论文标题
基于不连续的Galerkin的多尺度方法，用于异质弹性波方程
A discontinuous Galerkin based multiscale method for heterogeneous elastic wave equations
论文作者
论文摘要
在本文中，我们为强烈异质介质中的弹性波方程开发了局部多尺度模型策略，这是通过在用多尺度基础函数的粗网格中解决问题来实现的。我们使用内部罚款不连续的Galerkin（IPDG）来对包含重要异构媒体信息的多尺度基础函数。高效的多尺度函数的构建始于提取精心定义的光谱问题的主要模式，以代表重要的媒体特征，然后解决约束能量最小化问题。然后，应用了彼得罗夫 - 盖尔金的投影和系统化对粗网格的系统化。结果，为快速在线模拟获得了明确和节能的方案。只要一个适当地选择了过采样尺寸，该方法就表现出粗线和光谱收敛。我们严格分析了所提出方法的稳定性和收敛性。提供数值结果以显示多尺度方法的性能并确认理论结果。
In this paper, we develop a local multiscale model reduction strategy for the elastic wave equation in strongly heterogeneous media, which is achieved by solving the problem in a coarse mesh with multiscale basis functions. We use the interior penalty discontinuous Galerkin (IPDG) to couple the multiscale basis functions that contain important heterogeneous media information. The construction of efficient multiscale basis functions starts with extracting dominant modes of carefully defined spectral problems to represent important media feature, which is followed by solving a constraint energy minimization problems. Then a Petrov-Galerkin projection and systematization onto the coarse grid is applied. As a result, an explicit and energy conserving scheme is obtained for fast online simulation. The method exhibits both coarse-mesh and spectral convergence as long as one appropriately chose the oversampling size. We rigorously analyze the stability and convergence of the proposed method. Numerical results are provided to show the performance of the multiscale method and confirm the theoretical results.
