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W. F. Spotz and G. F. Carey, “A High-Order Compact Formulation for the 3D Poisson Equation,” Numerical Methods for Partial Differential Equations, Vol. 12, No. 2, 1996, pp. 235-243. doi:10.1002/(SICI)1098-2426(199603)12:2<235::AID-NUM6>3.0.CO;2-R

has been cited by the following article:

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

  AUTHORS: Alemayehu Shiferaw, Ramesh Chand Mittal

  KEYWORDS: Poisson’s Equation, Finite Difference Method, Tri-diagonal Matrix, Hockney’s Method, Thomas Algorithm

  JOURNAL NAME: American Journal of Computational Mathematics, Vol.1 No.4, December 9, 2011

  ABSTRACT: 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.