TY - JOUR
T1 - A residual-driven local iterative corrector scheme for the multiscale finite element method
AU - Nguyen, Lam H.
AU - Schillinger, Dominik
N1 - Publisher Copyright:
© 2018 Elsevier Inc.
PY - 2019/1/15
Y1 - 2019/1/15
N2 - 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.
AB - 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.
KW - Heterogeneous materials
KW - Iterative corrector scheme
KW - Multiscale finite element method
KW - Parallel computing
KW - Residual-driven correction
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U2 - 10.1016/j.jcp.2018.10.030
DO - 10.1016/j.jcp.2018.10.030
M3 - Article
AN - SCOPUS:85055579087
SN - 0021-9991
VL - 377
SP - 60
EP - 88
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -