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

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.

References in corpus (5)

• Review of Summation-by-parts schemes for initial-boundary-value problems
• Summation-By-Parts Operators and High-Order Quadrature
• Stable Coupling of Nonconforming, High-Order Finite Difference Methods
• High order finite difference methods for the wave equation with non-conforming grid interfaces
• Stable difference methods for block-oriented adaptive grids

Cited by in corpus (5)

• Elastic wave propagation in anisotropic solids using energy-stable finite differences with weakly enforced boundary and interface conditions
• Order Preserving Interpolation for Summation-by-Parts Operators at Non-Conforming Grid Interfaces
• Energy conservative SBP discretizations of the acoustic wave equation in covariant form on staggered curvilinear grids
• Energy stable and accurate coupling of finite element methods and finite difference methods
• Explicit coupling of acoustic and elastic wave propagation in finite difference simulations