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 | |
| Publication status | Published - Aug 2002 |
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Keywords
- Convection-diffusion equation
- Fourth-order compact scheme
- Grid ordering
- Iterative methods
- Multicoloring
ASJC Scopus subject areas
- Applied Mathematics
- Computational Mathematics
- Modelling and Simulation
Cite this
Convergence and performance of iterative methods for solving variable coefficient convection-diffusion equation with a fourth-order compact difference scheme. / Karaa, S.; Zhang, Jun.
In: Computers and Mathematics with Applications, Vol. 44, No. 3-4, 08.2002, p. 457-479.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Convergence and performance of iterative methods for solving variable coefficient convection-diffusion equation with a fourth-order compact difference scheme
AU - Karaa, S.
AU - Zhang, Jun
PY - 2002/8
Y1 - 2002/8
N2 - 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.
AB - 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.
KW - Convection-diffusion equation
KW - Fourth-order compact scheme
KW - Grid ordering
KW - Iterative methods
KW - Multicoloring
UR - http://www.scopus.com/inward/record.url?scp=0036681264&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0036681264&partnerID=8YFLogxK
U2 - 10.1016/S0898-1221(02)00162-1
DO - 10.1016/S0898-1221(02)00162-1
M3 - Article
VL - 44
SP - 457
EP - 479
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
SN - 0898-1221
IS - 3-4
ER -