A note on an accelerated high-accuracy multigrid solution of the convection-diffusion equation with high Reynolds number

Numerical Methods for Partial Differential Equations

Volumn 16, Issue 1, 2000, Pages 1-10

  Zhang, Jun ^a  

^a UNIVERSITY OF KENTUCKY   (United States)

Author keywords

Convection diffusion equation; Fourth order compact discretization schemes; Multigrid method; Residual transfer operators

Indexed keywords

EID: 0002405719     PISSN: 0749159X     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1098-2426(200001)16:1<1::AID-NUM1>3.0.CO;2-5     Document Type: Article

References (16)

1. M. M. Gupta, R. P. Manohar, and J. W. Stephenson, A single cell high order scheme for the convection-diffusion equation with variable coefficients, Int J Numer Meth Fluid 4 (1984), 641-651.
2. W. F. Spotz and G. F. Carey, High-order compact scheme for steady stream-function vorticity equations, Int J Numer Methods Eng 38 (1995), 3497-3512.
3. A. Brandt, Multi-level adaptive solution to boundary-value problems, Math Comp 31 (1977), 333-396.
4. A. Brandt and I. Yavneh, Accelerated multigrid convergence and high-Reynolds recirculating flows, SIAM J Sci Comp 14 (1993), 607-626.
5. P. M. de Zeeuw, Matrix-dependent prolongations and restrictions in a blackbox multigrid solver, J Comp Appl Math 33 (1990), 1-22.
6. A. Reusken, Fourier analysis of a robust multigrid method for convection-diffusion equations, Numer Math 71 (1995), 365-391.
7. J. Zhang, Accelerated multigrid high accuracy solution of the convection-diffusion equation with high Reynolds number, Numer Methods Partial Differential Eq 13 (1997), 77-92.
8. M. M. Gupta, J. Kouatchou, and J. Zhang, A compact multigrid solver for the convection-diffusion equations, J Comp Phys 132 (1997), 123-129.
9. J. Zhang, Minimal residual smoothing in multi-level iterative method, Appl Math Comp 84 (1997), 1-25.
10. J. Zhang, On convergence and performance of iterative methods with fourth-order compact schemes, Numer Methods Partial Differential Eq 14 (1998), 263-280.
11. J. Zhang, Residual scaling techniques in multigrid, I: equivalence proof, Appl Math Comp 86 (1997), 283-303.
12. J. Zhang, Multigrid acceleration techniques and applications to the numerical solution of partial differential equation, Ph.D. Thesis, George Washington Univ, 1997.
13. J. Kouatchou, A dynamic injection operator in a multigrid solution of the convection-diffusion equation, Int J Numer Meth Fluid 26 (1998), 1205-1216.
14. J. Zhang, Multigrid with inexact minimal residual smoothing acceleration, Appl Numer Math 24 (1997), 501-512.
15. V. A. Bandy, Black box multigrid for convection-diffusion equations on advanced computers, Ph.D. Thesis, Univ Colorado Denver, 1996.
16. J. Zhang, On convergence of iterative methods for a fourth-order discretization scheme, Appl Math Lett 10 (1997), 49-55.