Comparative Study of Finite Element Methods Using the Time-Accuracy-Size(TAS) Spectrum Analysis

We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit analysis can be performed to determine which...

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Bibliographic Details
Published in:SIAM journal on scientific computing 2018-01, Vol.40 (6), p.C779-C802
Main Authors: Chang, Justin, Fabien, Maurice S., Knepley, Matthew G., Mills, Richard T.
Format: Article
Language:English
Subjects:
finite element methods
MATHEMATICS AND COMPUTING
numerical accuracy
parallel computing
performance modeling
scientific software libraries
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Summary:We present a performance analysis appropriate for comparing algorithms using different numerical discretizations. By taking into account the total time-to-solution, numerical accuracy with respect to an error norm, and the computation rate, a cost-benefit analysis can be performed to determine which algorithm and discretization are particularly suited for an application. This work extends the performance spectrum model in for interpretation of hardware and algorithmic tradeoffs in numerical PDE simulation. As a proof-of-concept, popular finite element software packages are used to illustrate this analysis for Poisson’s equation.
ISSN:1064-8275
1095-7197
DOI:10.1137/18M1172260