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

American Journal of Computational Mathematics 2011年第4期1卷 285-293页

作者： Alemayehu shiferaw Ramesh Chand Mittal 不详

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

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Fast Finite Difference solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinates

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American Journal of Computational Mathematics 2013年第4期3卷 356-361页

作者： Alemayehu shiferaw R. C. Mittal Department of Mathematics Indian Institute of Technology Roorkee India

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.

关键词： Poisson’s Equation hockney’s Method Thomas Algorithm

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High Accurate Fourth-Order Finite Difference solutions of the Three Dimensional Poisson’s Equation in Cylindrical Coordinate

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American Journal of Computational Mathematics 2014年第2期4卷 73-86页

作者： Alemayehu shiferaw Ramesh Chand Mittal Department of Mathematics Indian Institute of Technology Roorkee India

In this work, by extending the method of hockney into three dimensions, the Poisson’s equation in cylindrical coordinates system with the Dirichlet’s boundary conditions in a portion of a cylinder for is solved directly. The Poisson equation is approximated by fourth-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.

关键词： Poisson’s Equation Tri-Diagonal Matrix Fourth-Order Finite Difference Approximation hockney’s Method Thomas Algorithm

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