Performance measurements of Python tensor contraction packages in the finite element context

Cimrman, Robert

doi:10.5281/zenodo.4750560

Cited by 2 publications

(5 citation statements)

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“…In relation to the reference implementation performance in Section 6.3, we first explore the influence of the operand memory layouts on the performance of the weak Laplacian and Navier-Stokes convection forms in Section 6.4 and then report both relative and absolute results for all the five forms in Section 6.5, considering only the default, SfePy-compatible, layout. All data presented below are available in the form of Pandas DataFrames [20] online [8].…”

Section: Performance Evaluation Resultsmentioning

confidence: 99%

“…The transpiler and einsum expression based weak form implementations are available in SfePy from version 2021.1, allowing a rapid prototyping of multi-physical finite element models and subsequent calculations in various fields such as biomechanics [30] or solid state physics [22]. All data used in preparation of this paper are available online [8].…”

Section: Discussionmentioning

confidence: 99%

“…On the other hand, the memory consumption is given as the maximum over the repeated evaluations, denoted M max , because it determines whether a problem can be calculated within available RAM or not. Although not included in the paper, the complete data [8] contain all the other statistics (means, minima, maxima, ranks etc. )…”

Section: Choice Of Performance Indicatorsmentioning

confidence: 99%

“…8, where the fastest layouts for each FE approximation order and einsum backend are listed, together with T ww / T ww…”

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confidence: 99%

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Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Cimrman

2021

Preprint

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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.

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Section: Performance Evaluation Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Choice Of Performance Indicatorsmentioning

confidence: 99%

“…8, where the fastest layouts for each FE approximation order and einsum backend are listed, together with T ww / T ww…”

mentioning

confidence: 99%

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Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Cimrman

2021

Preprint

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“…In (Cimrman, 2021a) a transpiler ** was proposed for translating generalized einsum-like expressions to the actual einsum expressions for evaluating multilinear finite element weak forms. A desirable side effect of this approach was an efficient (in terms of elapsed time) support for higher-order approximations, as was shown in the article (all obtained data are available online (Cimrman, 2021b)).…”

Section: Introductionmentioning

confidence: 92%

Leveraging Python tensor contraction packages for evaluating finite element weak forms

Cimrman¹

2022

Engineering Mechanics

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A new implementation of finite element matrix evaluation functions in the finite element code SfePy is introduced, leveraging several Python tensor contraction packages that implement a general function for evaluating expressions given using the Einstein summation convention. An example of the new weak form implementation is shown, and then results of a numerical study are presented comparing performance of the new implementation, the original implementation, and FEniCS suite.

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Performance measurements of Python tensor contraction packages in the finite element context

Cited by 2 publications

References 0 publications

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Fast Evaluation of Finite Element Weak Forms Using Python Tensor Contraction Packages

Leveraging Python tensor contraction packages for evaluating finite element weak forms

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