Research On Completely Matching Layer Algorithm Of CN - FDTD Based On Bilinear Transformation Method

Finite-difference time-domain (FDTD) method with the advantages of convenient dispersion method and wide applicability has become a commonused electromagnetics numerical method and been applied in many field. However, with the increasing deeply research, conventional FDTD method is restricted by Courant-Friedrichs-Lewy (CFL) stable condition, especially for the small scale conductor. This defection is gradually uncovered in recent years. Therefore, many unconditional stable FDTD method has been proposed in recent decades. Crank-Nicolson (CN) FDTD is one of novel unconditional stable FDTD method for electromagnetic simulations. This method has a high level of accuracy and all computing process only run in one step. In spite of the last solving equation of CN-FDTD forms a block tridiagonal matrix which solution would consume tremendous resource of computers, we can adopt some proximate method such as Douglas-Gunn (DG) and approximately decoupling (AD) method to decomposed the solving equation as several easy tri-diagonal matrix equations to be solved at last. In this way, the value of E and H can be obtained easily.Absorbing boundary condition (ABC) as a significant part of FDTD method is always a vital research point. At present, the most effective and widely used ABC is perfectly matched layer (PML), which is set a kind of idiosyncratic layer at the margins of the computational region. By choosing specific parameters of the PML material reasonably, the electromagnetic waves could transmit into this layers without any reflection, which isn’t related with the angle, frequency and polarization of the incidence waves. As the PML is a kind of lossy material, the incident waves would be attenuated instantly. Stretched-coordinate PML, a scheme of PML with comparative easy formulation in the corner of the computational region, is widely used in truncating the FDTD computation. For absorbing low frequency and evanescent waves, complex frequency shifted PML is introduced afterwards. In this dissertation, the main purpose of my research is to propose the appropriate PML for the unconditional stable CN FDTD method. All the algorithms adopted the SC-PML scheme and proposed algorithm is validated in numerical experiments. The main content and innovation points of this dissertation list as follows:1. Based on the bilinear transform (BT) method, CN-FDTD PML algorithm is proposed by using the SC-PML scheme. There are two algorithm. On one hand, auxiliary variables are introduced into the formulations. In this dissertation, this method is applied to truncate a 2-D free space and CNDG method is used for solveing the equation. The proposed algorithm is named asBT CNDG-PML in this dissertation. On the other, as the special form of FDTD formulation of SC-PML, the formulation of SC-PML can be manipulated in Z region before dispersion. In this dissertation, this method is used to truncate a 1-D one order Debye media. Especially, we don’t use any auxiliary variable to help, this proposed method is called as BZT CN-PML here. The BZT CN-PML have less auxiliary variables than previous CN-PML. In this case, computing time will be reduce. To validate the proposed algorithm, numerical experiments are introduced. From the result, the proposed algorithms meet unconditional stablility and have a good performance of absorbing electromagnetic waves.2. Based on the bilinear transform (BT) method, CN CFS-PML algorithm is proposed by using the SC-PML scheme. Both algorithm is realized in 2-D situation and according to the solving method, there are two algorithm and called as CNDG CFS-PML and CNAD CFS-PML respectively. Both algorithm are effective and unconditional stable. To be mentioned, since the drawback itself, the CNAD PML’s relative reflection error could slightly increase as the time interval of FDTD increases. However, it also keep unconditional property and meet the demand of simulation of engineering.Appropriate numerical experiments are carried out finally. All the results demonstrated that the proposed algorithms are unconditional stable and effective to absorb the electromagnetic waves. In this case, using the CN-PML with the unconditional stable PML can be less time consuming and improve the computational efficiency.