The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the follow...The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the following aspects: Firstly, two different methods, which are same in essence: the method of the unknown induction current expansion and the method of the integral operator expansion are used to solve the EFIE, Secondly, how to choose the wavelet basis function in wavelet MoM. For two dimension problem, the wavelet MoM is employed and compared with the conventional MoM in CPU time, computational precision and matrix spareness etc. Here, the fast wavelet transform (FWT) is used to compute the matrix elements rapidly and efficiently. Typical numerical results are presented to illustrate the concepts.展开更多
An integration technique based on use of Monte Carlo Integration is proposed for Method of Moments solution of Electric Field Integral Equation. As an example numerical analysis is carried out for the solution of the ...An integration technique based on use of Monte Carlo Integration is proposed for Method of Moments solution of Electric Field Integral Equation. As an example numerical analysis is carried out for the solution of the integral equation for unknown current distribution on metallic plate structures. The entire domain polynomial basis functions are employed in the MOM formulation which leads to only small number of matrix elements thus saving significant computer time and storage. It is observed that the proposed method not only provides solution of the unknown current distribution on the surface of the metallic plates but is also capable of dealing with the problem of singularity efficiently.展开更多
电场积分方程(electric field integral equation,EFIE)“低频崩溃”现象是指当电磁波波长远大于离散单元的尺寸时,分析结果不准确的现象。它的发生与计算机浮点数的字长有关,高精度浮点数的普及有助于缓解低频崩溃现象的发生,但目前还...电场积分方程(electric field integral equation,EFIE)“低频崩溃”现象是指当电磁波波长远大于离散单元的尺寸时,分析结果不准确的现象。它的发生与计算机浮点数的字长有关,高精度浮点数的普及有助于缓解低频崩溃现象的发生,但目前还没有关于不同精度的浮点数的低频崩溃临界阈值的研究报道。本文定量研究了不同字长浮点数的EFIE不发生低频崩溃的适用范围,以便在该适用范围内,研究人员仅须简单地修改现有EFIE代码的浮点数字长就可以进行电磁特性的准确分析而不发生低频崩溃,避免现有低频问题都需要修改基函数或积分方程等分析技术,为低频电磁分析增加了一种可选择的简便解决办法。经过数值算例的验证,高精度浮点数的EFIE可以将低频崩溃现象发生的离散网格的电尺寸降低到2.5×10^(−13),这已经能够处理我们常见的低频崩溃问题。展开更多
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...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.展开更多
文摘The recently developed theory of wavelet applied in the Method of Moments (MoM) to solve the electromagnetic field integral equation is presented in this paper. For one dimension problem, we briefly discuss the following aspects: Firstly, two different methods, which are same in essence: the method of the unknown induction current expansion and the method of the integral operator expansion are used to solve the EFIE, Secondly, how to choose the wavelet basis function in wavelet MoM. For two dimension problem, the wavelet MoM is employed and compared with the conventional MoM in CPU time, computational precision and matrix spareness etc. Here, the fast wavelet transform (FWT) is used to compute the matrix elements rapidly and efficiently. Typical numerical results are presented to illustrate the concepts.
文摘An integration technique based on use of Monte Carlo Integration is proposed for Method of Moments solution of Electric Field Integral Equation. As an example numerical analysis is carried out for the solution of the integral equation for unknown current distribution on metallic plate structures. The entire domain polynomial basis functions are employed in the MOM formulation which leads to only small number of matrix elements thus saving significant computer time and storage. It is observed that the proposed method not only provides solution of the unknown current distribution on the surface of the metallic plates but is also capable of dealing with the problem of singularity efficiently.
文摘电场积分方程(electric field integral equation,EFIE)“低频崩溃”现象是指当电磁波波长远大于离散单元的尺寸时,分析结果不准确的现象。它的发生与计算机浮点数的字长有关,高精度浮点数的普及有助于缓解低频崩溃现象的发生,但目前还没有关于不同精度的浮点数的低频崩溃临界阈值的研究报道。本文定量研究了不同字长浮点数的EFIE不发生低频崩溃的适用范围,以便在该适用范围内,研究人员仅须简单地修改现有EFIE代码的浮点数字长就可以进行电磁特性的准确分析而不发生低频崩溃,避免现有低频问题都需要修改基函数或积分方程等分析技术,为低频电磁分析增加了一种可选择的简便解决办法。经过数值算例的验证,高精度浮点数的EFIE可以将低频崩溃现象发生的离散网格的电尺寸降低到2.5×10^(−13),这已经能够处理我们常见的低频崩溃问题。
文摘多尺度复杂电子系统的电磁场问题难以用单一的计算电磁学方法进行高效数值计算.基于区域分解方法和惠更斯等效原理,提出了频域广义传输矩阵(generalized transition matrix,GTM)方法:将系统分解为多个子模块,通过电场积分方程(electric field integreal equation,EFIE)把各个子模块的电磁特性进行提炼,再考虑所有子模块之间的电磁耦合,计算系统整体电磁场分布.GTM方法把多尺度问题转化为尺度相对比较单一的问题进行处理,在分析各种复合结构、非均匀各向异性介质、大型相控阵天线等电磁散射特性时,提供了灵活的解决方案.论文给出了GTM在手征介质、开口腔体以及Vivaldi相控阵天线电磁特性分析中的应用算例,当未知量个数压缩到原来的十分之一时,GTM计算结果与直接用矩量法(methed of moment,MoM)求解的计算结果非常吻合.GTM可以简洁地表示目标问题的电磁散射特征,与传统MoM相比,大幅度减少了基函数的数量,具有较高的计算精度和效率.
文摘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.
