非均匀网格GA-A3DI-FDTD法分析微波电路

Analysis of microwave circuits by non-uniform mesh GA-A3DI-FDTD method

研究了一种减小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)及其在非均匀网格条件下的应用。首先对添加人工各向异性介质后的非均匀网格ADI-FDTD迭代公式进行修正,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。为了验证方法的正确性和有效性,对几种微波电路进行仿真,分别与传统ADI-FDTD相比较,并且比较对非均匀网格的不同处理方法对计算精度的影响。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,可以再减小三维ADI-FDTD数值色散。

To reduce the numerical dispersion of the 3-D Alternating-Direction Implicit Finite-Difference Time-Domain （ADI-FDTD） method for the non-uniform mesh case, a novel ADI-FDTD method is presented in this paper. As the wave propagation can be speeded up by introducing proper artificial anisotropy parameters into the 3-D ADI-FDTD method, the numerical dispersion can be reduced and the accuracy can be improved significantly. Firstly, the numerical formulations of the 3-D non-uniform mesh ADI-FDTD method are modified, Secondly, the new numerical dispersion relation is derived. And then the relative permittivity tensor of artificial anisotropy can be obtained by adaptive genetic algorithm （AGA）. In order to demonstrate the accuracy and efficiency of this new method, several microwave circuits are simulated as examples. In addition the reduction of numerical dispersion is investigated as a function of the relative permittivity tensor of artificial anisotropy for the non-uniform mesh case. It is found that this new method is accurate and efficient.