Arrangement of sources in the charge simulation method–the case of e‐wave scattering by one perfectly conducting cylinder of convex cross section shape

Abstract

AbstractThe charge simulation method has the following characteristics compared with other approximate methods for the scatteirng problems: (1) Only the zeroth and first‐order Hankel functions are used; (2) no processing of the singularities on the boundary is needed; (3) no numerical integration is necessary. As a result, it is an extremely simple method. However, the arrangements of the sources and contour points are arbitrary and such arrangements affect the accuracy of the approximate solutions. Previously, the source arrangements by the boundary contractions have been used in the charge simulation method. This choice provides good results if the shape of the scatterer is close to a circle or is a circle itself. The accuracy becomes poorer as the shape deviates more from the circle. Also, it is not possible to determine beforehand the arrangement that provides the best result. Hence, the boundary contraction is an important arrangement method. In this paper, arrangement of the sources and contour points is determined by means of the conformal mapping that transforms the boundary to a circle. Numerical calculations have been performed for typical convex shapes. It is found that the charge simulation method based on the present arrangement has the following properties. It exhibits much better accuracy than the arrangement by boundary contraction. The arrangement minimizing the error is found from the conformal mapping. Scatterers with edges on the boundary cannot be analyzed.