Integral Equation Fast Fourier Transform Method And Application

Due to the strong demand for engineering application, the electromagnetic radiation and scattering problems for 3-D objects has been a focus for a long time. As a strict numerical method, the traditional Method of Moments (MoM) has been widely used to solve the electromagnetic radiation and scattering problems. Because of its high memory requirement and computational complexity, the applications of the traditional Method of Moments are limited to solve low-frequency and resonance regimes electromagnetic problems. In this paper, a fast algorithm - integral equation fast Fourier transform (IE-FFT) is presented. The algorithm can greatly reduce the memory requirement and computational complexity for traditional Method of Moments. For the surface integral equation, the computational complexity and memory requirement of the algorithm is ( )O N 1.5 logN and ( )O N 1.5; for the volume integral equation and planar structures, the computational complexity and memory requirement of the algorithm is O ( N logN ) and O ( N ), where N is the number of unknowns.Firstly, several integral equation classifications are briefly introduced. As an integral equation solver, the Method of Moments is also introduced, including the details of the basic principles and the concrete realization process.Then, the basic principles and the numerical implementation of the integral equation fast Fourier transform are introduced. The error bound of the algorithm is assessed and the heart of the algorithm– Green's function interpolation is studied as a key point. By using Gaussian interpolation, the accuracy of the algorithm is improved. And the computational time and storage are reduced by using the floating stencil topology, while without sacrificing the accuracy.Secondly, the IE-FFT is applied to surface integral equation for solving the electromagnetic scattering problem on arbitrary shaped 3-D PEC objects and the major parameters of the algorithm are investigated in this thesis. And the electromagnetic problems for dielectric objects are solved by combining the IE-FFT with volume integral equation. Furthermore, the computational complexity of the algorithm is studied for both surface integral equation and volume integral equation.Finally, the electromagnetic scattering problem for thin coating or lossy dielectric coating objects is solved by combining the IE-FFT algorithm with impedance boundary condition (IBC). For arbitrary thickness coating, arbitrary shaped coating and composite conducting and dielectric objects, the electromagnetic scattering problem can be solved efficiently by applying the IE-FFT algorithm to volume-surface integral equation (VSIE).Furthermore, this research work has laid a solid foundation for the further study of the project.