求解泊松方程的六阶紧凑差分方案和多网格法

IF 1.9 4区 数学 Q1 MATHEMATICS Mathematical Sciences Pub Date : 2024-01-29 DOI:10.1007/s40096-023-00522-3
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引用次数: 0

摘要

摘要 本文基于二阶导数的六阶紧凑差分算子,提出了泊松方程的六阶紧凑差分方案。该方案与其他六阶方案的最大区别在于其右手包含源项的二次偏导,这使得该方案比其他六阶方案更加精确。所提方案与多网格法相结合,用于求解具有 Dirichlet 边界条件的二维和三维泊松方程。在几个数值实验中将结果与其他六阶方案进行了比较。数值结果表明,与其他同阶方案相比,拟议方案达到了预期精度,误差更小。此外,与传统迭代法相比,多网格法在加速收敛方面效率更高。
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Sixth-order compact difference scheme and multigrid method for solving the Poisson equation

Abstract

This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second derivative. The biggest difference between the proposed scheme and other sixth-order scheme is that the right hand contains second partial derivation of source term; this term makes the proposed scheme more accurate than other sixth-order schemes. The proposed scheme is combined with the multigrid method to solve two- and three-dimensional Poisson equations with Dirichlet boundary conditions. The result is compared with other sixth-order schemes in several numerical experiments. The numerical results show that the proposed scheme achieves the desired accuracy and has smaller errors than other schemes of the same order. Further, the multigrid method is higher efficient than traditional iterative method in accelerating the convergence.

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来源期刊
CiteScore
4.20
自引率
5.00%
发文量
44
期刊介绍: Mathematical Sciences is an international journal publishing high quality peer-reviewed original research articles that demonstrate the interaction between various disciplines of theoretical and applied mathematics. Subject areas include numerical analysis, numerical statistics, optimization, operational research, signal analysis, wavelets, image processing, fuzzy sets, spline, stochastic analysis, integral equation, differential equation, partial differential equation and combinations of the above.
期刊最新文献
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