A high order compact time/space finite difference scheme for the 2D and 3D wave equation with a damping layer

Abstract

We consider fourth order accurate compact schemes, in both space and time, for the second order wave equation with a variable speed of sound. For unbounded domains we add a fourth order accurate sponge layer to damp the outgoing waves. We demonstrate that usually this is more efficient than lower order schemes despite being implicit and conditionally stable. Fast time marching of the implicit scheme is accomplished by iterative methods such as multi-grid. Computations confirm the design convergence rate for the in-homogeneous, variable wave speed equation.