gibson, Thomas H.; Mitchell, Lawrence; Ham, David A.; Cotter, Colin J.

Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond Thumbnail


Authors

Thomas H. Gibson

Lawrence Mitchell

David A. Ham

Colin J. Cotter



Abstract

Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have become increasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle point and elliptic systems arising from these discretizations continue to be an ongoing challenge. One possible approach for addressing this issue is to employ a method known as hybridization, where the discrete equations are transformed such that classic static condensation and local post-processing methods can be employed. However, it is challenging to implement hybridization as performant parallel code within complex models whilst maintaining a separation of concerns between applications scientists and software experts. In this paper, we introduce a domain-specific abstraction within the Firedrake finite element library that permits the rapid execution of these hybridization techniques within a code-generating framework. The resulting framework composes naturally with Firedrake's solver environment, allowing for the implementation of hybridization and static condensation as runtime-configurable preconditioners via the Python interface to the Portable, Extensible Toolkit for Scientific Computation (PETSc), petsc4py. We provide examples derived from second-order elliptic problems and geophysical fluid dynamics. In addition, we demonstrate that hybridization shows great promise for improving the performance of solvers for mixed finite element discretizations of equations related to large-scale geophysical flows.

Citation

Gibson, T. H., Mitchell, L., Ham, D. A., & Cotter, C. J. (2020). Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond. Geoscientific Model Development, 13(2), 735-761. https://doi.org/10.5194/gmd-13-735-2020

Journal Article Type Article
Acceptance Date Nov 25, 2019
Online Publication Date Feb 25, 2020
Publication Date Feb 29, 2020
Deposit Date Mar 11, 2020
Publicly Available Date Mar 29, 2024
Journal Geoscientific Model Development
Print ISSN 1991-959X
Electronic ISSN 1991-9603
Publisher European Geosciences Union
Peer Reviewed Peer Reviewed
Volume 13
Issue 2
Pages 735-761
DOI https://doi.org/10.5194/gmd-13-735-2020

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