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Advances in Numerical Analysis
Volume 2010 (2010), Article ID 352174, 17 pages
A Family of Sixth-Order Compact Finite-Difference Schemes for the Three-Dimensional Poisson Equation
Department of Mathematics, North Carolina A & T State University, Greensboro, NC 27411, USA
Received 24 October 2009; Accepted 17 March 2010
Academic Editor: Yin Nian He
Copyright © 2010 Yaw Kyei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Wadsworth & Brooks-Cole Advanced Books & Software, Pacific Grove, Calif, USA, 1989.
- L. Ge and J. Zhang, “Symbolic computation of high order compact difference schemes for three dimensional linear elliptic partial differential equations with variable coefficients,” Journal of Computational and Applied Mathematics, vol. 143, no. 1, pp. 9–27, 2002.
- M. Piller and E. Stalio, “Finite-volume compact schemes on staggered grids,” Journal of Computational Physics, vol. 197, no. 1, pp. 299–340, 2004.
- W. F. Spotz and G. F. Carey, “High-order compact scheme for the steady stream-function vorticity equations,” International Journal for Numerical Methods in Engineering, vol. 38, no. 20, pp. 3497–3512, 1995.
- H. Sun, N. Kang, J. Zhang, and E. S. Carlson, “A fourth-order compact difference scheme on face centered cubic grids with multigrid method for solving 2D convection diffusion equation,” Mathematics and Computers in Simulation, vol. 63, no. 6, pp. 651–661, 2003.
- S. K. Lele, “Compact finite difference schemes with spectral-like resolution,” Journal of Computational Physics, vol. 103, no. 1, pp. 16–42, 1992.
- K. Ito, Z. Li, and Y. Kyei, “Higher-order, Cartesian grid based finite difference schemes for elliptic equations on irregular domains,” SIAM Journal on Scientific Computing, vol. 27, no. 1, pp. 346–367, 2005.
- Z. Li and K. Ito, “Maximum principle preserving schemes for interface problems with discontinuous coefficients,” SIAM Journal on Scientific Computing, vol. 23, no. 1, pp. 339–361, 2001.
- H. C. Elman and D. P. O'Leary, “Efficient iterative solution of the three-dimensional Helmholtz equation,” Journal of Computational Physics, vol. 142, no. 1, pp. 163–181, 1998.
- Y. A. Erlangga, C. Vuik, and C. W. Oosterlee, “On a class of preconditioners for solving the Helmholtz equation,” Applied Numerical Mathematics, vol. 50, no. 3-4, pp. 409–425, 2004.