Instabilities in Time Marching Methods for Scattering: Cause and Rectification

Abstract

ABSTRACT The occurrence of exponentially increasing instabilities is a common feature of time-marching methods for solving an integral equation arising in a transient scattering problem. The cause of this instability is shown to be related to the interior resonances of the scatterer at which the corresponding frequency domain integral equation fails to have a unique solution. This type of instability is eliminated by an averaging process. The necessary modifications to any existing computer programs are trivial and increase computational cost by about 10%.