Research On The Improved Absording Boundary Condition And The Alternative Direction Implicit FDTD

This thesis is concerned with the improved algorithm of Finite Difference Time Domain (FDTD) method-the improved algorithm of the Perfectly matched layer and the Alternative Direction Implicit FDTD (ADI-FDTD) method. The history and disadvantage of the FDTD scheme are introduced firstly , and the basis equations and some key techniques are presented. Moreover the temporal and spatial dispersive relations are also discussed and the criteria of their steps are derived, which is so called Courant-Friedrichs-Lewy (CFL) constraint condition in this paper.(1) In order to be applied for unboundary problems, the FDTD requires the use of appropriate absorbing boundary conditions. Many researchers have built up many methods to deal the problem, but the applications were difficulty. A new method based on incorporating the Z-transform method was presented in this paper and introduced into the FDTD implementation of UPML and CPML absorbing boundary condition. The advantage of this method is its simplicity and can be used into standard cells or unstandard cells.(2) Due to the difficulty of FDTD dealing with the dispersive material, this paper use the D-B method instead of E-H method, which is more suitable for dealing with dispersive material .The numerical experiments have verity this method.(3) Data compressing technique is employed to compress the field to reduce the memory needs. We present a technique in which discrete cosine transform and Wavelet Transform are used to compress the time domain field distribution on the surface of Huygens' box and we store it in the compressed file format that is much smaller than its original size. Numerical examples demonstrate the validation of this algorithm.(4) It is the CFL constraint conditions that influence the efficiency of conventional FDTD. To overcome this, we make a professional research on the ADI-FDTD scheme, and derive the basis equations from the original. Maxwell's equations by incorporating the signal processing techniques. (5) Due to the complexity of ADI-FDTD update equations , this method is not suitable for the electromagnetic scattering analysis. Therefore, this paper adopted the pure scattering field simulations. This method simplified the absorbed and adjacent boundary condition greatly in electromagnetic scattering problems. The numerical examples proved the vality of the method.(6)Furthermore, a comprehensive analysis of the numerical anisotropy and dispersion of the ADI-FDTD is presented. From the dispersion analysis, it is found that the ADI-FDTD method has advantages over the conventional FDTD of Yee's scheme in modeling structures with fine geometry where a...