Numerical reflection analysis of PML absorbing boundary in 3-D GA-A3DI-FDTD method
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摘要: 研究一种减小三维交替方向隐式时域有限差分法ADI-FDTD(Alternating-Direction Implicit Finite-Difference Time-Domain)数值色散的新方法GA-A3DI-FDTD(Genetic Algorithm Artificial Anisotropy ADI-FDTD).首先对添加人工各向异性介质后的三维ADI-FDTD迭代公式进行变形,得到新的数值色散关系,再利用自适应遗传算法AGA(Adaptive Genetic Algorithm)得到需要添加的人工各向异性介质的相对介电常数.并以空心波导作为数值算例,分析了由不同目标函数得到的人工各向异性介质对计算精度以及PML(Perfectly Matched Layers)吸收边界数值反射产生的影响,同时分别与传统ADI-FDTD相比较.结果表明通过正确选择目标函数,得到更加合适的人工各向异性介质,可以在减小三维ADI-FDTD数值色散的同时,有效地抑制由于人工各向异性介质的添加所造成的PML吸收边界数值反射的增强.Abstract: Attention was focused on a new method to reduce the numerical dispersion of the 3-D ADI-FDTD (three-dimensional alternating-direction implicit finite-difference time-domain) method through artificial anisotropy. First, the numerical formulations of the 3-D ADI-FDTD method were modified. Second, the new numerical dispersion relation was derived. And consequently the relative permittivity tensor of artificial anisotropy could be obtained by the AGA (adaptive genetic algorithm). In order to demonstrate the accuracy and efficiency of the 3-D GA-A3DI-FDTD (genetic algorithm artificial anisotropy ADI-FDTD) method, a hollow waveguide was simulated as an example. Both the relative phase velocity and the numerical reflection of PML (perfectly matched layers) absorbing boundary were investigated for different objective functions of the AGA. And the numerical results of the proposed method were compared with those of the conventional 3-D ADI-FDTD method. It is found that this new method is more accurate and efficient.
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