russell j. hewett

assistant professor

mathematics & CMDA

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


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 $L^2$ inner product. In applications where the wavespeed varies spatially at a subelement scale, these matrices are distinct over each element, necessitating additional storage. In this work, we propose a weight-adjusted DG (WADG) method that reduces storage costs by replacing the weighted $L^2$ 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.

All publications
SIAM Journal on Scientific Computing