An integral equation-fast Fourier transform (IE-FFT) algorithm is applied to the electromagnetic solutions of the combined field integral equation (CFIE) for scattering problems by an arbitrary-shaped three-dimensional perfect electric conducting object. The IE-FFT with CFIE uses a Cartesian grid for known Green's function to considerably reduce memory storage and speed up CPU time for both matrix fill-in and matrix vector multiplication when used with a generalized minimal residual method. The uniform interpolation of the Green's function on an equally spaced Cartesian grid allows a global FFT for field interaction terms. However, the near interaction terms do not take care for the singularity of the Green's function and should be adequately corrected. The IE-FFT with CFIE does not always require a suitable preconditioner for electrically large problems. It is shown that the complexity of the IE-FFT with CFIE is found to be approximately O(N1.5) and O(N1.5log N) for memory and CPU time, respectively.

中文翻译：

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结合场积分方程求解电磁散射问题的IE-FFT算法的高效实现

将积分方程-快速傅里叶变换（IE-FFT）算法应用于任意形状的三维完美导电物体散射问题的组合场积分方程（CFIE）的电磁解。带有 CFIE 的 IE-FFT 对已知格林函数使用笛卡尔网格，以在与广义最小残差方法一起使用时显着减少内存存储并加快 CPU 时间用于矩阵填充和矩阵向量乘法。等距笛卡尔网格上格林函数的均匀插值允许场交互项的全局 FFT。但是，近交互项不考虑格林函数的奇异性，应进行充分校正。带有 CFIE 的 IE-FFT 并不总是需要合适的预处理器来解决电气大问题。结果表明，使用 CFIE 的 IE-FFT 的复杂度约为○(ñ1.5） 和○(ñ1.5日志ñ) 分别用于内存和 CPU 时间。