A P-Version of Convolution Quadrature in Wave Propagation

Abstract

We consider a novel way of discretizing wave scattering problems using the general formalism of convolution quadrature, but instead of reducing the time step size (h-method), we achieve accuracy by increasing the order of the method (p-method). We base this method on discontinuous Galerkin time stepping and use the Z-transform. We show that for a certain class of incident waves, the resulting schemes observe a (root)-exponential convergence rate with respect to the number of boundary integral operators that need to be applied. Numerical experiments confirm the finding.