Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

L. Gao, D.E. Keyes
Journal of Computational Physics, volume 378, pp. 665-685, (2019)

Combining finite element and finite difference methods for isotropic elastic wave simulations in an energy-conserving manner

Keywords

Finite element method, Finite difference method, Interface treatment, Elastic wave equation, Discrete energy analysis, Simultaneous approximation terms

Abstract

​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.

Code

DOI: 10.1016/j.jcp.2018.11.031

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