一种降低交替方向隐式时域有限差分数值色散的方法

针对交替方向隐式时域有限差分方法(ADI-FDTD)数值色散严重的缺点,提出了一种低数值色散的各向同性 ADI-FDTD 方法.该方法在ADI-FDTD方法的差分近似微分中引入各向同性差分模板,并通过确定各向同性差分的加权系数来近似实现各向同性,然后人为修正空间的介质参数来减少各个方向上的数值色散误差,因此在模拟一定带宽的时域问题时可有效提高计算精度和计算效率.仿真结果表明,该方法在单频上可近似实现无数值色散误差,在所优化的频带附近其数值色散误差是 ADI-FDTD 方法的1%.

Efficient Method to Reduce the Numerical Dispersion in the Alternating Direction Implicit Finite-Difference Time-Domain Algorithm

To reduce the large numerical dispersion error for the alternating direction implicit finite-difference time-domain method (ADI-FDTD),an isotropic ADI-FDTD method with low numerical dispersion error was presented.Firstly,the isotropic difference templates were introduced to approximate the differential in the ADI-FDTD method,and the weighting coefficients of difference terms were determined for implementing isotropic numerical dispersion;Then the permittivity and permeability were adjusted manually to reduce the numerical dispersion error in any directions.Therefore the simulation accuracy and efficiency can be improved effectively for time domain problems with some finite bandwidths.Simulation results show that the proposed method is nearly free from dispersion for a monochromatic frequency,and the numerical dispersion error is decreased approximately by 1% compared with the ADI-FDTD method in the optimizing frequency band.