| Due to the increasing requirements of simulating the electromagnetic wave scattering of large-scale and complex structures, high-order and spectral methods have become very attractive because of their accuracy and efficiency. A spectral integral method, which is based on the surface integral equation, has been developed to solve the scattering problems of arbitrarily-shaped smooth targets in free space. In this method, the truncated Fourier series are introduced as basis functions, and the fast Fourier transform (FFT) algorithm has been used in calculating the impedance matrix. Also, the singularities in Green's functions have been specially treated using a method of singularity subtraction, which achieves a spectral accuracy in the integral. Furthermore, this spectral integral method has also been applied for inhomogeneous objects through a hybrid method. In this hybrid method, an additional boundary is applied to truncate the inhomogeneous object from the outer medium. The spectral integral method is used as a radiation boundary condition (RBC) for the exterior medium, while the finite element method (FEM) has been used for interior structure. To extend the spectral integral method into three-dimensional problems, we first review the spectral integral method based on spherical surface. The convergence and computational complexity are investigated using numerical experiments. Furthermore, a three-dimensional surface integral method based on cubic surface has been developed. Again, singularity subtraction is applied for the Green's functions. Due to the special properties of the surface, FFT algorithm is proposed to accelerate the solution of the integral equation. To apply the three-dimensional integral method to inhomogeneous problems, we develop a hybrid method, which combines the integral equation method and spectral element method. Both the spectral integral method and the hybrid method can be extended to layered media. |
