Higher Order Vector Finite Element Method For Three-Dimensional Electromagnetic Scattering And Radiation Analysis

In recent years the fields of computational electromagnetics have been seen a considerable surge in research on efficient accurate numerical methods, which have been stimulated by the demands for electromagnetic targets simulations. The emphases of this paper are concentrating on investigating of higher order vector finite element methods and its applications to three-dimensional electromagnetic scattering and radiation. First, higher order vector basis functions corresponding to three finite elements including tetrahedral elements, prism elements and hexahedral elements are studied. Second, a higher order vector finite element-boundary integral method (FE-BI) based on hexahedral elements is developed and employed to compute RCS of cavities and input-impedance of cavity-backed patch antennas. Third, two novel reliable preconditoners are introduced to accelerate the solutions of higher order vector FE-BI matrix equations. The effects of the incomplete LU decomposition involved on the preconditoners are investigated. Numerical results from RCS of cavities demonstrate the efficiency of the presented preconditioners. Finally, combined with model order reduction techniques (MORe) including asymptotic waveform evaluation (AWE), Galerkin AWE (GAWE), projection via Arnoldi, and well-conditioned AWE (WCAWE), several higher order vector FE-BI methods are developed and are capable of producing fast accurate robust wide-band simulations with just one expansion point. The studies of this paper demonstrate high accuracy and efficiency of higher order vector finite element methods and show tremendous potential for the solutions of electromagnetic engineering problems.