Two-grid analysis of minimal residual smoothing as a multigrid acceleration technique

Applied Mathematics and Computation

Volumn 96, Issue 1, 1998, Pages 27-45

  Zhang, Jun ^a  

^a 4 192 EEICS Building ^*  (United States)

Author keywords

Minimal residual smoothing; Multigrid acceleration techniques; Multigrid method; Two grid analysis

Indexed keywords

EID: 0003957147     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0096-3003(97)10105-9     Document Type: Article

References (23)

1. J. Zhang, Minimal residual smoothing in multi-level iterative method, Appl. Math. Comput. 84 (1997) 1-25.
2. P. Wesseling, An Introduction to Multigrid Methods, Wiley, Chichester, 1992.
3. A. Brandt, I. Yavneh, Accelerated multigrid convergence and high-Reynolds recirculating flows, SIAM J. Sci. Comput. 14 (1993) 607-626.
4. A. Brandt, V. Mikulinsky, On recombining iterants in multigrid algorithms and problems with small islands, SIAM J. Sci. Comput. 16 (1995) 20-28.
5. A. Reusken, Steplength optimization and linear multigrid methods, Numer. Math. 58 (1991) 819-838.
6. P. Vaněk, Fast multigrid solver, Appl. Math. 40 (1995) 1-20.
7. J. Zhang, Acceleration of five-point red-black Gauss-Seidel in multigrid for two dimensional Poisson equation, Appl. Math. Comput. 80 (1996) 73-93.
8. J. Zhang, A cost-effective multigrid projection operator, J. Comput. Appl. Math. 76 (1996) 325-333.
9. J. Zhang, Residual scaling techniques in multigrid, I: Equivalence proof, Appl. Math. Comput. 86 (1997) 283-303.
10. Y. Saad, M.H. Schultz, GMRES: A generalized minimal residual method for solving nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 7 (1986) 856-869.
11. C. Lanczos, Solution of systems of linear equations by minimized iterations, J. Res. Nat. Bur. Stand. 49 (1952) 33-53.
12. P. Sonneveld, CGS: A fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 10 (1989) 36-52.
13. L. Zhou, H.F. Walker, Residual smoothing techniques for iterative methods, SIAM J. Sci. Comput. 15 (1994) 297-312.
14. H.A. van der Vorst, BI-CGSTAB: A fast and smoothly converging variant of Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Stat. Comput. 13 (1992) 631-644.
15. R.W. Freund, N.M. Nachtigal, QMR: A quasi-minimal residual method for non-Hermitian linear systems, Numer. Math. 60 (1991) 315-339.
16. R.W. Freund, A transpose-free quasi-minimal residual algorithm for non-Hermitian linear systems, SIAM J. Sci. Comput. 14 (1993) 470-482.
17. W. Schönauer, Scientific Computing on Vector Computers, North-Holland, Amsterdam, 1987.
18. R. Weiss, Convergence Behavior of Generalized Conjugate Gradient Methods, Ph.D. Thesis, University of Karlsruhe, Germany, 1990.
19. C. Brezinski, M. Redivo-Zaglia, Hybrid procedures for solving linear systems, Numer. Math. 67 (1994) 1-19.
20. R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, NJ, 1962.
21. L.A. Hageman, D.M. Young, Applied Iterative Methods, Academic Press, New York, 1981.
22. K. Stüben, U. Trottenberg, Multigrid methods: Fundamental algorithms, model problem analysis and applications. Monograph, GMD-Studien Nr. 96, Postfach 1240, Schloss Birlinghoven, D-5205 St. Augustin 1, 1984.
23. J. Zhang, Multigrid acceleration techniques and applications to the numerical solutions of partial differential equations, Ph.D. Thesis, The George Washington University, Washington, DC 20052, 1997.