Numerical Analysis of Electromagnetic Scattering Using Constrained Interpolation Profile Method

The field of computational electromagnetics (CEM) was significantly broadened by the pioneer work of Yee, when the time-dependent Maxwell’s equations are solved numerically in an isotropic medium [1]. This algorithm is called finite-difference time-domain (FDTD) Method, and it has second-order accuracy in temporal and spatial domain [2]. Since FDTD method is relatively simple to implement, efficient and robust for many types of problems, it has been widely used nowadays. However, the conventional Yee’s FDTD method suffers from the numerical dispersion or the anisotropy: the numerical velocity of propagation is dependent on the mesh size, time step size, and the direction of propagation. This anisotropy causes the accumulative phase error which reduces the global accuracy when analysis domain is relatively large. Recently, the application of the characteristic-based constrained interpolation profile (CIP) method to the field of CEM was proposed by Yabe et al. [3]. CIP method can accurately solve hyperbolic equations with third-order accuracy in space. Okubo [4] showed that CIP method provides higher accuracy comparing with FDTD method under the condition of the same cell size. He also concluded that CIP method requires less memory and less calculation time for the same accuracy. However, to the best of authors’ knowledge, the three-dimensional scattering analysis using CIP method has not been reported so far. This paper proposes an approach utilizing CIP method to solve the EM scattering problem and shows the algorithms that enable the analysis of three-dimensional problems including perfect conducting (PEC) objects and dielectric objects. The radar cross sections (RCS) of PEC sphere and dielectric sphere are calculated to demonstrate the possibility to use CIP method as alternative CEM tools.