解一类具有周期系数的Helmholtz方程的小波谱方法

Wavelet-spectral methods for solving a class of Helmholtz equations with periodic coefficients

在现代光学理论及应用中,经常要讨论周期结构介质中的散射问题,其中周期结构通常被称为衍射光栅。在某些假设条件下,这些问题可用Helmholtz型的方程来描述。考虑一类具有周期系数的Helmholtz方程,它是一类衍射光栅问题的数学模型,研究这类问题的数值解法。采用的策略是小波谱方法,即在一个坐标方向使用谱方法,在另一个坐标方向采用小波Galerkin方法,得到相应的误差估计。

The scattering problem in periodic structural mediums often discussed in the theory and applications of modern micro-optics, where periodic structural mediums are often called diffraction gratings. Under some assumptions, these problems may be described by a class of Helmhotz equations with periodic coefficients. Numerical method for solving the class of equations is studied. The used strategy is the wavelet-spectral methods, i.e., the spectral method is used in an axial direction and the wavelet Galarkin method is used in another axial direction. Error estimates for the wavelet-spectral methods are established.