Weight-adjusted discontinuous Galerkin methods: wave propagation in heterogeneous media
For computational scientists simulating wave propagation in heterogeneous media, this method reduces memory requirements without sacrificing accuracy or stability.
The paper tackles the storage cost problem in discontinuous Galerkin methods for wave propagation in heterogeneous media, where dense elemental mass matrices vary per element. The proposed weight-adjusted DG method reduces storage costs while maintaining energy stability, with a-priori error estimates and numerical validation.
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.