将有限元法和有限差分法结合用于能量守恒的各向同性弹性波模拟
Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner
AI总结：
本文提出了一种将有限元法和有限差分法结合用于各向同性弹性波模拟的方法，通过弱加约束的界面条件实现能量守恒，以应对复杂的地形条件。
摘要：
我们考虑了来自地震应用的各向同性弹性波方程的数值模拟，具有非平凡的陆地地形。更灵活的有限元方法被应用于模拟域的浅层区域以考虑地形，而更高效的有限差分方法则应用于模拟域的深层区域。我们证明了尽管起始于弹性波方程的不同 formulations，这两种离散化方法可以通过弱加约束的界面条件无缝连接。通过离散能量分析推导出适当的界面处理，从而得到一个整体上能量守恒的离散化方案。数值示例用于演示所提出界面处理的有效性。
英文摘要：
We consider numerical simulation of the isotropic elastic wave equations arising from seismic applications with non-trivial land topography. The more flexible finite element method is applied to the shallow region of the simulation domain to account for the topography, and combined with the more efficient finite difference method that is applied to the deep region of the simulation domain. We demonstrate that these two discretization methods, albeit starting from different formulations of the elastic wave equation, can be joined together smoothly via weakly imposed interface conditions. Discrete energy analysis is employed to derive the proper interface treatment, leading to an overall discretization that is energy-conserving. Numerical examples are presented to demonstrate the efficacy of the proposed interface treatment.
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