The Shortley-Weller embedded finite-difference method for the 3D Poisson equation with mixed boundary conditions
作者： Z. Jomaa , C. Macaskill
DOI: 10.1016/J.JCP.2010.01.021
关键词: Mathematics 、 Poisson's equation 、 Finite difference method 、 Quadratic equation 、 Finite difference 、 Domain (mathematical analysis) 、 Boundary value problem 、 Mathematical analysis 、 Uniqueness theorem for Poisson's equation 、 Mixed boundary condition
摘要: This paper describes a method for the solution of 3D Poisson equation, subject to mixed boundary conditions, on an irregularly shaped domain. A finite difference is used, with domain embedded in rectangular grid. Quadratic treatment conditions shown be necessary obtain uniform error O(@D^2). contrasts Dirichlet case where both quadratic and linear treatments give O(@D^2) error, although coefficient may much larger case. Explicit estimates demonstrating this behaviour are found 1D similar 2D numerical examples. Finally, extension approach N-dimensional given, N>3.
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