Inner-outer GMRES algorithm for MLFMA implementation

Method of moments (MoM) solutions of surface integral equations are among the most successful methods for solving scattering and radiation problems involving metallic objects. A simple and effective preconditioning technique is introduced for the iterative solution of multilevel fast multipole algorithm (MLFMA) equation systems from the combined field integral equation (CFIE). The preconditioner is derived from the near zone strong interaction matrix elements of the coupling matrix and its iteration avoids the typical fill-in problem associated with direct factorization methods. Using the preconditioner with an inner generalized minimum residual (GMRES) solver results in excellent convergence with fewer iterative steps. This keeps a low memory requirement and helps to alleviate the influence of the lost convergence information for the conventional restarted GMRES.