Accelerating the Multilevel Fast Multipole Method with Parallel Preconditioner for Large-Scale Scattering Problems

摘要

A novel parallel framework is proposed for the iterative solution of the multilevel fast multipole method (MLFMM). The inversion of the near-field impedance matrix is used as the preconditioner matrix to improve the convergence history of the ill-conditioned linear system formulated by electric field integral equation. In order to accelerate the inversion of the near field impedance matrix with huge number of unknowns, the parallel technique is used to construct the preconditioner matrix. Our numerical experiments reveal that with an efficiently parallelized MLFMM and the effective parallel preconditioner, we are able to solve problems with millions of unknowns in a few hours. Both the number of iteration steps and the overall simulation time can be saved significantly. For closed-surface problems analyzed by the combined-field integral equation, the number of iterations can also be reduced significantly by the proposed method. Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.