一种高精度求解磁场积分方程的高阶矩量法

袁浩波 1; 高屾林 1; 李兵 2; 梁昌洪 1

doi:10.7652/xjtuxb201312011

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一种高精度求解磁场积分方程的高阶矩量法

更新时间：2025-07-09

- 一种高精度求解磁场积分方程的高阶矩量法
- Higher Order Moment Method for Magnetic Field Integral Equations with High Accuracy
- 西安交通大学学报 2013年47卷第12期页码：61-65
- 作者机构：
  
  西安电子科技大学天线与微波技术重点实验室,西安,710071
- 作者简介：
- 基金信息：
  
  : 2013-04-02。作者简介: 袁浩波(1980—),男,副教授。基金项目: 国家自然科学基金资助项目(61072018);中央高校基本科研业务费专项资金资助项目(K50511020032)
- DOI：10.7652/xjtuxb201312011
  中图分类号： TN011
- 网络首发：2013-12-10，
  
  纸质出版：2013
- 稿件说明：
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袁浩波 1, 高屾林 1, 李兵 2, 等. 一种高精度求解磁场积分方程的高阶矩量法[J]. 西安交通大学学报, 2013,47(12):61-65.

Higher Order Moment Method for Magnetic Field Integral Equations with High Accuracy[J]. 2013, 47(12): 61-65.
袁浩波 1, 高屾林 1, 李兵 2, 等. 一种高精度求解磁场积分方程的高阶矩量法[J]. 西安交通大学学报, 2013,47(12):61-65. DOI： 10.7652/xjtuxb201312011.

Higher Order Moment Method for Magnetic Field Integral Equations with High Accuracy[J]. 2013, 47(12): 61-65. DOI： 10.7652/xjtuxb201312011.

摘要

针对矩量法求解磁场积分方程时精度较差的问题

采用非均匀有理B样条(NURBS)建模的高阶矩量法求解磁场积分方程

采用Duffy变换消除自阻抗元素中的奇异性。对于相邻面片间互阻抗的近奇异性积分

首先采用一种简单的双曲函数变换消除内层面积分中R

-2

形式的近奇异性

然后采用Duffy变换消除外层面积分中的对数奇异性

并通过准确地计算阻抗矩阵元素得到了一种高精度的矩量法。对两个闭合导体模型进行双站雷达散射截面(RCS)仿真计算

并分别与解析结果和电场积分方程的结果进行比较

研究结果表明该方法的误差不到0.5 dB。这种高精度的磁场积分方程方法可以取代常用的混合场积分方程方法

并为下一步构造迭代收敛速度更快的新方法打下了良好的基础。

Abstract

The magnetic field integral equations(MFIE)solved by moment methods(MOM)show low accuracy. A higher order moment method for solving the MFIE is introduced. Duffy transformation is chosen to cancel the singularities in the self-term impedances. As to the near singularities in the impedances of two neighboring patches

a hyperbolic function is adopted to cancel the R

-2

near singularities in the inner surface integrals

and then another Duffy transformation is employed to cancel the logarithmic singularities in the outer surface integrals

thus a high accurate moment method is achieved. For two closed conducting models

the bistatic radar cross section(RCS)simulation by the proposed method is with error less than 0.5 dB. This method for MFIE can replace the commonly used one for

combined field integral equations(CFIE)

and may lay a foundation to construct new methods with higher convergence rate.

关键词

Keywords

references

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DJORDJEVIC M, NOTAROS B M. Double higher order method of moments for surface integral equation modeling of metallic and dielectric antennas and scatterers [J]. IEEE Transactions on Antennas and Propagation, 2004, 52(8): 2118-2129.

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LI Jianbing, WANG Xuesong, QU Longhai. Calculation of physical optics integrals over NURBS surface using a delaminating quadrature method [J]. IEEE Transactions on Antennas and Propagation, 2012, 60(5): 2388-2397.

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SAAD Y. Iterative methods for sparse linear systems [M]. Boston, USA: PWS Publishing, 1996: 236-237.

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