Error analysis of equivalence principle algorithm on different equivalence surfaces

Abstract

Equivalence principle algorithm( EPA) is a domain decomposition algorithm based on the Huygens' equivalence principle to solve large scale scattering problems. The errors of the equivalence principle operator( EPO) in EPA using cubic,spherical and smooth cubic equivalence surfaces were analyzed to find the source of errors. The sources of the error were investigated and a simple scheme to improve its accuracy was developed. From the numerical examples,it shows that the error of equivalent magnetic current is mainly concentrated on geometrical discontinuity of the equivalence surface,and affected by both the discontinuity of the normal vector on the equivalence surface and the choice of basis functions. Therefore it is suggested to choose smooth equivalence surfaces if possible rather than to use cubic ones directly.