Time-domain Dirichlet-to-Neumann map and its discretization

In this work we consider the wave equation in homogeneous, unbounded domains and its numerical solution. In particular, we are interested in the effect that the shape of a bounded obstacle has on the quality of some numerical schemes for the computation of the exterior Dirichlet-to-Neumann map. We discretize the Dirichlet-to-Neumann map in time by convolution quadrature and investigate how the correct choice of time step depends on the highest frequency present in the system, the shape of the scatterer and the type of convolution quadrature used (linear multistep or Runge–Kutta) and its convergence order.