The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity
The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity
复制标题
DOI：
10.1016/j.jcp.2019.06.058
复制
发表时间：
2019-11
期刊：
影响因子：
--
通讯作者：
L. H. Nguyen;D. Schillinger
中科院分区：
文献类型：
--
作者：
L. H. Nguyen;D. Schillinger
作者最近提出的残差驱动的迭代校正方案的线性问题，开辟了一条途径，以实现最佳的细网格精度的多尺度有限元法（MsFEM）。在这篇文章中，我们专注于一系列的算法和变分扩展，使有效的剩余驱动校正非线性局部化问题。这些措施包括协同组合的牛顿和校正迭代，以降低算法的复杂性，使用校正度的自由度的Galerkin投影，以消除重复重新计算的多尺度基函数在牛顿迭代，和自然的残差为基础的战略，全自动细网格自适应。我们通过相场断裂和塑性的数值例子说明，残余驱动的自适应校正的MsFEM实现了全精细尺度保真度，同时也比原始MsFEM计算更有效。我们还表明，对于本地化问题，它显着提高了准确性和鲁棒性超过标准过采样。
The residual-driven iterative corrector scheme recently presented by the authors for linear problems has opened a pathway to achieve the best possible fine-mesh accuracy in the multiscale finite element method (MsFEM). In this article, we focus on a series of algorithmic and variational extensions that enable efficient residual-driven correction for nonlinear localization problems. These include a synergistic combination of Newton and corrector iterations to reduce the algorithmic complexity, the use of corrector degrees of freedom in the Galerkin projection to eliminate the repeated recomputation of multiscale basis functions during Newton iterations, and a natural residual-based strategy for fully automatic fine-mesh adaptivity. We illustrate through numerical examples from phase-field fracture and plasticity that the MsFEM with residual-driven adaptive correction achieves full fine-scale fidelity while also being computationally more efficient than the pristine MsFEM. We also show that for localization problems, it significantly increases accuracy and robustness over standard oversampling.