Using tap basis to implement the equivalence principle algorithm for domain decomposition in integral equations

Abstract

A domain decomposition scheme based on the equivalence principle, also known as Huygens' principle, for integral equation solvers and the method of moments is introduced here. The equivalence principle allows the replacement of unknown currents distributed in a volume in space by equivalent currents residing on the surface that bounds the volume. In this manner, a problem of high complexity can be replaced by a surface of simpler shape. A tap basis is introduced to model the current that intercepts with the equivalence surfaces. Using this scheme, the current continuity is conserved and the singularity of the charges is avoided. The solution is shown to be accurate. © 2006 Wiley Periodicals, Inc.