Research Of Finite-Element Time-Domain Method In Computational Electromagnetics

In this dissertation, some research has been done for the finite element time domain (FETD) method.For the FETD method based on the second-order vector wave equation, the first order impedance boundary condition (IBC) is combined with the perfectly matched layer (PML) absorbing boundary condition (ABC) to improve the absorbing effect of the PML ABC. Numerical results clearly show that the PML backed with the first order IBC performs better and can reduce more reflection errors than the PML backed with the perfect electrically conducting (PEC) wall.Using Taylor series expansions, the second order waveguide IBC in the time domain is introduced. It is employed to terminate the PML ABC for the FETD method simulation of waveguide problems. The better absorbing effect is gained compared with that obtained by the PML ABC backed with the first order IBC.When large problems are simulated in the FETD method, it is very time-consuming to solve large sparse matrix equations. To tackle this difficulty, a kind of domain decomposition method-tearing and interconnecting algorithm used in the FETD method is presented. Using this method, some quasi-period structures have been simulated efficiently.In the FETD method based on a direct discretization of the first-order coupled Maxwell curl equations, edge elements (Whitney-I form) to expand the electric field and face elements (Whitney-II form) for the magnetic field are employed. Since the curl of an edge-element is the linear combination of those face-elements whose faces contain the given edge, only the Maxwell-Ampere equation composes a sparse linear matrix equation for the electric field update, the Maxwell-Faraday equation is explicit. The Crank-Nicolson (CN) scheme and the alternation-direction implicit (ADI) scheme are implemented in this method leading to unconditionally stable vector finite element time domain methods.The accuracy of the ADI-FETD method and the CN-FETD method is compared. Theoretical analysis and numerical tests demonstrate that the ADI-FETD method has no splitting error which exists in the ADI-FDTD method. The ADI-FETD method is exactly a two step scheme for CN-FETD method, and the accuracy of the two methods is the same.