Application of perturbed multiresolution preconditioner technique combined with MLFMA for scattering problem

A new multiresolution (MR) preconditioner is presented in this paper, and it is combined with the multilevel fast multipole algorithm (MLFMA) for the analysis of electromagnetic scatters; Furthermore, the MR preconditioner is modified to be more effective by including a perturbation which is constructed from the principle value term of the magnetic field integral equation (MFIE) operator for solving the electric field integral equation (EFIE), and the modified MR preconditioner is named perturbed MR preconditioner. The MR preconditioner is a physics-based preconditioning scheme for the Method-of-Moments (MoM) methods, which is derives from the generation of a MR basis. And the MR basis functions are constructed as linear combinations of Rao-Wilton-Glisson (RWG) basis functions. Unlike other preconditioners, the perturbed MR preconditioner requires a low memory occupation and computational cost for its generation and application. The use of the perturbed MR preconditioner combined with the MLFMA can speeds up the convergence rate of the iterative solvers effectively.