Fast Fourier Transforms in Electromagnetics

This Chapter review the fast Fourier transform (FFT) technique and its application to computational electromagnetics, especially to the fast solver algorithms including the Conjugate Gradient Fast Fourier Transform (CG‐FFT) method, Precorrected Fast Fourier Transform (pFFT) method, Adaptive Integral Method (AIM), Greens Function Interpolation with FFT (GI‐FFT) method and Integral Equations with FFT (IE‐FFT) method. The basic ideas used in the FFT applications are addressed while the brief introduction to integral equation method is conducted. The general formulation and procedure in the integral equation method, surface integral equations, volume integral equations, solutions to integral equations, and their implementations of fast Fourier transform algorithm are also briefed together with fast convolution using fast Fourier transform. Fast integral equation method developed based on fast Fourier transform are reviewed where conjugate gradient fast Fourier transform method, and precorrected fast Fourier transform method (where projection operators and interpolation operators are also highlighted), adaptive integral method, Greens function interpolation with FFT approach and integral equations with FFT method are also described. While the matching schemes for gradients of Green's functions are addressed, accuracy and complexity, memory requirement and computational cost, and error controls and estimations are also discussed.