The Adaptive Cross Approximation Algorithm for Accelerated Method of Moments Computations of EMC Problems

Abstract

This paper presents the adaptive cross approximation (ACA) algorithm to reduce memory and CPU time overhead in the method of moments (MoM) solution of surface integral equations. The present algorithm is purely algebraic; hence, its formulation and implementation are integral equation kernel (Green's function) independent. The algorithm starts with a multilevel partitioning of the computational domain. The interactions of well-separated partitioning clusters are accounted through a rank-revealing LU decomposition. The acceleration and memory savings of ACA come from the partial assembly of the rank-deficient interaction submatrices. It has been demonstrated that the ACA algorithm results in O(NlogN) complexity (where N is the number of unknowns) when applied to static and electrically small electromagnetic problems. In this paper the ACA algorithm is extended to electromagnetic compatibility-related problems of moderate electrical size. Specifically, the ACA algorithm is used to study compact-range ground planes and electromagnetic interference and shielding in vehicles. Through numerical experiments, it is concluded that for moderate electrical size problems the memory and CPU time requirements for the ACA algorithm scale as N/sup 4/3/logN.