Numerical solution of exterior Maxwell problems by Galerkin BEM and Runge-Kutta convolution quadrature (Q1944004)

The paper is concerned with the numerical approximation of time-dependent boundary integral equations arising in electromagnetic scattering. The authors consider the three-dimensional exterior scattering problem from a perfectly conducting obstacle in a homogeneous isotropic medium. In order to solve the resulting time-domain electric field integral equation they use a Runge-Kutta convolution quadrature for the time discretization and a Galerkin BEM with Raviart-Thomas elements of lowest order for the spatial discretization. They analyze the involved operators in the Laplace domain and obtain error estimates for the semi-discrete scheme and for the fully discrete scheme. Numerical experiments in the case of a spherical scatterer indicate that the derived error estimates are sharp.