An Alternative Direction Decomposition Scheme and Error Analysis for Parabolic Equation Model

Alternate direction implicit (ADI) method has been widely used to analyze the tunnel propagation or electromagnetic scattering problem for the finite difference method. In this paper, a novel alternate direction decomposition (ADD) scheme is proposed to simplify the split-step Fourier transform (SSFT) algorithm in parabolic equation (PE) model. The spatial matrix of electric field is decoupled into two subarrays by ADD-SSFT algorithm, which is used to decrease the computational burden for 3-D PE problems in a large scale environment after the integration order exchanged. Also, the phase error of this approximation is analyzed to show the algorithm performance, along with several numerical results, including the tunnel cases with traditional modal theory, and they are provided to validate and calibrate the PE model, and demonstrate the efficiency and accuracy of the proposed algorithm. Moreover, the scattering computation is investigated and compared with multilevel fast multipole method to show that ADD-SSFT is appropriate for solving the scattering problems for the electrical large target.