理论反射系数对于完全匹配层边界的吸收效果影响分析

Analysis of the Impact of the Theoretical Reflection Coefficient on the Perfectly Matched Layer Absorbing Boundary

本文基于平面波理论和空间二阶精度差分格式推导出声波方程数值模拟中的完全匹配层边界条件反射系数公式,并基于该公式系统分析了理论反射系数对于完全匹配层吸收效果的影响。实验结果表明,对于小入射角度(小于30°)的入射波,当理论反射系数R取10^(-4)时,完全匹配层有最优的吸收效果;对于入射角度为40°、50°和60°的入射波,当理论反射系数R分别取10^(-5)、10^(-6)和10^(-8)时完全匹配层边界反射系数最小;而对更大角度的入射波,需要更小的理论反射系数R才能使得完全匹配层达到最优的吸收效果。

This paper derives the reflection coefficient formula of the perfectly matched layers（denoted as＂PML＂）for the numerical simulation of the acoustic wave equation,based on the plane wave theory and the second-order accuracy spatial difference scheme.Then,the impact of the theoretical reflection coefficient Ron the absorption effect of the PML is analyzed.The experimental results demonstrate that,for the incident wave with a small incident angle（less than 30°）,when Ris equal to 10-4,the PML absorbing boundary condition has the optimal absorption effect.And for the incident wave with the incident angles of 40°,50°and 60°,when the Ris equal to 10-5,10-6 and 10-8 respectively,the PML absorbing boundary condition has the smallestactual reflection coefficients.While for the incident wave with a large incident angle,in order to achieve the optimal absorption effect,it is necessary to take a smaller R.