MRTD和高阶FDTD算法的数值色散特性的分析

Analysis of numerical dispersion properties of MRTD and higher-order FDTD schemes

时域多分辨分析(MRTD)算法和高阶时域有限差分法(HO-FDTD)是目前解决电大尺寸电磁结构仿真的有效手段。导出了基于Daubechies小波尺度函数的MRTD算法和HO-FDTD算法的通用差分公式和数值色散方程,并详细讨论了空间步长、时间步长以及电磁波传播方向对二者数值色散误差的影响。结果证明,MRTD算法与HO-FDTD算法非常相似,但HO-FDTD算法的数值色散特性优于具有相同展开项个数的MRTD算法。

The Mutliresolution Time-domain method （MRTD） and the Higher-order Finite-difference Time-domain method （HO-FDTD） are efficient ways to simulate the electrical-large electromagnetic structures. The general difference formula and the numerical dispersion equation for the MRTD scheme based on the Daubechies scaling functions and the FDTD method with higher-order approximate were deduced, The effects of spatial grid, time interval and propagation angle on the dispersion error were discussed in details. The numerical results show that MRTD schemes are similar to HO-FDTD methods; however, the numerical dispersion property of HO-FDTD is superior to that of MRTD scheme with the same number of the expending polynomial.