Weight-adjusted discontinuous Galerkin methods: matrix-valued weights and elastic wave propagation in heterogeneous media

Abstract

Weight-adjusted inner products are easily invertible approximations to weighted $L^2$ inner products. These approximations can be paired with a discontinuous Galerkin (DG) discretization to produce a time-domain method for wave propagation which is low storage, energy stable, and high order accurate for arbitrary heterogeneous media and curvilinear meshes. In this work, we extend weight-adjusted DG (WADG) methods to the case of matrix-valued weights, with the linear elastic wave equation as an application. We present a DG formulation of the symmetric form of the linear elastic wave equation, with upwind-like dissipation incorporated through simple penalty fluxes. A semi-discrete convergence analysis is given, and numerical results confirm the stability and high order accuracy of WADG for several problems in elastic wave propagation.

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Cited by in corpus (3)

• A weight-adjusted discontinuous Galerkin method for the poroelastic wave equation: penalty fluxes and micro-heterogeneities
• A weight-adjusted discontinuous Galerkin method for wave propagation in coupled elastic-acoustic media
• High order weight-adjusted discontinuous Galerkin methods for wave propagation on moving curved meshes