An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation
An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation作者机构：不详
出 版 物：《American Journal of Computational Mathematics》 (美国计算数学期刊（英文）)
年 卷 期：2011年第1卷第4期
页 面：285-293页
主 题：Poisson’s Equation Finite Difference Method Tri-diagonal Matrix Hockney’s Method Thomas Algorithm
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.
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