UPML吸收边界条件统一建模与优化方法

Unified Modeling and Optimization of UPML Absorbing Boundary Conditions

单轴各向异性介质完全匹配层(UPML)是时域有限差分方法(FDTD)的一种理想的吸收边界条件,但多个子区域的迭代运算增加了UPML实现的难度和耗用资源.通过寻找UPML区域中介质属性的变化规律,提出实现UPML吸收边界条件的统一建模方法,并在此基础上提出两种精简辅助变量占用空间的优化算法———六区域分割方法和压缩变量方法.计算结果表明,统一建模方法只需三次循环即可完成三个方向所有介质参数及迭代系数的初始化;六区域分割方法虽然节省了大量无用存储空间,但速度最慢;压缩变量方法不仅节省存储空间、方便编程实现,而且提高了仿真速度.

Transformation of dielectric properties in uniaxial anisotropic perfectly matched layer（UPML） regions is explored and unified modeling of UPML is proposed.Two condensing optimized algorithms for auxiliary variables,six regions＇ intersected method and parameter-compressed method,are proposed.In three cycles all initialization of medium parameters and iterative coefficients in three directions are completed with unified modeling method.Though the six regions＇ intersected method saves a lot of memory,it is the slowest.The parameter-compressed method saves space,which is programmed easily and runs the fastest.