Wide-angle Parabolic Equation Method With Alternating Direction Implicit Scheme For EM Scattering Problems

Computational electromagnetics can be divided into two categories, the low frequency method and the high frequency method. The low frequency methods, such as finite difference time domain(FDTD), method of moments(MOM) and finite element method(FEM), can effectively solved the electrically small scattering problems. However, more memory requirements are needed for these methods. The high-frequency methods need less computer resources with high speed, but the accuracy is poor. However, the prabolic equation method(PE) take a bridge between them.A three-dimensional problem can be converted into a series of two-dimensional problems by the traditional parabolic equation method which is based on finite difference scheme, thus the memory requirement can be saved largely. In this thesis, the alternating direction implicit(ADI) scheme was applied to reduce the computation complexity by solving the fields in one dimension. Therefore, both the memory requirement and CPU time can be saved largely.The main works of this thesis are listed as follows:Firstly, the basic principles of parabolic equation method is introduced, including the form of parabolic equation, the principle of perfectly matched layer, near and far field transformation principle and wide-angle parabolic equation.Then the alternating direction implicit(ADI) scheme is studied and a wide-angle parabolic equation based on ADI scheme is presented.At last, we introduce the parallel algorithm to accelerate the proposed method.