时域积分方程MOT算法的推迟位时间卷积数值积分新方法

doi:10.3969/j.issn.0372-2112.2015.01.024

电子学报 ›› 2015, Vol. 43 ›› Issue (1): 151-159.DOI: 10.3969/j.issn.0372-2112.2015.01.024

时域积分方程MOT算法的推迟位时间卷积数值积分新方法

贾苗苗, 赵延文, 郑宇腾, 蔡强明

电子科技大学电子工程学院, 四川成都 611731

收稿日期:2013-03-11 修回日期:2014-04-02 出版日期:2015-01-25
- 作者简介:
- 贾苗苗 女, 1986年出生于山东, 电子科技大学博士研究生.主要研究兴趣包括时域积分方程法及其快速算法、电磁散射与逆散射等.E-mail:mmiaojia@126.com;赵延文 男, 1965年出生于四川, 电子科技大学教授, 博士生导师, 中国电子学会高级会员.主要研究兴趣包括计算电磁学、非均匀介质中的场与波、电磁散射与逆散射等, 在国内外发表学术论文100余篇, 并获国家科技进步二等奖1项、省部级科技进步奖2项.E-mail:ywzhao@uestc.edu.cn;郑宇腾 男, 1988年出生于甘肃兰州, 电子科技大学博士研究生.主要研究兴趣包括频域积分方程矩量法及其快速算法、电磁散射与逆散射等;蔡强明 男, 1987年出生于四川仪陇, 电子科技大学博士研究生.主要研究兴趣包括计算电磁学、电磁散射与逆散射等.
- 基金资助:
- 国家自然科学基金 (No.61371050,No.60971033); 国家部级基金 (No.9140A03010613DZ02030)

A Novel Numerical Integration Method for Convolution with the Retarded Potentials in Time-Domain Integral Equation MOT Algorithm

JIA Miao-miao, ZHAO Yan-wen, ZHENG Yu-teng, CAI Qiang-ming

School of Electronic Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China

Received:2013-03-11 Revised:2014-04-02 Online:2015-01-25 Published:2015-01-25
- Supported by:
- National Natural Science Foundation of China (No.61371050, No.60971033); National Ministries Foundation (No.9140A03010613DZ02030)

摘要/Abstract

摘要：

通过变量代换平滑三角形上推迟位(标量位函数和矢量位函数)并消除推迟矢量位旋度的奇异性,使得采用数值积分法就能够精确快速地计算任意正则时间基函数与推迟位函数及推迟矢量位旋度之间的时间卷积运算,可用于基于任意类型时间基函数的时域电场、时域磁场及其混合场积分方程时间步进(MOT)算法.与时间卷积运算的解析法对比分析表明,该时间卷积数值积分方法能够精确快速地计算基于任意类型时间基函数和不同时间步长条件下时域积分方程MOT算法的阻抗矩阵元素;而具体的计算实例也表明,阻抗矩阵的精确计算显著地提升了时域积分方程MOT算法的后时稳定性和求解精度.

关键词: 时域积分方程, 时间步进算法, 后时不稳定性

Abstract:

A novel variable transformation is presented to smooth and eliminate the singularity of the retarded potential (scalar and vector potential) and the curl of the vector potential by variable substitution.So the convolution between any regular time basis function and retarded potential (or its curl)can be calculated quickly and accurately using the numerical integration method,the advantage is that it can be used in the MOT algorithm of the time-domain field integral equations,no matter how the time basis functions are.Compared to the analytical time convolution method,this numerical integration method can accurately and quickly calculate the impedance matrix elements of MOT algorithm with any type of time basis functions and different time-step,and as several numerical results will demonstrate,this novel numerical method can largely improve the accuracy and the stability of the MOT algorithm.

Key words: time-domain integral equations (TDIE), marching-on-in time (MOT) algorithm, late-time instability

中图分类号:

TN911.23

贾苗苗, 赵延文, 郑宇腾, 等. 时域积分方程MOT算法的推迟位时间卷积数值积分新方法[J]. 电子学报, 2015, 43(1): 151-159.

JIA Miao-miao, ZHAO Yan-wen, ZHENG Yu-teng, et al. A Novel Numerical Integration Method for Convolution with the Retarded Potentials in Time-Domain Integral Equation MOT Algorithm[J]. Acta Electronica Sinica, 2015, 43(1): 151-159.

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时域积分方程MOT算法的推迟位时间卷积数值积分新方法

A Novel Numerical Integration Method for Convolution with the Retarded Potentials in Time-Domain Integral Equation MOT Algorithm

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