Abstract
We conduct convergence analysis on some classical stationary iterative methods for solving the two-dimensional variable coefficient convection-diffusion equation discretized by a fourth-order compact difference scheme. Several conditions are formulated under which the coefficient matrix is guaranteed to be an M-matrix. We further investigate the effect of different orderings of the grid points on the performance of some stationary iterative methods, multigrid method, and preconditioned GMRES. Three sets of numerical experiments are conducted to study the convergence behaviors of these iterative methods under the influence of the flow directions, the orderings of the grid points, and the magnitude of the convection coefficients.
| Original language | English |
|---|---|
| Pages (from-to) | 457-479 |
| Number of pages | 23 |
| Journal | Computers and Mathematics with Applications |
| Volume | 44 |
| Issue number | 3-4 |
| DOIs | |
| State | Published - Aug 2002 |
Bibliographical note
Funding Information:*This author’s research was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532.
Funding
*This author\u2019s research was supported in part by the U.S. National Science Foundation under Grants CCR-9902022, CCR-9988165, and CCR-0092532.
| Funders | Funder number |
|---|---|
| U.S. Department of Energy Chinese Academy of Sciences Guangzhou Municipal Science and Technology Project Oak Ridge National Laboratory Extreme Science and Engineering Discovery Environment National Science Foundation National Energy Research Scientific Computing Center National Natural Science Foundation of China | CCR-0092532, CCR-9902022, CCR-9988165 |
Keywords
- Convection-diffusion equation
- Fourth-order compact scheme
- Grid ordering
- Iterative methods
- Multicoloring
ASJC Scopus subject areas
- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics