Calderon preconditioning approaches for PMCHWT formulations for Maxwell's equations

摘要

Preconditioning methods based on Calderon's formulae for the Poggio-Miller-Chang-Harrington-Wu-Tsai formulations for Maxwell's equations in 3D are discussed. Five different types of formulations are proposed. The first three use different basis functions for surface electric and magnetic currents. The first type is a preconditioning just by appropriately ordering the coefficient matrix using the Gramian matrix as the preconditioner. Other two types utilise preconditioners constructed using matrices needed in the main fast multipole method algorithms. The fourth and fifth types are similar to the second and third types, but they use the same basis functions for both surface electric and magnetic currents. We make several numerical experiments with proposed preconditioners to confirm the efficiency of these proposed methods.