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

JOURNAL OF COMPUTATIONAL PHYSICS

卷:377

Article

Nguyen, Lam H.¹  Schillinger, Dominik¹ 

[1] Univ Minnesota, Dept Civil Environm & Geoengn, 500 Pillsbury Dr SE, Minneapolis, MN 55455 USA

关键词: Multiscale finite element method;    Residual-driven correction;    Iterative corrector scheme;    Parallel computing;    Heterogeneous materials;   

DOI  :  10.1016/j.jcp.2018.10.030

来源: Elsevier

【 摘 要 】

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, wellsuited 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. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free