The Application of Improved Spherical Harmonics Expansion-Based Multilevel Fast Multipole Algorithm in the Solution of Volume-Surface Integral Equation

Abstract

During the solution of volume-surface integral equation (VSIE), to reduce the core memory requirement of the radiation patterns (RPs) of the basis functions, an improved spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) using the mixed-potential representation and the triangle-/tetrahedron-based grouping scheme is applied. Numerical results show that accompanying with a faster speed, the memory requirement of the RPs in the improved SE-MLFMA is several times less than that in the conventional MLFMA without compromising accuracy. A result employing the OpenMP parallelization and vector arithmetic logic unit (VALU) hardware acceleration technique is also shown to illustrate the robustness and scalability of the improved SE-MLFMA method.