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 |
| Summary: | <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> |
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| ISSN: | 1991-959X 1991-9603 |