An Integral-Equation-Based Method for Efficient and Accurate Solutions of Scattering Problems with Highly Nonuniform Discretizations

We present a full-wave electromagnetic solver for analyzing multiscale scattering problems with highly nonuniform discretizations. The developed solver employs an elegant combination of potential integral equations (PIEs) with the magnetic-field integral equation (MFIE) to improve the iterative convergence properties of matrix equations obtained via method of moments, especially derived from highly nonuniform discretizations for which PIEs suffer from ill conditioning. A mixed-form multilevel fast multipole algorithm with incomplete tree structures is employed to efficiently and accurately solve the obtained matrix equations. The solver circumvents the well-known low-frequency problem originating from the breakdown of the conventional surface formulations and the standard MLFMA for highly nonuniform discretizations. The accuracy and efficiency of the proposed solver are demonstrated on canonical but challenging scattering problems.