Advanced Acceleration Techniques For Parallel Multilevel Fast Multipole Method

Analysis of electromagnetic scattering from3-D electrically-large complex geometries has attracted much attention in computational electromagnetic scattering. With the fast development of computer technology and numerical algorithms, it is possible to give accurate results using rigorous full-wave methods. However, for the electrically-large geometries or the multiscale problems, exact result requires plenty of computational complexity and memory. It is impossible to efficiently compute the scattering of a complex geometry on a personal computer. As a possible remedy, the parallel technique is an effective method to make full use of the computer resources and improve the computing efficiency. With the fast development of high-performance computer technique, parallel technique has been widely used in variable fields of science computing, engineering technology. Therefore, this paper focuses on the parallel techniques and their applications in computational electromagnetics. The main contribution includes:1. A novel parallel framework is proposed for the iterative solution of the multilevel fast multipole method. Parallel principle is based on the different characteristics of memory requirement and CPU time in different levels of the multilevel fast multipole method. 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. The parallel technique is used to construct the preconditioner matrix. The numerical experiments reveal that with an efficiently parallelized MLFMM and the effective parallel preconditioner, significant convergence improvement is achieved. Accordingly, the simulation time can be greatly reduced.2. The multilevel Green’s function interpolation method (MLGFIM) combined with multilevel fast multipole method (MLFMM) is presented for solving the electromagnetic scattering from the objects with fine structures. Since the MLGFIM regardless of the size of the group size, the number of unknowns in each box can be less than a required number. As a result, the problems of the dense near-field impedance matrix arise from the dense discretizations are solved. Compared with the simulation results from the MLFMM, it is shown the accuracy and efficiency of the proposed method.3. The asymptotic phase-curve basis functions combined with multilevel fast multipole method (AP-CRWG-MLFMM) is presented for solving the electromagnetic scattering from the electrically large objects. The parallel technique is used to further improve its ability to calculate the electrically large objects. The Ray-Propogation Fast Multipole Method (RPFMM) is applied to simplify the tralstion when the two groups are well separated. The numerical results show this method combined with the parallel AP-CRWG-MLFMM can improve the computing speed greatly.4. The parallel finite element-boundary integral method (FE-BI) is developed to analyze the electromagnetic scattering and radiation of the coated objects, the final coefficient matrix is made up of a complex dense BIE sub-matrix and a complex sparse FEM sub-matrix. The FE-BI method suffers from a very slow convergence rate with the iterative solvers since the coefficient matrix arising from FE-BI is very ill-conditioned. As the preconditioner for the FE-BI matrix equation, the parallel absorb boundary condition (ABC) matrix is proposed to accelerate the convergence of the final FE-BI matrix. The numerical results are presented to demonstrate the accuracy and efficiency of the proposed method.