精确稳定求解时域电场积分方程的一种新方法

时域电场、磁场和混合场积分方程已被广泛用来分析散射体的时域散射响应.基于适当的空间积分方法和隐式的时间步进算(MOT)法在求解时域磁场和混合场积分方程时总是稳定的,然而在求解TDEFIE时则是不稳定的.在本文中,时域电场积分方程的非奇异性积分采用标准的高斯求积法来计算;而利用参数坐标变换和极坐标变换将其奇异性积分转换成为可以分区域精确快速计算的非奇异性积分.通过数值实验表明,利用该方法可以非常精确稳定地求解时域电场积分方程,即使是在时间迭代后期也不必采用任何求平均的过程;另外,该方法可以用于任意时间基函数并可以推广到高阶空间基函数的情形.

A New Method for Stable and Accurate Solution of Time-Domain Electric Field Integral Equation

The time-domain electric,magnetic and combined field integral equations(TDEFIE,TDMFIE and TDCFIE) have been applied widely to the analysis of transient scattering from conducting bodies.The marching-on-in-time(MOT) schemes,relying on suitable spatial integral rules and implicit time-stepping method,for solving the TDCFIE and TDMFIE have been found to be stable.Unfortunately,the same is not true for the TDEFIE.In this article,the non-singular integral is evaluated using the standard Gaussian quadrature rules,and the transformations of the parametric coordinates and plane polar coordinates are employed to transform the singular integrals of TDEFIE into non-singular integrals,which can be accurately and efficiently evaluated by dividing the original domain of integration into sub-domains.Simulation results demonstrate that this approach produces rather stable and more accurate results without resort to any averaging processes.In addition,this method suits to any temporal basis functions and can be extended to high-order spatial basis functions.