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首页> 外文期刊>Journal of Computational Physics >The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity
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The multiscale finite element method for nonlinear continuum localization problems at full fine-scale fidelity, illustrated through phase-field fracture and plasticity

机译：全尺度保真度下非线性连续内定位问题的多尺度有限元方法，通过相位裂缝和可塑性说明

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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. (C) 2019 Elsevier Inc. All rights reserved.
机译：作者最近针对线性问题提出的残差驱动迭代校正方案为在多尺度有限元法（MsFEM）中实现尽可能高的精细网格精度开辟了一条途径。在这篇文章中，我们重点讨论了一系列算法和变分扩展，这些扩展能够有效地对非线性定位问题进行残差驱动校正。其中包括牛顿迭代和校正器迭代的协同组合，以降低算法复杂性；在伽辽金投影中使用校正器自由度，以消除牛顿迭代过程中多尺度基函数的重复重新计算；以及基于自然残差的全自动细网格自适应策略。我们通过相场断裂和塑性的数值例子说明，带有残余驱动自适应校正的MsFEM实现了完全的精细尺度保真度，同时计算效率也高于原始MsFEM。我们还表明，对于定位问题，它比标准过采样显著提高了精度和鲁棒性。（C） 2019爱思唯尔公司版权所有。

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