References for Multigrid and Multi-Level Solution of Convection-Diffusion
Equations
Here are some references related to solving convection-diffusion equations
by multigrid or multi-level methods.
If you have other relevant references that are not listed here,
please send me an e-mail message (jzhang@cs.uky.edu). (This reference list
is biased in favor of computational results, algorithm tests of
convection-dominated problems.)
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Achi Brandt and Irad Yavneh,
Accelerated multigrid convergence and high Reynolds recirculating flow,
SIAM Journal on Scientific Computing, Vol. 14, 607--626 (1993).
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Paul M. de Zeeuw,
Matrix-dependent prolongations and restrictions in a blackbox
multigrid solver,
Journal of Computational and Applied Mathematics, Vol. 3, 1--27 (1990).
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Murli M. Gupta, Ram P. Manohar and John W. Stephenson,
A single cell high order scheme for the convection-diffusion equation with
variable coefficient,
International Journal of Numerical Methods in Fluids, Vol. 4, 641--651 (1984).
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Murli M. Gupta, Jules Kouatchou and Jun Zhang,
A compact multigrid solver for convection-diffusion equations,
Journal of Computational Physics, Vol. 132(1), 123--129 (1997).
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Arnold Reusken,
Fourier analysis of a robust multigrid method for
convection-diffusion equation,
Numerische Mathematik, Vol. 71, 365--398 (1995).
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John W. Ruge and Klaus Stuben,
Algebraic multigrid,
in Multigrid Methods (S.F. McCormick, ed.), SIAM, Philadelphia, 1987.
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Yousef Saad and Jun Zhang,
BILUM: block versions of multi-elimination and multi-level ILU preconditioner
for general sparse linear systems,
Technical Report UMSI 97/126, Minnesota Supercomputer Institute,
University of Minnesota, Minneapolis, MN 55455, 1997.
-
P. Wesseling,
An Introduction to Multigrid Methods,
John Wiley & Sons, Chichester, 1992.
-
Jun Zhang,
Accelerated multigrid high accuracy solution of the convection-diffusion
equation with high Reynolds number,
Numerical Methods for Partial Differential Equations, Vol. 13, 77--92 (1997).
For problems and suggestions, send e-mail to:
jzhang@cs.uky.edu.
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