Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media

Abstract

Time-domain discontinuous Galerkin (DG) methods for wave propagation require accounting for the inversion of dense elemental mass matrices, where each mass matrix is computed with respect to a parameter-weighted L2 inner product. In applications where the wavespeed varies spatially at a sub-element scale, these matrices are distinct over each element, necessitating additional storage. In this work, we propose a weight-adjusted DG (WADG) method which reduces storage costs by replacing the weighted L2 inner product with a weight-adjusted inner product. This equivalent inner product results in an energy stable method, but does not increase storage costs for locally varying weights. A-priori error estimates are derived, and numerical examples are given illustrating the application of this method to the acoustic wave equation with heterogeneous wavespeed.

arXiv commentSubmitted to SISC

References in corpus (3)

• Nodal Discontinuous Galerkin Methods on Graphics Processors
• Nodal Discontinuous Galerkin Simulations for Reverse-Time Migration on GPU Clusters
• GPU-accelerated Bernstein-Bezier discontinuous Galerkin methods for wave problems

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