Abstract
A new fourth-order compact difference scheme for the three-dimensional (3D) convection diffusion equation with variable coefficients is presented. The novelty of this new difference scheme is that it only requires 15 grid points and that it can be decoupled with two colors. The entire computational grid can be updated in two parallel subsweeps with a Gauss-Seidel type iterative method. This is compared with the known 19-point fourth-order compact difference scheme which requires four colors to decouple the computational grid. Numerical results, with multigrid methods implemented on a shared memory parallel computer, are presented to compare the 15- and 19-point fourth-order compact schemes.
| Original language | English |
|---|---|
| Pages (from-to) | 65-80 |
| Number of pages | 16 |
| Journal | Mathematics and Computers in Simulation |
| Volume | 54 |
| Issue number | 1-3 |
| DOIs | |
| State | Published - Nov 30 2000 |
Bibliographical note
Funding Information:The research of the author Jun Zhang was supported in part by the US National Science Foundation under the Grant CCR-9902022, and in part by the University of Kentucky Center for Computational Sciences. The research of the author Lixin Ge was supported by the University of Kentucky Center for Computational Sciences. The author Jules Kouatchou is affiliated with Morgan State University and his research was supported by NASA under the Grant no. NAGS-3508.
Keywords
- 3D convection diffusion equation
- Fourth-order compact difference schemes
- Multigrid method
- Parallel computation
ASJC Scopus subject areas
- Theoretical Computer Science
- General Computer Science
- Numerical Analysis
- Modeling and Simulation
- Applied Mathematics