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应用科学学报 ›› 2011, Vol. 29 ›› Issue (4): 417-422.doi: 10.3969/j.issn.0255-8297.2011.04.014

• 电子技术 • 上一篇    下一篇

预条件CMRH方法加速求解半空间三维电磁散射问题

李清波， 曹凤莲， 周平   

  1. 淮阴师范学院物理与电子电气工程学院，江苏淮安223300
  • 收稿日期:2010-06-07 修回日期:2011-03-07 出版日期:2011-07-30 发布日期:2011-07-30
  • 作者简介:周平，博士，教授，研究方向：电磁场数值分析、电磁散射特性等，E-mail: zhouping@hytc.edu.cn
  • 基金资助:

    江苏省高校自然科学基金(No.06KJD510028) 资助

Preconditioned Restarted Changing Minimal Residual Method for Solving 3D EM Problems in a Half Space

  1. School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian 223300,
    Jiangsu Province，China
  • Received:2010-06-07 Revised:2011-03-07 Online:2011-07-30 Published:2011-07-30

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摘要：

为了高效求解半空间三维电磁散射问题中离散电场积分方程产生的大型对称稠密复线性矩阵，将半空间多层快速多极子方法与CMRH方法相结合，其中多层快速多极子方法用于加速CMRH方法中的矩阵矢量乘运算.为了验证文中方法的有效性，分别计算了位于有耗半空间的圆柱体、长方体以及某导弹模型的散射特性. 结果表明，所提出的方法不仅可以滤除高频误差，平滑低频误差，而且能使求解半空间离散电场积分方程的迭代次数和计算时间比现在广泛使用的广义最小余量法显著减少. 同时，CMRH方法与稀疏近似逆预条件、对称超松弛预条件结合可进一步提高求解效率.

关键词: 并矢格林函数, 实镜像方法, 多层快速多极子方法, CMRH, 稀疏近似逆

Abstract:

Abstract: In order to efficiently solve large-scale asymmetric dense linear matrix in discrete field integral
equations, a preconditioned restarted changing minimal residual method based on the Hessenberg process
(CMRH) is proposed. It is used to implement the modified multilevel fast multi-pole algorithm (MLFMA)
to compute the scattering problem of perfect electric conductors in a lossy half space. MLFMA is used
to accelerate matrix vector multiplication of the CMRH. Scattering characteristics of the cylinder, the box
and the missile model are presented. Numerical results show that the CMRH method can efficiently reduce
both iteration number and convergence time as compared to the generalized minimal residual (GMRES).
Furthermore, CMRH is more easily combined with sparse approximate inverse (SAI) and symmetric successive
over relaxation (SSOR) preconditioning techniques, making it more practical.

Key words: dyadic Green function, real image method, multilevel fast multi-pole algorithm, changing minimal residual method based on the Hessenberg process (CMRH), sparse approximate inverse (SAI)

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