Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
<p>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 co...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Copernicus Publications
2020-02-01
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| Series: | Geoscientific Model Development |
| Online Access: | https://www.geosci-model-dev.net/13/735/2020/gmd-13-735-2020.pdf |
| _version_ | 1818032997461393408 |
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| author | T. H. Gibson L. Mitchell D. A. Ham C. J. Cotter |
| author_facet | T. H. Gibson L. Mitchell D. A. Ham C. J. Cotter |
| author_sort | T. H. Gibson |
| collection | DOAJ |
| description | <p>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.</p> |
| first_indexed | 2024-12-10T06:16:16Z |
| format | Article |
| id | doaj.art-9c393193eb9945c887254eeb5cac39a2 |
| institution | Directory Open Access Journal |
| issn | 1991-959X 1991-9603 |
| language | English |
| last_indexed | 2024-12-10T06:16:16Z |
| publishDate | 2020-02-01 |
| publisher | Copernicus Publications |
| record_format | Article |
| series | Geoscientific Model Development |
| spelling | doaj.art-9c393193eb9945c887254eeb5cac39a22022-12-22T01:59:27ZengCopernicus PublicationsGeoscientific Model Development1991-959X1991-96032020-02-011373576110.5194/gmd-13-735-2020Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyondT. H. Gibson0L. Mitchell1D. A. Ham2C. J. Cotter3Department of Mathematics, Imperial College London, London, SW7 2AZ, UKDepartment of Computer Science, Durham University, Durham, DH1 3LE, UKDepartment of Mathematics, Imperial College London, London, SW7 2AZ, UKDepartment of Mathematics, Imperial College London, London, SW7 2AZ, UK<p>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.</p>https://www.geosci-model-dev.net/13/735/2020/gmd-13-735-2020.pdf |
| spellingShingle | T. H. Gibson L. Mitchell D. A. Ham C. J. Cotter Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond Geoscientific Model Development |
| title | Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond |
| title_full | Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond |
| title_fullStr | Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond |
| title_full_unstemmed | Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond |
| title_short | Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond |
| title_sort | slate extending firedrake s domain specific abstraction to hybridized solvers for geoscience and beyond |
| url | https://www.geosci-model-dev.net/13/735/2020/gmd-13-735-2020.pdf |
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