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Automating the finite element method

Journal article
Authors Anders Logg
Published in Archives of Computational Methods in Engineering
Volume 14
Issue 2
Pages 93-138
ISSN 1134-3060
Publication year 2007
Published at Department of Mathematical Sciences, Mathematics
Pages 93-138
Language en
Links dx.doi.org/10.1007/s11831-007-9003-...
Subject categories Mathematics, Computational Mathematics

Abstract

The finite element method can be viewed as a machine that automates the discretization of differential equations, taking as input a variational problem, a finite element and a mesh, and producing as output a system of discrete equations. However, the generality of the framework provided by the finite element method is seldom reflected in implementations (realizations), which are often specialized and can handle only a small set of variational problems and finite elements (but are typically parametrized over the choice of mesh). This paper reviews ongoing research in the direction of a complete automation of the finite element method. In particular, this work discusses algorithms for the efficient and automatic computation of a system of discrete equations from a given variational problem, finite element and mesh. It is demonstrated that by automatically generating and compiling efficient low-level code, it is possible to parametrize a finite element code over variational problem and finite element in addition to the mesh.

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