Solving the volume-surface integral equation using the spherical harmonics expansion based multilevel fast multipole algorithm

To reduce the memory storage requirements of the radiation patterns (RPs) in the multilevel fast multipole algorithm (MLFMA) of solving the volume-surface integral equation (VSIE), the spherical harmonics expansion of the RPs associated with the triangular-tetrahedral mesh elements is implemented in solving the mixed-potential form of VSIE. Compared with the conventional VSIE-MLFMA solution, numerical examples show that the storage cost of the RPs can be significantly reduced without loss of accuracy in the proposed solution of VSIE.