Comparison of algorithms to solve sparse matrix in EM scattering problem

Abstract

In applying the method of moments to solve the EM scattering problems, it is necessary to solve a large matrix when the dimension of the scatterer is larger than several wavelengths. Tremendous amount of computer CPU time will be spent on solving the matrix equation. When only the far field properties such as scattering cross section is of interest, we can use the sparse matrix technique to reduce the amount of compucation. In this paper, some algorithms are compared to solve the sparse matrix. The Gaussian elimina$ion algorithm, Cholesky decomposition algorithm, several versions of conjugate gradient methods are used. The number of multiplications and divisions(fl0ps) are counted for comparing the efficiency of these algorithms. The effect of the nonzero element positions to the efficiency is also studied by defining the clustering index.