Imperial College London


Faculty of Natural SciencesDepartment of Mathematics

Professor of Computational Mathematics



+44 (0)20 7594 3468colin.cotter




755Huxley BuildingSouth Kensington Campus






BibTex format

author = {Gibson, T and Mitchell, L and Ham, D and Cotter, C},
doi = {10.5194/gmd-13-735-2020},
journal = {Geoscientific Model Development},
pages = {735--761},
title = {Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond},
url = {},
volume = {13},
year = {2020}

RIS format (EndNote, RefMan)

AB - 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.
AU - Gibson,T
AU - Mitchell,L
AU - Ham,D
AU - Cotter,C
DO - 10.5194/gmd-13-735-2020
EP - 761
PY - 2020///
SN - 1991-959X
SP - 735
TI - Slate: extending Firedrake's domain-specific abstraction to hybridized solvers for geoscience and beyond
T2 - Geoscientific Model Development
UR -
UR -
VL - 13
ER -