各向异性介质在三维ADI-FDTD中的应用

该文研究一种减小三维交替方向隐式时域有限差分法（ADI-FDTD）数值色散的新方法。通过在三维字间中合理添加各向异性介质，达到调整相速的目的，从而减小数值色散，使计算结果更加精确。首先对添加各向异性介质后的三维ADI-FDTD迭代公式进行变形，并得到新的数值色散关系，从而求解得到各向异性介质的相对介电常数。以空心波导和具有介质不连续性的波导作为数值算例，分析不同的各向异性介质和添加方法对计算精度的影响，并与传统ADI-FDTD得到的结果和计算资源占用情况进行比较。结果表明通过正确选择各向异性介质和添加方法，可以有效地减小三维ADI-FDTD数值色散。

Application of Artificial Anisotropy in 3-D ADI-FDTD Method

Attention is focused on a new method to reduce the numerical dispersion of the 3-D Alternating-Direction Implicit Finite-Difference Time-Domain(ADI-FDTD) method through artificial anisotropy. As the wave propagation can be speeded up by introducing proper anisotropy parameters into the 3-D ADI-FDTD method, the numerical dispersion can be reduced and the accuracy can be improved significantly. First, the numerical formulations of the 3-D ADI-FDTD method are modified. Secondly, the new numerical dispersion relation is derived. And consequently the relative permittivity tensor of artificial anisotropy can be obtained. In order to demonstrate the accuracy and efficiency of this new method, a hollow waveguide and a waveguide with discontinuous structure are simulated as examples. In addition the reduction of numerical dispersion is investigated as a function of the relative permittivity tensor of artificial anisotropy. Furthermore, the numerical results and the computational requirements of the proposed method are compared with those of the conventional 3-D ADI-FDTD method. It is found that this new method is accurate and efficient.