A Hybrid SIM-SEM Method for 3-D Electromagnetic Scattering Problems

A new method combining the spectral integral method and spectral element method (SIM-SEM) is proposed to simulate 3-D electromagnetic scattering from inhomogeneous objects. In this hybrid technique (a special case of the finite element boundary integral (FEM-BI) combination), the SEM with the mixed-order curl conforming vector Gauss-Lobatto-Legendre (GLL) basis functions are used to represent the interior electric field with high accuracy, while the SIM on a cuboid surface is used as an exact radiation boundary condition. The Toeplitz property of the SIM matrix is utilized to reduce the memory and CPU time costs in an iterative solver by using the fast Fourier transform algorithm. Unlike the traditional FEM-BI combination where the BI portion usually dominates the computational complexity, the computational costs are much lower in the SIM-SEM method. Numerical results verify the accuracy and capability of this method, confirming that the SIM-SEM method is a good alternative for solving scattering problems from inhomogeneous objects.