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
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.
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