Fast Convolution Quadrature Based Impedance Boundary Conditions

Abstract

We consider an eddy current problem in time-domain relying on impedance boundary conditions on the surface of the conductor(s). We pursue its full discretization comprising (i) a finite element Galerkin discretization by means of lowest order edge elements in space, and (ii) temporal discretization based on Runge-Kutta convolution quadrature (CQ) for the resulting Volterra integral equation in time. The final algorithm also involves the fast and oblivious approximation of CQ. For this method we give a comprehensive convergence analysis and establish that the errors of spatial discretization, CQ and of its approximate realization add up to the final error bound.