【摘要】 考虑随机交界面的光栅问题.首先将其抽象为具有相关边界条件的Helmholtz方程,并给定扰动交界面;然后提出一种基于形状导数和有限元方法的数值方法求解随机交界面的光栅问题,得到了随机交界面光栅问题期望的二阶逼近与方差的三阶逼近形式;最后给出误差估计和数值例子.更多还原

【Abstract】 We considered grating problems of random interface.Firstly,it was abstracted to be Helmholtz equations with relevant boundary conditions,and given the perturbation interface.Secondly,a numerical method based on shape derivative and the finite element method was proposed to solve the grating problem of random interface.The expected second-order approximation and the third-order approximation of variance for the grating problem of random interface were obtained.Finally,the estimation of error and numerical examples were given.更多还原