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针对带界面的一维Helmholtz方程的数值求解问题，基于保梯度法的思想，采用贴体和非贴体两种网格，构造三种高精度有限差分格式。在推导界面处的差分方程时，最多用到三个网格点，且格式对应的方程组的系数矩阵均为三对角形式，从而可以快速求解。数值算例表明所提格式整体求解精度可达四阶，特别是在大波数情形时也变化不大。
Abstract：For the numerical solution of the one-dimensional Helmholtz equation with an interface, three high-order finite difference schemes are constructed based on the gradient preserved method, employing both body-fitted and non-body-fitted grids. When constructing the difference equations at the interface, a maximum of three grid points are involved, and the coefficient matrices of the resulting systems all exhibit a tridiagonal structure, enabling efficient computation. Numerical experiments demonstrate that the proposed schemes achieve fourth-order accuracy globally, with minimal degradation even at large wavenumbers.
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基本信息:
DOI：10.14155/j.cnki.35-1293/g4.2026.03.001
中图分类号:O241.3
引用信息:
[1]叶林薇,晏云.求解带界面的一维Helmholtz方程的高精度有限差分方法[J].武夷学院学报,2026,45(03):8-16.DOI:10.14155/j.cnki.35-1293/g4.2026.03.001.
基金信息:
福建省自然科学基金面上项目(2022J01897); 闽南师范大学校长基金(KJ18091)
2026-03-25
2026-03-25