论文标题
高对比度系数的不均匀弹性问题的多尺度方法
A multiscale method for inhomogeneous elastic problems with high contrast coefficients
论文作者
论文摘要
在本文中，我们开发了有限的能量最小化通用的多尺度有限元法（CEM-GMSFEM），具有混合边界条件（Dirichlet和Neumann），以用于高对比度介质中的弹性方程。通过分别对混合边界条件的特殊处理，并结合了CEM-GMSFEM的松弛和约束版本的构建，我们发现该方法具有一些优势，例如目标区域与精确的对比度的独立性，而过度更新域的尺寸对数值准确性产生了重大影响。此外，据我们所知，这是CEM-GMSFEM与给定弹性方程的混合边界条件收敛的第一个证明。提供了一些数值实验来证明该方法的性能。
In this paper, we develop the constrained energy minimizing generalized multiscale finite element method (CEM-GMsFEM) with mixed boundary conditions (Dirichlet and Neumann) for the elasticity equations in high contrast media. By a special treatment of mixed boundary conditions separately, and combining the construction of the relaxed and constraint version of the CEM-GMsFEM, we discover that the method offers some advantages such as the independence of the target region's contrast from precision, while the sizes of oversampling domains have a significant impact on numerical accuracy. Moreover, to our best knowledge, this is the first proof of the convergence of the CEM-GMsFEM with mixed boundary conditions for the elasticity equations given. Some numerical experiments are provided to demonstrate the method's performance.
