Efficient MLFMA, RPFMA, and FAFFA algorithms for EM scattering by very large structures

Based on the addition theorem, the principle of a multilevel ray-propagation fast multipole algorithm (RPFMA) and fast far-field approximation (FAFFA) has been demonstrated for three-dimensional (3-D) electromagnetic scattering problems. From a rigorous mathematical derivation, the relation among RPFMA, FAFFA, and a conventional multilevel fast multipole algorithm (MLFMA) has been clearly stated. For very large-scale problems, the translation between groups in the conventional MLFMA is expensive because the translator is defined on an Ewald sphere with many sampling kˆ directions. When two groups are well separated, the translation can be simplified using RPFMA, where only a few sampling kˆ directions are required within a cone zone on the Ewald sphere. When two groups are in the far-field region, the translation can be further simplified by using FAFFA where only a single kˆ is involved in the translator along the ray-propagation direction. Combining RPFMA and FAFFA with MLFMA, three algorithms RPFMA-MLFMA, FAFFA-MLFMA, and RPFMA-FAFFA-MLFMA have been developed, which are more efficient than the conventional MLFMA in 3-D electromagnetic scattering and radiation for very large structures. Numerical results are given to verify the efficiency of the algorithms.