A residual-driven local iterative corrector scheme for the multiscale finite element method
A residual-driven local iterative corrector scheme for the multiscale finite element method
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DOI：
10.1016/j.jcp.2018.10.030
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发表时间：
2019-01
期刊：
影响因子：
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通讯作者：
L. H. Nguyen;D. Schillinger
中科院分区：
文献类型：
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作者：
L. H. Nguyen;D. Schillinger
我们描述了一种局部迭代校正方案，它显著提高了多尺度有限元方法(Msfem)的精度。我们的技术是基于对每个多尺度基函数的局部校正器问题的定义，该多尺度基函数由先前多尺度解的残差驱动。每个校正器问题产生一个局部校正器解，该局部校正器解决方案提高了元素界面上相应的多尺度基函数的精度。我们将残差驱动校正策略转化为一种易于实现的迭代方案，并且由于校正器问题的局部性，非常适合于并行计算。我们证明了迭代格式收敛到可能的最优细网格解。最后，我们以缺少尺度分离为特征的多尺度基准来说明我们方法的有效性，包括基于MicroCT的具有骨小梁微结构的椎骨的应力分析。
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.