Method of absorbing boundary conditions: Phenomena of error stabilization

摘要

In the problem of diffraction of a time-truncated electromagnetic signal by a perfectly conducting obstacle, the unknown can be chosen to be either the total field around the obstacle or the electric field diffracted by the obstacle. Both problems are usually modelled by time-dependent Maxwell's system in an exterior domain. Their numerical approximation involves an ABC method (so-called Silver-Muller method), which leads to solving two mixed problems in a bounded domain. From a continuous viewpoint, these two problems are equivalent and both solutions tend to zero at long time. From a numerical viewpoint, the long time behaviors of the two solutions differ. The approximate diffracted electric field still tends to zero, but the approximate total electric field stabilizes on a nonzero stationary state. This paper contains numerical experiments showing these so-called phenomena of error stabilization. They are explained by means of an asymptotic analysis of a more general problem. [References: 15]