基于Z变换的拉伸坐标完全匹配层的改进算法

Modified algorithm of stretched coordinate perfectly matched layer based on Z -transform method

针对基于Z变换方法的拉伸坐标完全匹配层(SC-PML)提出了一种改进算法。新算法采用匹配Z变换技术将复拉伸坐标变量仿真为无限脉冲响应数字滤波器。与以前发表的SC-PML实现方法相比,新算法的主要优点是在PML的角和棱上仅仅需要一个辅助变量,从而节约了许多内存。而且,所提出的方法在不用修改的情况下,就能应用于仿真广义的FDTD计算域,诸如有耗、色散、各向异性或非线性。另外,还提出了一种应用在高阶差分方程中最小化内存的新算法。两个三维数字仿真实例验证了新算法的有效性。

A modified Z-transform-based algorithm for implementing the stretched coordinate perfectly matched layer （SC-PML） in the finite-difference time-domain （FDTD） method is proposed for truncating three-dimensional open domains. In the modified algorithm, complex stretched coordinate variables are modeled as a set of infinite impulse response digital filters by using the matched Z-transform method. The main advantage is that the proposed algorithm requires only one additional auxiliary variable in all corners and edges of the PML regions and hence saves lots of memory requirement as compared with that in the published papers about the SCPML. Also, the proposed method can be applied to simulating general FDTD computational domains such as lossy, dispersive, anisotropic, or nonlinear without any modifications. In addition, a new memory-minimized algorithm for the high-order difference equation is presented. Two numerical tests in three-dimensional case have been provided to validate the proposed algorithm.