  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.
