采用分部外推BCGS-FFT方法快速求解电磁散射问题  

An efficient partial extrapolation BCGS-FFT method for solving electromagnetic scattering problems

作　　者：韩晓冰[1] 张潇 王露洁 周远国 任强 HAN Xiaobing;ZHANG Xiao;WANG Lujie;ZHOU Yuanguo;REN Qiang(College of Communication and Information Engineering,Xi’an University of Science and Technology,Xi’an 710054,China;School of Electronics and Information Engineering,Beihang University,Beijing 100191,China)

机构地区：[1]西安科技大学通信与信息工程学院,西安710054 [2]北京航空航天大学电子信息工程学院,北京100191

出　　处：《电波科学学报》2021年第5期667-676,共10页Chinese Journal of Radio Science

基　　金：陕西省自然科学基础研究计划(2020JM-515);国家自然科学基金(61801009)。

摘　　要：为了快速求解电磁散射问题中具有震荡性、奇异性、慢收敛性的索末菲积分,提出了一种利用分部外推算法加速索末菲尾部积分计算,并结合稳定双共轭快速傅里叶变换(stabilized biconjugate gradient fast Fourier transform,BCGS-FFT)算法求解电磁散射问题场分布情况的新方法.首先给出电场积分方程(electric field integral equation, EFIE)的表达形式,且在求解过程的索末菲积分中应用一种便捷的椭圆积分路径来最小化索末菲积分的震荡性与奇异性,在索末菲尾部积分使用Levin分部外推法来提高积分收敛速度,以此来快速填充并矢格林函数矩阵.然后对新方法进行了多种数值实验,验证算法的精确度,并对比了新方法与传统BCGS-FFT方法的计算效率,发现在保持相同计算精度的条件下,新方法可节省20%~37%的计算时间.该方法能应用于复杂散射体嵌入多层空间的电磁散射计算,为快速求解目标区域的电磁散射场提供了一种新的方法.In order to quickly solve electromagnetic scattering problem of oscillation, singularity, slow convergence in Sommerfeld integrals, a new method is proposed which is a partition-extrapolation method used to accelerate the Sommerfeld tail integral calculation, and combined with the stabilized biconjugate fast Fourier transform(BCGS-FFT) algorithm for solving electromagnetic scattering problems field distribution. First of all, the expression form of the electric field integral equation(EFIE) is given. And a convenient elliptic integral path is applied to minimize the oscillation and singularity of the sommerfeld integral in the process of solving the EFIE. The Levin extrapolation method is used at the tails of the Sommerfeld integral to improve the integral convergence speed in order to quickly fill the dyadic Green’s function matrixes. Then a variety of numerical experiments are carried out for the new method,which have verified the accuracy of the algorithm, and compared the calculation efficiency of the new method with that of the traditional BCGS-FFT method. It is found that the new method can save 20%-37% of the calculation time underthe condition of maintaining the same calculation accuracy. This method can be applied to the electromagnetic scattering calculation of complex scatterer embedded in multi-layer space and provides a new method for solving the electromagnetic scattering field of target region quickly.

关 键 词：分部外推法 电磁散射 电场积分方程(EFIE) 格林函数 稳定双共轭快速傅里叶变换(BCGS-FFT) 

分 类 号：O451[理学—无线电物理]