We consider the finite difference discretization of isotropic elastic wave equations on nonuniform grids. The intended applications are seismic studies, where heterogeneity of the earth media can lead to severe oversampling for simulations on uniform grids. To address this issue, we demonstrate how to properly couple two non-overlapping neighboring subdomains that are discretized uniformly, but with different grid spacings. Specifically, a numerical procedure is presented to impose the interface conditions weakly through carefully designed penalty terms, such that the overall semi-discretization conserves a discrete energy resembling the continuous energy possessed by the elastic wave system.
翻译:我们考虑的是非统一网格上的异位弹性波方程式的有限差异分化。 打算应用的用途是地震研究,其中地球介质的异质可能导致在统一网格上对模拟进行严重过度采样。 为解决这一问题,我们演示了如何适当地将两个不重叠的相邻次域对齐,这些相邻区域是统一的,但有不同的网格间距。 具体地说,我们提出了一个数字程序,通过精心设计的处罚条件,对界面条件进行微弱的强制,这样整个半分解半分解法可以保存一种与弹性波系统所拥有连续能量相仿的离散能量。