为实现交变隐式时域有限差分法在周期结构电磁散射特性分析中应用,基于常规FDTD(finite-difference time-domain)中的UPML(uriaxial perfectly matched layer)吸收边界条件,导出了适用于周期结构三维ADI(alternating-direction implicit)-FDTD算法的UPML迭代计算式,并对其特有的一类非三对角系数矩阵提出了解决方案.数值算例表明,在时间步长是常规FDTD时间步长的6倍时,匹配层反射误差仅-30 dB.同时,应用UPML的ADI-FDTD仍然能够保持无条件稳定,并有足够的计算精度和更高的计算效率.但受数值色散误差的影响,CFL(courant-friedrich-levy)条件数一般宜小于8.%To apply the ADI-FDTD(alternating-direction implicit finite-difference time-domain) algorithm to analyzing the electromagnetic scattering characteristics of the periodic structures, the formulations of uniaxial perfectly matched layer (UPML) for periodic structural three-dimensional ADI-FDTD algorithm,as well as the treatment of the special non-tridiagonal matrix were proposed based on the conventional UPML formulations.The reflection error of the proposed ADI-UPML absorber can be -30 dB when the time-step size is six times of the conventional FDTD method.Numerical results show that this scheme can still remain unconditionally stable, and has enough precision and better effectiveness, but the CFL (courant-friedrich-levy) number should be fewer than eight due to the numerical dispersion error.
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