MLFMA/VIE-MoM大型矩阵方程的快速迭代求解方法  

A Fast Iterative Method for Solving Large Matrix Equations Generated by MLFMA/VIE-MoM

作　　者：王文博[1] 徐金平[1] 

机构地区：[1]东南大学毫米波国家重点实验室,江苏南京210096

出　　处：《电子学报》2010年第9期2009-2013,共5页Acta Electronica Sinica

基　　金：国家自然科学基金委创新群体基金(No.606221002)

摘　　要：本文针对体积分方程矩量法(VIE-MoM)分析三维非均匀介质电磁散射问题所导出的大型矩阵方程的求解问题,基于多层快速极子技术(MLFMA)算法研究了快速近似迭代方法.提出了一种基于MLFMA分组方案对系数矩阵进行重组并提取强耦合元素的近场预条件器的构造方法,有效地提高了广义最小余量法(GMRES)的迭代收敛速度.提出了一种在迭代计算过程中的近似矩阵向量乘积方案,明显降低了单步计算过程中MLFMA远区耦合作用的计算时间.计算实例表明,采用本文的迭代加速技术可使计算速度提高3至5倍,有效地提高了VIE-MoM大型矩阵方程的迭代求解速度.A fast iterative method based on the implementation of multilevelfast multiple algorithm（MLFMA） is proposed for solving the large scale matrix equation generated by the method of moment solution to volume integral equation（VIE-MoM） for 3-D inhomogeneous dielectrics.Firstly,the whole coefficient matrix elements are realigned based on the scheme of the groups of MLFMA.By extracting strong coupling elements,a fast method for constructing the near-field preconditioner is proposed to accelerate the convergence rate when the matrix equation is solved by the generalized minimum residual（GMRES） algorithm.And then,an approximate method is put forward in partly iterative steps when the relative error reaches to a specific value,which shortens the computational time of the far field contribution during each iterative step.Numerical examples show that the combination use of these two fast methods can raise the speed of computation for 3 to 5 times,which is very effective to improve the efficiency of GMRES algorithm for large matrix equation solution.

关 键 词：矩量法 体积分方程 多层快速多极子 预条件 近似迭代方法 

分 类 号：TN011[电子电信—物理电子学]