Physics-based preconditioner for iterative algorithms in multi-scatterer and multi-boundary method of moments formulations

An e cient method to solve electromagnetic scattering problems involving several metallic scatterers or bodies composed of dielectric and metallic regions is proposed. So far, the method of moments has successfully been applied to large arrays of identical scatterers when it was combined with preconditioned iterative algorithms to solve for the linear system of equations. Here, the method is generalized to geometries that are composed of several metallic elements of di erent shapes and sizes, and also to scatterers that are composed of metallic and dielectric regions. The method uses in its core an iterative algorithm, preferably the transpose-free quasi-minimum residual (TFQMR) algorithm, and a block diagonal Jacobi preconditioner. For best performance, the blocks for the preconditioner are chosen according to individual scatterers or groups of scatterers for the array case, and according to the electric and magnetic current basis functions for dielectric=metallic scatterers. The iterative procedure converges quickly for an optimally chosen preconditioner, and is robust even for a non-optimal preconditioner. Reported run times are compared to run times of an e ciently programmed LU factorization, and are shown to be signi cantly lower