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.)
  1. Achi Brandt and Irad Yavneh, Accelerated multigrid convergence and high Reynolds recirculating flow, SIAM Journal on Scientific Computing, Vol. 14, 607--626 (1993).
  2. 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).
  3. 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).
  4. 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).
  5. Arnold Reusken, Fourier analysis of a robust multigrid method for convection-diffusion equation, Numerische Mathematik, Vol. 71, 365--398 (1995).
  6. John W. Ruge and Klaus Stuben, Algebraic multigrid, in Multigrid Methods (S.F. McCormick, ed.), SIAM, Philadelphia, 1987.
  7. 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.
  8. P. Wesseling, An Introduction to Multigrid Methods, John Wiley & Sons, Chichester, 1992.
  9. 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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