Paper Info
Title
An efficient implementation of fourth-order compact finite difference scheme for Poisson equation with Dirichlet boundary conditions.
Abstract
Fourth-order compact finite difference scheme has been proposed for solving the Poisson equation with Dirichlet boundary conditions for some time. An efficient implementation of such numerical scheme is often desired for practical usage. In this paper, based on fast discrete Sine transform, we design an efficient algorithm to implement this scheme. To do this, Poisson equation is first discretized by fourth-order compact finite difference method. The subsequent discretized system is not solved by the usual method—matrix inversion, instead it is solved with the fast discrete Sine transform. By doing this way, the computational cost of proposed algorithm for such scheme with large grid numbers can be greatly reduced. Detailed numerical algorithm of this fast solver for one-dimensional, two-dimensional and three dimensional Poisson equation has been presented. Numerical results in one dimension, two dimensions, three dimensions and four dimensions have shown that the applied compact finite difference scheme has fourth order accuracy and can be efficiently implemented.
Year
DOI
Venue
2016
10.1016/j.camwa.2016.02.022
Computers & Mathematics with Applications
Keywords
Field
DocType
Poisson equation,Fourth-order,Compact finite difference scheme,Discrete Sine transform
Discretization,Mathematical optimization,Compact finite difference,Discrete Poisson equation,Poisson's equation,Mathematical analysis,Uniqueness theorem for Poisson's equation,Dirichlet boundary condition,Finite difference coefficient,Discrete sine transform,Mathematics
Journal
Volume
Issue
ISSN
71
9
0898-1221
Citations 
PageRank 
References 
3
0.46
5
Authors
5
Name
Order
Citations
PageRank
Hanquan Wang110211.88
Yong Zhang2294.56
Xiu Ma340.82
Jun Qiu430.46
Yan Liang530.46