A residual-driven local iterative corrector scheme for the multiscale finite element method

Lam H. Nguyen, Dominik Schillinger

Research output: Contribution to journalArticle

Abstract

We describe a local iterative corrector scheme that significantly improves the accuracy of the multiscale finite element method (MsFEM). Our technique is based on the definition of a local corrector problem for each multiscale basis function that is driven by the residual of the previous multiscale solution. Each corrector problem results in a local corrector solution that improves the accuracy of the corresponding multiscale basis function at element interfaces. We cast the strategy of residual-driven correction in an iterative scheme that is straightforward to implement and, due to the locality of corrector problems, well-suited for parallel computing. We show that the iterative scheme converges to the best possible fine-mesh solution. Finally, we illustrate the effectiveness of our approach with multiscale benchmarks characterized by missing scale separation, including the microCT-based stress analysis of a vertebra with trabecular microstructure.

LanguageEnglish (US)
Pages60-88
Number of pages29
JournalJournal of Computational Physics
Volume377
DOIs
StatePublished - Jan 15 2019

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finite element method
Finite element method
vertebrae
stress analysis
Parallel processing systems
Stress analysis
casts
mesh
microstructure
Microstructure

Keywords

  • Heterogeneous materials
  • Iterative corrector scheme
  • Multiscale finite element method
  • Parallel computing
  • Residual-driven correction

Cite this

A residual-driven local iterative corrector scheme for the multiscale finite element method. / Nguyen, Lam H.; Schillinger, Dominik.

In: Journal of Computational Physics, Vol. 377, 15.01.2019, p. 60-88.

Research output: Contribution to journalArticle

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