Surface Integral Equation Solutions by Hierarchical Vector Basis Functions and Spherical Harmonics Based Multilevel Fast Multipole Method

The method of moments solution of electromagnetic surface integral equation formulations for perfect electric conductors or impedance boundary objects is obtained using hierarchical vector basis functions. The singular and hypersingular integrals involved in the near field coupling matrix are computed fully numerically using adaptive singularity cancellation technique. Multilevel fast multipole method with spherical harmonics expansion of the k-space representations of the basis vectors and the incoming waves at the finest level is utilized for its memory and computation time efficient implementation. Improved performance of the proposed techniques in terms of accuracy, computational time, and memory requirements is demonstrated by comparing various results with some of the existing implementations available in the literature.