A multigrid method based on incomplete Gaussian elimination

Numerical Linear Algebra with Applications

Volumn 3, Issue 5, 1996, Pages 369-390

  Reusken, Arnold ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Incomplete Gaussian elimination; Multigrid

Indexed keywords

EID: 21444442790     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-1506(199609/10)3:5<369::AID-NLA89>3.0.CO;2-M     Document Type: Article

References (18)

1. O. Axelsson and P. S. Vassilevski. Algebraic multilevel preconditioning methods I. Numer. Math., 56, 157-177, 1989.
2. O. Axelsson and P. S. Vassilevski. Algebraic multilevel preconditioning methods II. SIAM J. Numer. Anal, 27, 1569-1590, 1990.
3. A. George and J. Liu. Computer Solution of Large Sparse Positive Definite Systems. Prentice Hall, Englewood Cliffs, NJ, 1981.
4. W. Hackbusch. Multigrid Methods and Applications. Springer, Berlin, Heidelberg, New York, 1985.
5. W. Hackbusch. The frequency decomposition multi-grid method. I. Application to anisotropic equations. Numer. Math., 56, 229-245, 1989.
6. W. Hackbusch. The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method. Numer. Math., 63, 433-453, 1992.
7. D. Heller. Some aspects of the cyclic reduction algorithm for block tridiagonal linear systems. SIAM J. Numer. Anal., 13, 484-496, 1976.
8. W. Layton. On the principal axes of diffusion in difference schemes for 2D transport problems. J. Comput. Phys., 90, 336-347, 1990.
9. S. D. Margenov and P. S. Vassilevski. Algebraic multilevel preconditioning of anisotropic elliptic problems. SIAM J. Sci. Comput., 15, 1026-1037, 1994.
10. A. Reusken. Fourier analysis of a robust multigrid method for convection-diffusion equations. Numer. Math., 71, 365-398, 1995.
11. A. Reusken. A new robust mulligrid method for 2D convection-diffussion problems. In Fast Solvers for Flow Problems, Proceedings of the Tenth GAMM Seminar Kiel, W. Hackbusch and G. Wittum, editors. Notes on Numerical Fluid Mechanics, 49, 229-240, 1995.
12. A. Reusken. On a robust multigrid solver. Computing, 56, 303-322, 1996.
13. J. Schröder and U. Trottenberg. Reduktionsverfahren für differenzengleichungen bei randwertaufgaben I. Numer. Math., 22, 37-68, 1973.
14. R. Stevenson. Robustness of the additive and multiplicative frequency decomposition multi-level method. Computing, 54, 331-346, 1995.
15. P. N. Swarztrauber. A direct method for the discrete solution of separable elliptic equations. SIAM J. Numer. Anal., 11, 1136-1150, 1974.
16. P. Wesseling. An Introduction to Multigrid Methods. Wiley, Chichester. 1992.
17. J. Xu. Iterative methods by space decomposition and subspace correction. SIAM Review, 34, 581-613, 1992.
18. H. Yserentant. Old and new convergence proofs for multigrid methods. Acta Numerica, 285-326, 1993.