Frequency-domain and time-domain solvers of parabolic equation for rotationally symmetric geometries

Abstract

Both the frequency-domain and the time-domain body of revolution parabolic equations (FD-BoR-PE, TD-BoR-PE) are derived in this paper. By taking advantage of the rotationally symmetrical property, better performance of the PE method can be achieved for the analysis of bodies of revolution (BoRs). In each transverse plane, only the unknowns of a line, which starts from the center and passes through the node on the generatrix, need to be calculated. Then the unknowns for each transverse plane can be obtained by Fourier series summation for each Fourier mode and the calculation can be taken with a marching manner along the paraxial direction of the PE. As a result, the computational resources can be reduced greatly when compared with the traditional CN, alternating direction implicit (ADI) and alternating group explicit (AGE) finite difference schemes. Both the propagating and scattering problems are given to demonstrate the validity and efficiency of the proposed methods.