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
N1 - 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.
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
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U2 - 10.1016/S0898-1221(02)00162-1
DO - 10.1016/S0898-1221(02)00162-1
M3 - Article
AN - SCOPUS:0036681264
SN - 0898-1221
VL - 44
SP - 457
EP - 479
JO - Computers and Mathematics with Applications
JF - Computers and Mathematics with Applications
IS - 3-4
ER -