High-Order Schemes and Multigrid Methods
The main purpose of this research is to show that high-order finite difference
approximations can be efficient and stable when used in conjunction with
multigrid methods to solve partial differential equations.
We focus on 2D and 3D elliptic equations such as the Poisson, and the
convection-diffusion equations.
Selected Publications
- Murli M. Gupta, Jules Kouatchou and Jun Zhang,
A compact multigrid solver for convection-diffusion equations,
J. Comp. Phys., 132, p. 123-129 (1997).
- Murli M. Gupta, Jules Kouatchou and Jun Zhang,
Comparison of second and fourth order discretizations for
multigrid Poisson solvers,
J. Comp. Phys., 132, p. 226-232 (1997).
- Jules Kouatchou,
Asymptotic stability of a 9-point multigrid algorithm for the
convection-diffusion equations,
Electronic Transaction in Numerical Analysis, 6,
p. 153-161, Dec. 1997.
- Jules Kouatchou,
A dynamic injection operator in a multigrid solution of the
convection-diffusion equation,
Int. J. Num. Meth. in Fluids, 26, p. 1205-1216 (1998).
- Jules Kouatchou,
Multigrid solution of 3D convection-diffusion equations: stability
analysis of a high-order scheme,
Preprint, The Fourth International Congress on Industrial and Applied
Mathematics, p. 198, Edinburgh, Scotland, July 5-9, 1999.
- Jules Kouatchou and Jun Zhang,
Optimal injection operator in multigrid solution of the three
dimensional Poisson equation,
International Journal of Computer Mathematics,
Vol. 76, p. 173-190 (2000).
- Jun Zhang, Lixin Ge and Jules Kouatchou,
A two colorable fourth order compact difference scheme and parallel
iterative solution of the 3D convection-diffusion equation,
Mathematics and Computers in Simulation,
Vol. 54 (1-3), p. 67-83 (2000).
- Jun Zhang, Jules Kouatchou and Mohamed Othman,
On cyclic reduction and finite difference schemes,
Journal of Computational and Applied Mathematics,
Vol. 145, No. 1, p. 213-222 (2002).
It is better to be poor but honest than to be a lying
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