基于改进型UPML吸收边界条件的电磁波数值模拟

THE NUMERICAL MODELING OF ELECTROMAGNETIC WAVES BASED ON THE IMPROVED UPML ABSORBING BOUNDARY CONDITION

基于分裂场的完全匹配层(PML)吸收边界条件完成了对非物理反射波的吸收,初步实现了有限区域对无限开放空间的数值模拟,然而在计算区域的边界上需要对场分量进行分裂,增加了Maxwell方程组中独立方程的个数,使场分量迭代复杂,增大了数值计算量.单轴各向异性完全匹配层(UPML)边界条件则不需要对场分量进行分裂,迭代公式简单,便于程序实现,本文在常规UPML上增加了自由可变因子,使得对低频成分的反射波具有更好的吸收效果.本文首先推导了TMz波的改进型UPML方程组,给出了改进型UPML的介电参数分布方式,详细介绍了该算法的程序实现步骤,并以数值算例进行验证,分别采用基于分裂场的PML、常规UPML和改进型UPML边界条件进行数值计算,并从波场快照、时间域反射误差和频率域反射误差等方面,对比了三者的吸收效果,结果表明;在电磁波传播后期,改进型UPML吸收边界条件对低频率成分的反射波具有更好的吸收效果,更真实地模拟了开放的无限空间.

The split Perfectly Matched Layer （PML） Absorbing Boundary Condition （ABC） ac- complished the absorption of nonphysical reflections, preliminarily realized the numerical modeling of open infinite space to the finite area, however, on the edge of the ABC area, the field component in calculation need to be split, which will increasing the number of independent equations and the calculation capacity in Maxwell＇s equations. The Uniaxial- anisotropic Perfectly Matched Layer （UPML） boundary conditions do not need to split the field component, and the iterative formula is easy convenient to programming, except to the decay parameters in the conventional UPML, another two real variable factors are intro- duced, which is exclusively for the reflections of low frequency. The TMZ wave equations of improved UPML is deduced, the dielectric parameter distribution mode is given, and the program implementation steps of the algorithm was introduced in detail, then the merit- s were verified by a numerical modeling example of electromagnetic waves, with the split PML, the conventional UPML and the improved UPML boundary conditions, respectively, by comparing the absorption effect from the aspects of the snapshots, and the time domain reflection errors and the frequency domain reflection errors, the results show that the im- proved UPML boundary condition possess an apparent advantage over absorbing the low frequency reflections in the latter period of the wave propagation, which is more realistically simulates the infinite and open space with little truncation.