An Efficient Direct Method to Solve the Three Dimensional Poisson’s Equation  

作　　者：Alemayehu Shiferaw Ramesh Chand Mittal 

机构地区：[1]不详

出　　处：《American Journal of Computational Mathematics》2011年第4期285-293,共9页美国计算数学期刊（英文）

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.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 

分 类 号：O1[理学—数学]