| In this dissertation, I present my research results in computational electromagnetics and pseudospectral methods. In 1-D, the comparisons of staggered and non-staggered finite difference and spectral methods have been done. I also give some new penalty methods for 1-D scalar hyperbolic equation and Maxwell's equations. It is shown that the advantage of staggering for low-order methods diminishes when we go to high-order and spectral methods, which is verified in numerical experiments.;In 2-D, I present a new polar PML method, a mapped ML method, and well-posed PML methods. Simulations of scattering by perfect electrically conducting (PEC) circular, elliptic, and rectangular cylinders using multidomain pseudospectral methods with the proposed absorbing layer methods have been done to validate the methods. For comparison, results of finite difference time domain (FD-TD) computations of the same problems are also presented, and spectral methods are shown to be superior to FD-TD methods.;Absorbing layers for more general 2-D structures are also discussed, where we give a multidomain implementation of the PML methods and an approximately matched layer method. Simulations of scattering by PEC parallelogram and triangular cylinders have been done to verify our claims. The proposed methods give better results than some other extensions of the PML method do.;In 3-D, we have developed split-field and well-posed PML methods in spherical and cylindrical coordinates. A general multidomain pseudospectral scheme is developed to simulate scattering by a PEC cube, a PEC sphere and a PEC finite cylinder. Efficacy of our proposed PML methods is demonstrated in numerical experiments.;For the simulation of scattering by bodies of revolution (axis symmetric), we develop a multidomain pseudospectral scheme with the mapped ML method as the absorbing boundary condition, where PML methods are not applicable. We solve modified BOR Maxwell's equations with proper boundary conditions at the axis that remove the singularity there. Simulations of scattering of both axially and obliquely incident waves by both smooth and non-smooth PEC scatterers have been done. The scheme has been extended to simulate scattering by dielectric spheres in the last chapter. |
