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Spectral element method-based parabolic equation for EM-scattering problems. (English) Zbl 1367.65175

Summary: The traditional parabolic equation (PE) method is based on the finite difference (FD) scheme. However, the scattering object cannot be well approximated for complex geometries. As a result, a large number of meshes are needed to discretize the complex scattering objects. In this paper, the spectral element method is introduced to better approximate the complex geometry in each transverse plane, while the FD scheme is used along the paraxial direction. This proposed algorithm begins with expanding the reduced scattered fields with the Gauss-Lobatto-Legendre polynomials and testing them by the Galerkin’s method in each transverse plane. Then, the calculation can be taken plane by plane along the paraxial direction. Numerical results demonstrate that the accuracy can be improved by the proposed method with larger meshes when compared with the traditional PE method.

MSC:

65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35Q60 PDEs in connection with optics and electromagnetic theory
78A45 Diffraction, scattering
35K99 Parabolic equations and parabolic systems
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