A hybrid numerical method for elastic wave propagation in discontinuous media with complex geometry

TL;DR

This paper introduces a high-order hybrid numerical method combining finite differences and discontinuous Galerkin techniques for elastic wave propagation in complex media, ensuring accuracy and energy conservation.

Contribution

It presents a novel hybrid approach that integrates Cartesian grid finite differences with unstructured grid discontinuous Galerkin methods using optimized projection operators.

Findings

Achieves high-order accuracy in elastic wave simulations.

Conserves discrete energy in the numerical scheme.

Demonstrates optimal convergence in experiments.

Abstract

We develop a high order accurate numerical method for solving the elastic wave equation in second-order form. We hybridize the computationally efficient Cartesian grid formulation of finite differences with geometrically flexible discontinuous Galerkin methods on unstructured grids by a penalty based technique. At the interface between the two methods, we construct projection operators for the pointwise finite difference solutions and discontinuous Galerkin solutions based on piecewise polynomials. In addition, we optimize the projection operators for both accuracy and spectrum. We prove that the overall discretization conserves a discrete energy, and verify optimal convergence in numerical experiments.