文章基本信息

标题：An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation
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作者：Alemayehu Shiferaw ; Ramesh Chand Mittal
期刊名称：American Journal of Computational Mathematics
印刷版ISSN：2161-1203
电子版ISSN：2161-1211
出版年度：2011
卷号：1
期号：4
页码：285-293
DOI：10.4236/ajcm.2011.14035
出版社：Scientific Research Publishing
摘要：In this work, the three dimensional Poisson’s equation in Cartesian coordinates with the Dirichlet’s boundary conditions in a cube is solved directly, by extending the method of Hockney. The Poisson equation is approximated by 19-points and 27-points fourth order finite difference approximation schemes and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The efficiency of this method is tested for some Poisson’s equations with known analytical solutions and the numerical results obtained show that the method produces accurate results. It is shown that 19-point formula produces comparable results with 27-point formula, though computational efforts are more in 27-point formula.
关键词：Poisson’s Equation; Finite Difference Method; Tri-diagonal Matrix; Hockney’s Method; Thomas Algorithm