A p-version of convolution quadrature in wave propagation

Abstract

In this talk, we present a novel approach towards boundary element methods for wave propagation. It is based on the convolution quadrature idea by Lubich, but instead of relying on reducing the timestep size to achieve higher accuracy, we use the p-refinement paradigm of increasing the order of the method while keeping the timestep size fixed. To get an easily computable and analyzable scheme, we rely on the ideas of discontinuous Galerkin timestepping. This allows us to design a scheme which is root-exponentially convergent for certain very smooth initial conditions. We talk about possibilities to analyze this new scheme, as well its practical implementation and challenges. Finally, we show some numerical examples of the method in practice.