A Multiscale Hybrid Method
Abstract.
In this work we propose, analyze, and test a new multiscale finite element method called Multiscale Hybrid (MH) method. The method is built as a close relative to the Multiscale Hybrid Mixed (MHM) method, but with the fundamental difference that a novel definition of the Lagrange multiplier is introduced. The practical implication of this is that both the local problems to compute the basis functions, as well as the global problem, are elliptic, as opposed to the MHM method (and also other previous methods) where a mixed global problem is solved and constrained local problems are solved to compute the local basis functions. The error analysis of the method is based on a hybrid formulation, and a static condensation process is done at the discrete level, so the final global system only involves the Lagrange multipliers. We tested the performance of the method by means of numerical experiments for problems with multiscale coefficients, and we carried out comparisons with the MHM method in terms of performance, accuracy, and memory requirements.
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Acknowledgments.
The authors acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer (http://sdumont.lncc.br), which have contributed to the research results reported within this paper.
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Information & Authors
Information
Published In
SIAM Journal on Scientific Computing
Pages: A1628 - A1657
DOI: 10.1137/22M1542556
ISSN (online): 1095-7197
Copyright
© 2024 Society for Industrial and Applied Mathematics.
History
Submitted: 21 December 2022
Accepted: 24 January 2024
Published online: 13 May 2024
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Funding Information
EOLIS: MATH-AMSUD 21-MATH-04
ANID-Chile: FONDECYT-1181572
Leverhulme Trust: RPG-2021-238
Funding: The work of the first author was partially supported by the Leverhulme Trust through the Research Project grant RPG-2021-238. The work of the third author was partially supported by Project EOLIS (MATH-AMSUD 21-MATH-04) and by ANID-Chile through grant FONDECYT-1181572.
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