Improving the spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA)

The spherical harmonics expansion-based multilevel fast multipole algorithm (SE-MLFMA) is improved by using the mixed-potential representation of the combined field integral equation (CFIE) that is different from the most commonly used dyadic formulation in the existing MLFMA literature. The memory storage requirement and computation time for the spherical harmonics expansion of the radiation patterns of the basis functions are reduced effectively. Numerical results show that for the solution of CFIE, the memory cost by the radiation patterns is less than half of that in the conventional SE-MLFMA proposed by Eibert without any loss of accuracy.