Performance of Preconditioned Iterative Methods in Computational Electromagnetics

摘要

The numerical solution of electromagnetic scattering problems involves the projection of an exact equation onto a finite dimensional space, and the solution of the resulting matrix equation. By using iterative algorithms, the analysis of scatterers that are an order of magnitude larger electrically may be feasible. Two approaches to achieving the solutions in less time are examined and applied to several typical electromagnetic scattering problems. First, through extensions to the conjugate gradient and biconjugate gradient algorithms, multiple excitations for the same matrix can be simultaneously treated. Depending on the type of problem, the number of excitations, and the algorithm employed, substantial time savings may be achieved. Second, the performance of preconditioning combined with the conjugate gradient, biconjugate gradient, and Chebyshev algorithms is evaluated for typical electromagnetic scattering problems. Preconditioners based on significant structural features of the matrix are able to reduce the overall execution time.