A highly efficient parallel approach of multi-level fast multipole algorithm

Based on the different characteristics of memory requirement and CPU time at different levels in the Multi-Level Fast Multipole Algorithm (MLFMA), a new highly efficient parallel approach is proposed, which employs different techniques to parallelize the plane waves and translation matrices at different levels. The formulae for efficiently implementing this proposed approach are presented by theoretical analysis and numerical experiments. Several techniques have also been employed to reduce memory requirement. The proposed parallel approach is implemented and investigated numerically, showing that the proposed approach is very accurate and efficient. The radar cross-section (RCS) of a conducting sphere with a diameter of 144 lambda (wavelength), simulated by over 10 millions unknowns, is successfully computed in the Center for Electromagnetic Simulation (CEMS) in the Beijing Institute of Technology (BIT), demonstrating the strong computation power of this proposed approach. The comparison of numerical performance between Center for Computation Electromagnetics (CCEM) in University of Illinois at Urbana-Champaign (UIUC) and our CEMS is also presented in this paper.