Experiments in 3D with a three-point hierarchical basis preconditioner

Applied Numerical Mathematics

Volumn 23, Issue 1, 1997, Pages 159-175

  Stevenson, Rob ^a  

^a RADBOUD UNIVERSITY NIJMEGEN   (Netherlands)

Author keywords

Additive Schwarz preconditioner; Anisotropic equation; Finite elements; Hierarchical basis; Robustness; Space decomposition

Indexed keywords

ANISOTROPY; DIFFERENTIAL EQUATIONS; FINITE ELEMENT METHOD; HIERARCHICAL SYSTEMS; MATHEMATICAL OPERATORS; ROBUSTNESS (CONTROL SYSTEMS);

ANISOTROPIC PROBLEMS;

BOUNDARY VALUE PROBLEMS;

EID: 0031073828     PISSN: 01689274     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-9274(96)00066-9     Document Type: Article

References (18)

1. I. Babuška and A.K. Aziz, On the angle condition in the finite element method, SIAM J. Numer. Anal. 13 (2) (1976) 214-226.
2. F.A. Bornemann and H. Yserentant, A basic norm equivalence for the theory of multilevel methods, Numer. Math. 64 (1993) 455-476.
3. W. Dahmen, B. Kleemann, Prössdorf and R. Schneider, A multiscale method for the double layer potential equation on a polyhedron, in: H.P. Dikshit and C. A. Micchelli, eds., Advances in Computational Mathematics (World Scientific Publishing, 1994) 1-40.
4. W. Dahmen and A. Kunoth, Multilevel preconditioning, Numer. Math. 63 (1992) 315-344.
5. M. Griebel and P. Oswald, On additive schwarz preconditioners for sparse grid discretizations, Numer. Math. 66 (1994) 449-464.
6. M. Griebel and P. Oswald, On the abstract theory of additive and multiplicative Schwarz algorithms, Numer. Math. 70 (1995) 163-180.
7. W. Hackbusch, The frequency decomposition multi-grid method I. Application to anisotropic equations, Numer. Math. 56 (1989) 229-245.
8. W. Hackbusch, The frequency decomposition multi-grid method II. Convergence analysis based on the additive Schwarz method, Numer. Math. 63 (1992) 433-453.
9. J. Junkherr, Multigrid methods for weakly singular integral equations of the first kind, Ph.D. thesis, Christian-Albrechts-Universität Kiel (1994).
10. P. Oswald, Multilevel Finite Element Approximation: Theory and Applications (Teubner, Stuttgart, 1994).
11. R.P. Stevenson, Robustness of multi-grid applied to anisotropic equations on convex domains and on domains with re-entrant corners, Numer. Math. 66 (1993) 373-398.
12. R.P. Stevenson, The frequency decomposition multi-level method: A robust additive hierarchical basis preconditioner, Math. Comp. 65 (215) (1996) 983-997.
13. R.P. Stevenson, A robust hierarchical basis preconditioner on general meshes, Report 9533, University of Nijmegen (1995); also: Numer. Math., to appear.
14. R.P. Stevenson, A robust hierarchical basis preconditioner on general meshes, Report 9533, University of Nijmegen (1995); also: Numer. Math., to appear.
15. R.P. Stevenson, Robustness of the additive and multiplicative frequency decomposition multi-level method, Computing 54 (1995) 331-346.
16. J. Wang, New convergence estimates for multilevel algorithms for finite-element approximations, J. Comput. Appl. Math. 50 (1994) 593-604.
17. J. Xu, Iterative methods by space decomposition and subspace correction, SIAM Rev. 34 (1992) 581-613.
18. H. Yserentant, Old and new convergence proofs for multigrid methods, Acta Numerica (1993) 285-326.