论文标题
显式和持势的约束能量最大程度地降低了多尺度不连续的盖尔金方法，用于在异质介质中的波传播
Explicit and Energy-Conserving Constraint Energy Minimizing Generalized Multiscale Discontinuous Galerkin Method for Wave Propagation in Heterogeneous Media
论文作者
论文摘要
在这项工作中，我们为异源介质中的时域标量波方程提出了局部多尺度模型减少方法。一个细网格用于捕获系数场的异质性，并且该方程在不连续的Galerkin离散设置中的粗网格上全球求解。模型还原方法的主要思想是在局部光谱问题中提取主要模式，以表示重要特征，通过约束能量最小化问题在粗大的过采样区域中构建多尺度基础功能，并执行Petrov-Galerkin投影，并在粗网格上进行对称。该方法是逃脱和节能，只要选择了过采样尺寸，就可以表现出粗线和光谱收敛。我们研究方法的稳定性和收敛性。我们还对Marmousi模型提出了数值结果，以测试该方法的性能并验证理论结果。
In this work, we propose a local multiscale model reduction approach for the time-domain scalar wave equation in a heterogenous media. A fine mesh is used to capture the heterogeneities of the coefficient field, and the equation is solved globally on a coarse mesh in the discontinuous Galerkin discretization setting. The main idea of the model reduction approach is to extract dominant modes in local spectral problems for representation of important features, construct multiscale basis functions in coarse oversampled regions by constraint energy minimization problems, and perform a Petrov-Galerkin projection and a symmetrization onto the coarse grid. The method is expicit and energy conserving, and exhibits both coarse-mesh and spectral convergence, provided that the oversampling size is appropriately chosen. We study the stability and convergence of our method. We also present numerical results on the Marmousi model in order to test the performance of the method and verify the theoretical results.
