Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates
Fast Finite Difference Solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates作者机构:Department of Mathematics Indian Institute of Technology Roorkee India
出 版 物:《American Journal of Computational Mathematics》 (美国计算数学期刊(英文))
年 卷 期:2013年第3卷第4期
页 面:356-361页
学科分类:07[理学] 0701[理学-数学] 070101[理学-基础数学]
主 题:Poisson’s Equation Hockney’s Method Thomas Algorithm
摘 要:In this work, the three-dimensional Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly, by extending the method of Hockney. The Poisson equation is approximated by second-order finite differences and the resulting large algebraic system of linear equations is treated systematically in order to get a block tri-diagonal system. The accuracy 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.