北京航空航天大学学报 ›› 2015, Vol. 41 ›› Issue (10): 1867-1872.doi: 10.13700/j.bh.1001-5965.2015.0214

• 电磁理论与应用 • 上一篇    下一篇

等效原理算法在不同等效面下的误差分析

党训旺1, 李懋坤1,2, 杨帆1,2, 许慎恒1,2   

  1. 1. 清华大学电子工程系, 北京 100084;
    2. 清华信息科学与技术国家实验室(筹), 北京 100084
  • 收稿日期:2015-04-10 修回日期:2015-04-24 出版日期:2015-10-20 发布日期:2015-11-02
  • 通讯作者: 李懋坤(1979-),男,辽宁锦州人,副教授,maokunli@tsinghua.edu.cn,主要研究方向为计算电磁学. E-mail:maokunli@tsinghua.edu.cn
  • 作者简介:党训旺(1992-),男,河北盐山人,博士研究生,dxw13@mails.tsinghua.edu.cn
  • 基金资助:
    清华大学电子工程系传信研究基金

Error analysis of equivalence principle algorithm on different equivalence surfaces

DANG Xunwang1, LI Maokun1,2, YANG Fan1,2, XU Shenheng1,2   

  1. 1. Department of Electronic Engineering, Tsinghua University, Beijing 100084, China;
    2. Tsinghua National Laboratory for Information Science and Technology(TNist), Beijing 100084, China
  • Received:2015-04-10 Revised:2015-04-24 Online:2015-10-20 Published:2015-11-02

摘要: 等效原理算法(EPA)借鉴了区域分解的思想,并基于惠更斯等效原理实现了对大规模散射问题的计算.本文对EPA中的等效原理算子(EPO)进行了误差分析,选取了立方体、球体和进行了光滑处理的立方体等作为等效面寻找误差来源,并提出了误差改进的建议.根据计算结果,等效磁流在等效面上描述的误差一般集中在等效面表面的几何不连续处,且主要受等效面上的法向向量不连续性和基函数的选取的影响.故在选取等效面时应尽量考虑使用平滑的等效面,而不是直接使用立方体等效面.

关键词: 惠更斯等效原理, 区域分解方法, 误差分析, 计算电磁学, RWG基函数

Abstract: Equivalence principle algorithm (EPA) is a domain decomposition algorithm based on the Huygens' equivalence principle to solve large scale scattering problems. The errors of the equivalence principle operator (EPO) in EPA using cubic, spherical and smooth cubic equivalence surfaces were analyzed to find the source of errors. The sources of the error were investigated and a simple scheme to improve its accuracy was developed. From the numerical examples, it shows that the error of equivalent magnetic current is mainly concentrated on geometrical discontinuity of the equivalence surface, and affected by both the discontinuity of the normal vector on the equivalence surface and the choice of basis functions. Therefore it is suggested to choose smooth equivalence surfaces if possible rather than to use cubic ones directly.

Key words: Huygens equivalence principle, domain decomposition method, error analysis, computational electromagnetics, RWG basis function

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