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Optimisations for quadrature representations of finite element tensors through automated code generation


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Type

Article

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Authors

Ølgaard, KB 
Wells, GN 

Abstract

We examine aspects of the computation of finite element matrices and vectors which are made possible by automated code generation. Given a variational form in a syntax which resembles standard mathematical notation, the low-level computer code for building finite element tensors, typically matrices, vectors and scalars, can be generated automatically via a form compiler. In particular, the generation of code for computing finite element matrices using a quadrature approach is addressed. For quadrature representations, a number of optimisation strategies which are made possible by automated code generation are presented. The relative performance of two different automatically generated representations of finite element matrices is examined, with a particular emphasis on complicated variational forms. It is shown that approaches which perform best for simple forms are not tractable for more complicated problems in terms of run time performance, the time required to generate the code or the size of the generated code. The approach and optimisations elaborated here are effective for a range of variational forms.

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Keywords

Algorithms, Performance, Finite element method, code generation, VARIATIONAL FORMS, MATRICES, COMPILER

Journal Title

ACM Transactions on Mathematical Software

Conference Name

Journal ISSN

0098-3500
1557-7295

Volume Title

37

Publisher

Association for Computing Machinery, Inc.