On a robust multigrid solver

Computing (Vienna/New York)

Volumn 56, Issue 3, 1996, Pages 303-322

  Reusken, A ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Anisotropy; Convection dominated; Elliptic problems; Multigrid

Indexed keywords

APPROXIMATION THEORY; BOUNDARY VALUE PROBLEMS; CONVERGENCE OF NUMERICAL METHODS; FOURIER TRANSFORMS; PROBLEM SOLVING;

COARSE GRIDS; CONVECTION DIFFUSION EQUATION; ELLIPTIC PROBLEMS; ROBUST MULTIGRID SOLVER; SCHUR COMPLEMENT; TWO GRID CONVERGENCE RATE; TWO GRID METHOD;

ALGORITHMS;

EID: 0030398919     PISSN: 0010485X     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02238516     Document Type: Article

References (15)

1. Axelsson, O.: On multigrid methods of the two-level type. In: Multigrid methods (Hackbusch, W., Trottenberg. U , eds.). pp. 352-367. Berlin Heidelberg New York: Springer 1982.
2. Axelsson, O., Vassilevski, P. S.: Algebraic multilevel preconditioning methods I. Numer. Math. 56, 157-177 (1989).
3. Axelsson, O., Vassilevski, P. S.: Algebraic multilevel preconditioning methods II. SIAM J. Numer. Anal. 27, 1569-1590 (1990).
4. Bank, R. E., Dupont, T. F., Yserentant, H.: The hierarchical basis multigrid method. Numer. Math. 52, 427-458 (1988).
5. Hackbusch, W.: Multigrid methods and applications. Berlin Heidelberg New York: Springer 1985.
6. Hackbusch, W.: The frequency decomposition multi-grid method. I. Application to anisotropic equations. Numer. Math. 56, 229-245 (1989).
7. Hackbusch, W.: The frequency decomposition multi-grid method. II. Convergence analysis based on the additive Schwarz method. Numer. Math. 63, 433-453 (1992).
8. Maitre, J. F., Musy, F.: The contraction number of a class of two-level methods; an exact evaluation for some finite element subspaces and model problems. In: Multigrid methods (Hackbusch, W., Trottenberg, U., eds.), pp. 201-216. Berlin Heidelberg New York: Springer 1982.
9. Margenov, S. D., Vassilevski, P. S.: Algebraic multilevel preconditioning of anisotropic elliptic problems. SIAM J. Sci. Comput. 15, 1026-1037 (1994).
10. Reusken, A.: Fourier analysis of a robust multigrid method for convection-diffusion equations. Numer. Math. 71, 365-397 (1995).
11. Stevenson, R.: Robustness of the additive and multiplicative frequency decomposition multi-level method. Computing 54, 331-346 (1995).
12. Vassilevski, P. S., Etova, M. H.: Computation of constants in the strengthened Cauchy inequality. SIAM J. Sci. Statist. Comp. 13, 655-665 (1992).
13. Wesseling, P.: An introduction to multigrid methods. Chichester: Wiley 1992.
14. Xu, J.: Iterative methods by space decomposition and subspace correction. SIAM Rev. 34, 581-613 (1992).
15. Yserentant, H.: Old and new convergence proofs for multigrid methods. Acta Numerica 285-326 (1993).