一维带PML的Helmholtz方程的四阶差分法

A FOURTH-ORDER FINITE DIFFERENCE SCHEME FOR THE ONE-DIMENSIONAL HELMHOLTZ EQUATION WITH PML

本文构造了一维带PML(Perfectly Matched Layer,完全匹配层)的Helmholtz方程的四阶差分格式.首先,建立了带参数的四阶差分格式,分析了数值波数与真实波数之间的误差.然后,基于极小化数值频散的思想,提出了差分格式优化系数的整体选取策略和加细选取策略.最后,数值算例结果表明带加细参数的四阶差分格式有效地抑制了数值频散,提高了数值精度,在计算大波数问题时具有显著优势.

In this paper,we develop a fourth-order finite difference scheme for the one-dimensional Helmholtz equation with PML(the perfectly matched layer).Firstly,a fourth-order finite difference scheme with parameters is proposed,and the error between the numerical wavenumber and the real wavenumber is analyzed.Then,based on the idea of minimizing numerical dispersion,we propose a global choice strategy and a refined choice strategy for choosing optimal parameters of the finite difference scheme.Numerical results are given to illustrate that the fourth-order finite difference scheme with refined parameters not only suppress the numerical dispersion,but also improve the accuracy,which has advantages in dealing with large wave number problems.