Complex Source Beam-Moment Method Procedure for Accelerating Numerical Integral Equation Solutions of Radiation and Scattering Problems

Abstract

A new hybrid complex source beam-moment method (CSB-MoM) procedure is presented to accelerate the matrix-vector product (MVP) computation in the iterative solution of moment method integral equation problems. The scattering object in this CSB-MoM algorithm is partitioned into groups in a manner similar to the fast multipole method (FMM). However, unlike FMM, the interactions between well separated groups are computed by using the complex source beams (CSBs), which represent the radiation from the basis elements in the group. The directional properties of CSBs allow a fast evaluation for these interactions such that the overall MVP is computed very efficiently. The direct solution time and the storage requirement of the CSB-MoM method is numerically shown to be O(N3/2) by optimally selecting the number of groups. A low-memory version of A new hybrid complex source beam-moment method (CSB-MoM) procedure is presented to accelerate the matrix-vector product (MVP) computation in the iterative solution of moment method integral equation problems. The scattering object in this CSB-MoM algorithm is partitioned into groups in a manner similar to the fast multipole method (FMM). However, unlike FMM, the interactions between well separated groups are computed by using the complex source beams (CSBs), which represent the radiation from the basis elements in the group. The directional properties of CSBs allow a fast evaluation for these interactions such that the overall MVP is computed very efficiently. The direct solution time and the storage requirement of the CSB-MoM method is numerically shown to be O(N3/2) by optimally selecting the number of groups. A low-memory version of the CSB-MoM method is also presented wherein separated group interactions are computed on-the-fly.the CSB-MoM method is also presented wherein separated group interactions are computed on-the-fly.