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

doi:10.3969/j.issn.0372-2112.2015.01.024

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

更新时间：2025-07-16

- A Novel Numerical Integration Method for Convolution with the Retarded Potentials in Time-Domain Integral Equation MOT Algorithm
- Acta Electronica Sinica Vol. 43, Issue 1, Pages: 151-159(2015)
- 作者机构：
  
  电子科技大学电子工程学院,四川,成都,611731
- 作者简介：
- 基金信息：
  
  National Natural Science Foundation of China (No.61371050, No.60971033);National Ministries Foundation (No.9140A03010613DZ02030)
- DOI：10.3969/j.issn.0372-2112.2015.01.024
  CLC： TN911.23
- Published：2015
- 稿件说明：
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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.
DOI：

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. DOI： 10.3969/j.issn.0372-2112.2015.01.024.

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.

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.

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