ACCURATE ANALYSIS OF REFLECTOR ANTENNAS USING FAFFA-MLFMA ALGORITHM

摘要

The traditional methods to analyze reflector antennas are based on the physical optics (PO) and geometrical theory of diffraction (GTD), which are high-frequency approximation methods. The modern development of fast algorithms and high-speed computers makes it possible to analyze the reflector antennas accurately based on the integral equation method. In this paper, we propose an efficient algorithm to accelerate the solution of the combined field integral equation using the multilevel fast multipole algorithm (MLFMA) combined with the fast far-field approximation (FAFFA). MLFMA is a fast N log N algorithm, which has found wide applications. However, the translation between groups in MLFMA is expensive because spherical Hankel functions and Legendre polynomials are involved and the translator is defined on an Eward sphere with many k directions. When two groups are in the far-field region, however, the translation can be greatly simplified by FAFFA where only a single k direction is involved in the translator. Numerical results show that both the computational load and memory requirement can be reduced using the FAFFA-MLFMA algorithm with little loss of accuracy. For over-a-million-unknown problems, the reduction of CPU time can reach as much as 40%. Using the FAFFA-MLFMA algorithm, the reflector antennas can be accurately analyzed and the current distribution on the reflector can be obtained.