Title:	Fast evaluation of finite element weak forms using python tensor contraction packages
Authors:	Cimrman, Robert
Citation:	CIMRMAN, R. Fast evaluation of finite element weak forms using python tensor contraction packages. Advances in engineering software, 2021, roč. 159, č. 20. July 2021. ISSN 0965-9978.
Issue Date:	2021
Publisher:	Elsevier
Document type:	článek article
URI:	2-s2.0-85110434316 http://hdl.handle.net/11025/45055
ISSN:	0965-9978
Keywords in different language:	Finite element method;Tensor contractions;Weak form transpiler;Numerical performance study
Abstract in different language:	In finite element calculations, the integral forms are usually evaluated using nested loops over elements, and over quadrature points. Many such forms (e.g. linear or multi-linear) can be expressed in a compact way, without the explicit loops, using a single tensor contraction expression by employing the Einstein summation convention. To automate this process and leverage existing high performance codes, we first introduce a notation allowing trivial differentiation of multi-linear finite element forms. Based on that we propose and describe a new transpiler from Einstein summation based expressions, augmented to allow defining multi-linear finite element weak forms, to regular tensor contraction expressions. The resulting expressions are compatible with a number of Python scientific computing packages, that implement, optimize and in some cases parallelize the general tensor contractions. We assess the performance of those packages, as well as the influence of operand memory layouts and tensor contraction paths optimizations on the elapsed time and memory requirements of the finite element form evaluations. We also compare the efficiency of the transpiled weak form implementations to the C-based functions available in the finite element package SfePy.
Rights:	© Elsevier
Appears in Collections:	Články / Articles OBD

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