Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
Multiscale Modeling, Homogenization and Nonlocal Effects: Mathematical and Computational Issues
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DOI：
10.1090/conm/754/15175
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Q. Du;B. Engquist;Xiaochuan Tian
中科院分区：
文献类型：
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作者：
Q. Du;B. Engquist;Xiaochuan Tian
在这项工作中，我们回顾了同质化主题和非局部建模之间的联系，并讨论了相关的计算问题。通过进一步探索这种联系，我们希望促进不同研究前沿思想的交叉融合。我们说明同质化如何有助于表征非局部模型中假设的非局部相互作用的性质和形式。我们还提供了一些关于非局域性研究如何帮助开发更有效的均质化数值方法的观点。
In this work, we review the connection between the subjects of homogenization and nonlocal modeling and discuss the relevant computational issues. By further exploring this connection, we hope to promote the cross fertilization of ideas from the different research fronts. We illustrate how homogenization may help characterizing the nature and the form of nonlocal interactions hypothesized in nonlocal models. We also offer some perspective on how studies of nonlocality may help the development of more effective numerical methods for homogenization.