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.
Bibliographical noteFunding Information:
The authors gratefully acknowledge support from the National Science Foundation via the NSF grant CISE-1565997 . The first author (L.H. Nguyen) was partially supported by a Doctoral Dissertation Fellowship awarded by the University of Minnesota for the academic year 2017–2018. The second author (D. Schillinger) gratefully acknowledges support from the National Science Foundation through the NSF CAREER Award No. 1651577 .
- Heterogeneous materials
- Iterative corrector scheme
- Multiscale finite element method
- Parallel computing
- Residual-driven correction