Research On CN - FDTD - PML Algorithm Based On Auxiliary Differential Equation

K. S. Yee proposed a novel and efficient numerical method for solving the Maxwell’s equations in 1966, which named as the finite-difference time-domain (FDTD) method. Since Berenger developed the perfect matched layer (PML) theory in 1994, it has been well studied as it can hold good absorbing performance. As an explicit method, the time-step of FDTD method is restricted by the CFL stability constraint. On other hand, as the frequency we deal with becomes much higher, the uncondional stable method has aroused widespread concerns. The typical unconditional stability algorithms contain the ADI-FDTD algorithm based on the Alternating-Direction-Implicit method, the LOD-FDTD algorithm based on the Locally-One-Dimensional method, the CN-FDTD algorithm based on the Crank-Nicolson method and so on. However, the ADI-FDTD algorithm and the LOD-FDTD algorithm can be considered as a 2nd order perturbation to the CN scheme with large anisotropy. Thus, the emphasis of this thesis is to research and propose unconditional stable CN-FDTD-PML formulations whitch can be solved efficiently. Numerical tests have been carried out to validate the proposed PML algorithms.The main achievements and originality of this thesis are listed as follows.1. Combined with the Crank-Nicolson Approximate-Decoupling FDTD (CNAD-FDTD) method and the Complex Frequency Shifted PML (CFS-PML) formulations, a novel, unconditional stable and unsplitted PML algorithm named as CNAD-CFS-PML has been proposed in this thesis. Compared with the ADI-PML algorithm, this proposed algorithm can simplify the derivation process and improve the computational efficiency by avoiding split one full time-step into two halves.2. Combined with the Crank-Nicolson Douglas-Gunn FDTD (CNDG-FDTD) method and the Stretched Coordinate PML (SC-PML) formulations, an efficient, unconditional stable and unsplitted PML algorithm named as CNDG-SC-PML has been proposed in this thesis. Compared with the CNAD-CFS-PML algorithm, this new algorithm can hold better absorbing performance with the same computational efficiency.