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

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Title: Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
Authors: Gibson, T
Mitchell, L
Ham, D
Cotter, C
Item Type: Journal Article
Abstract: Within the finite element community, discontinuous Galerkin (DG) and mixed finite element methods have becomeincreasingly popular in simulating geophysical flows. However, robust and efficient solvers for the resulting saddle-point andelliptic systems arising from these discretizations continue to be an on-going challenge. One possible approach for addressingthis issue is to employ a method known as hybridization, where the discrete equations are transformed such that classic staticcondensation and local post-processing methods can be employed. However, it is challenging to implement hybridization as performant parallel code within complex models, whilst maintaining separation of concerns between applications scientistsand software experts. In this paper, we introduce a domain-specific abstraction within the Firedrake finite element library thatpermits the rapid execution of these hybridization techniques within a code-generating framework. The resulting frameworkcomposes naturally with Firedrake’s solver environment, allowing for the implementation of hybridization and static condensa-tion as runtime-configurable preconditioners via the Python interface to PETSc, petsc4py. We provide examples derived from second order elliptic problems and geophysical fluid dynamics. In addition, we demonstrate that hybridization shows greatpromise for improving the performance of solvers for mixed finite element discretizations of equations related to large-scalegeophysical flows.
Issue Date: 25-Feb-2020
Date of Acceptance: 26-Nov-2019
URI: http://hdl.handle.net/10044/1/75411
DOI: 10.5194/gmd-13-735-2020
ISSN: 1991-959X
Publisher: Copernicus Publications
Start Page: 735
End Page: 761
Journal / Book Title: Geoscientific Model Development
Volume: 13
Copyright Statement: © Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License (https://creativecommons.org/licenses/by/4.0/)
Sponsor/Funder: Natural Environment Research Council (NERC)
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: NE/K008951/1
EP/L000407/1
EP/M011054/1
Keywords: Science & Technology
Physical Sciences
Geosciences, Multidisciplinary
Geology
MIXED FINITE-ELEMENTS
SHALLOW-WATER EQUATIONS
DISCONTINUOUS GALERKIN METHODS
HDG
SCHEMES
INDEFINITE
H(DIV)
DISCRETIZATION
CONVERGENCE
ACCURACY
04 Earth Sciences
Publication Status: Published
Appears in Collections:Faculty of Engineering
Mathematics
Computing
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences
Grantham Institute for Climate Change