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应用科学学报 ›› 2006, Vol. 24 ›› Issue (5): 479-484.

• 论文 • 上一篇    下一篇

稀疏化递归Cholesky分解预条件技术加速PO-MoM迭代求解

牛臻弋, 徐金平   

  1. 东南大学毫米波国家重点实验室, 江苏南京 210096
  • 收稿日期:2005-06-02 修回日期:2005-08-24 出版日期:2006-09-30 发布日期:2006-09-30
  • 作者简介:牛臻弋,博士生,研究方向:计算电磁学、天线与电磁兼容,E-mail:nzy@seu.edu.cn;徐金平,教授,博导,研究方向:计算电磁学、电磁兼容、天线与电磁散射、毫米波与亚毫米波理论与技术,E-mail:jpxu@seu.edu.cn

Sparse Recursive Cholesky Factorization Preconditioning Technique for Acceleration of Iterative Solution to PO-MoM Problems

NIU Zhen-yi, XU Jin-ping   

  1. State Key Laboratory of Millimeter Waves, Southeast University, Nanjing 210096, China
  • Received:2005-06-02 Revised:2005-08-24 Online:2006-09-30 Published:2006-09-30

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81

被引次数

5

摘要： 提出了一种新的稀疏化递归Cholesky分解预条件技术,并应用于加速物理光学和矩量法(PO-MoM)混合方法分析大型复杂载体上线天线的辐射问题.基于积分方程积分核的物理意义,忽略MoM区与PO区的耦合,构造出一个PO-MoM混合方法系数矩阵的稀疏近似阵.然后采用Cholesky分解方法将该稀疏阵的逆阵进行递归分解,得到一个矩阵连乘形式的预条件阵.将该预条件阵用于预条件广义最小留数(GM RES)法迭代求解线性方程组,应用该技术对卫星和舰船两个电大尺寸复杂载体模型上天线辐射问题进行了求解.结果表明,采用这种新的预条件技术可以大大加快方程组迭代求解的收敛速度,明显提高计算效率.

关键词: 物理光学和矩量法, 复杂载体, 预条件, Cholesky分解, 线天线

Abstract: A novel sparse recursive Cholesky factorization preconditioning technique is proposed for accelerating analyses of radiation problems of wire antennas mounted on large complex platforms with a hybrid method of physical optics and moments (PO-MoM).Based on the physical meanings of the electric field integral equation (EFIE) kernel and neglecting coupling between MoM and PO regions, an approximate sparse matrix of the coefficient matrix derived from the PO-MoM hybrid method is obtained.Inverse of the sparse matrix is then factorized recursively with Cholesky factorization. Thereafter, a preconditioner in a form of successive multiplication is constructed.It is used in a preconditioned generalized minimal residual (GMRES) method to iteratively solve the systems of linear equations.The proposed preconditioning technique is applied to solve radiation problems of antennas mounted on a satellite model and a ship model in electrically large size.Numerical results demonstrate that the new preconditioning technique is efficient in reducing the number of iterations in solving the linear systems derived from PO-MoM.

Key words: wire antenna, PO-MoM, Cholesky factorization, preconditioning, complex platform

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