Solutions of new potential integral equations using approximate stable diagonalization of the Green's function

We present efficient and accurate solutions of scattering problems involving dense discretizations with respect to wavelength. Recently developed potential integral equations (PIEs) for stable solutions of low-frequency problems are used to formulate such challenging problems, where the electric current density and magnetic vector potential are defined as unknowns. For solving problems discretized with large numbers of unknowns, we further use an approximate diagonalization of the Green's function within the multilevel fast multipole algorithm (MLFMA). The capability of the implementation based on PIEs and MLFMA is demonstrated on canonical problems, whose solutions are difficult via the conventional formulations and/or standard acceleration methods.