Two-level Schwarz algorithms with overlapping subregions for mortar finite elements

SIAM Journal on Numerical Analysis

Volumn 44, Issue 4, 2006, Pages 1514-1534

  Kim, Hyea Hyun ^a   Widlund, Olof B ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

Domain decomposition; Elliptic finite element problems; Mortar finite elements; Overlapping Schwarz algorithms; Preconditioned conjugate gradients

Indexed keywords

ALGORITHMS; FINITE ELEMENT METHOD; ITERATIVE METHODS; PROBLEM SOLVING;

DOMAIN DECOMPOSITION; ELLIPTIC FINITE ELEMENT PROBLEMS; MORTAR FINITE ELEMENTS; OVERLAPPING SCHWARZ ALGORITHMS; PRECONDITIONED CONJUGATE GRADIENTS;

CONJUGATE GRADIENT METHOD;

EID: 34547937722     PISSN: 00361429     EISSN: None     Source Type: Journal    
DOI: 10.1137/050635857     Document Type: Article

References (18)

1. Y. ACHDOU AND Y. MADAY, The mortar element method with overlapping subdomains, SIAM J. Numer. Anal., 40 (2002), pp. 601-628.
2. F. B. BELGACEM, The mortar finite element method with Lagrange multipliers, Numer. Math., 84 (1999), pp. 173-197.
3. F. B. BELGACEM, Discretisations 3D Non Conformes pour la Méthode de Decomposition de Domaine des Elément avec Joints: Analyse Mathématique et Mise en Œvre pour le Probleme de Poisson, Ph.D. thesis, Université Pierre et Marie Curie, Paris, Tech. report HI-72/93017, Electricité de France, 1993.
4. F. B. BELGACEM AND Y. MADAY, Adaptation de la méthode des éléments avec joints au couplage spectral élḿents finis en dimension 3. Etude de l'érreur pour l'équation de Poisson, Tech. report HI-72/7095, Electricité de France, 1992.
5. F. B. BELGACEM AND Y. MADAY, The mortar element method for three dimensional finite elements, RAIRO Modél. Math. Anal. Numér., 31 (1997), pp. 289-302.
6. C. BERNARDI AND Y. MADAY, Spectral, spectral element, and mortar element methods, in Theory and Numerics of Differential Equations (Durham, 2000), Universitext, Springer-Verlag, Berlin, 2001, pp. 1-57.
7. C. BERNARDI, Y. MADAY, AND A. T. PATERA, A new nonconforming approach to domain decomposition: The mortar element method, in Collège de France Seminar, H. Brezis and J.-L. Lions, eds., Pitman Res. Notes Math. Ser. 299, Longman Scientific, Harlow, 1994, pp. 13-51. This paper appeared as a technical report about five years earlier.
8. S. C. BRENNER, Lower bounds of two-level additive Schwarz preconditioners with small overlap, SIAM J. Sci. Comput., 21 (2000), pp. 1657-1669.
9. T. F. CHAN, B. F. SMITH, AND J. ZOU, Overlapping Schwarz methods on unstructured meshes using nonmatching coarse grids, Numer. Math., 73 (1996), pp. 149-167.
10. M. DRYJA AND O. B. WIDLUND, An Additive Variant of the Schwarz Alternating Method for the Case of Many Subregions, Tech. report 339, also Ultracomputer Note 131, Department of Computer Science, Courant Institute, New York, 1987.
11. M. DRYJA AND O. B. WIDLUND, Domain decomposition algorithms with small overlap, SIAM J. Sci. Comput., 15 (1994), pp. 604-620.
12. C. KIM, R. D. LAZAROV, J. E. PASCIAK, AND P. S. VASSILEVSKI, Multiplier spaces for the mortar finite element method in three dimensions, SIAM J. Numer. Anal., 39 (2001), pp. 519-538.
13. J. NEČAS, Les méthodes directes en théorie des équations elliptiques, Masson et Cie, Éditeurs, Paris, 1967.
14. B. F. SMITH, P. E. BJØRSTAD, AND W. D. GROPP, Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, UK, 1996.
15. A. TOSELLI AND O. WIDLUND, Domain Decomposition Methods - Algorithms and Theory, Springer Ser. Comput. Math. 34, Springer-Verlag, Berlin, 2005.
16. B. I. WOHLMUTH, A mortar finite element method using dual spaces for the Lagrange multiplier, SIAM J. Numer. Anal., 38 (2000), pp. 989-1012.
17. B. I. WOHLMUTH, Discretization methods and iterative solvers based on domain decomposition, Lecture Notes in Comput. Sci. Engrg. 17, Springer-Verlag, Berlin, 2001.
18. X. ZHANG, Multilevel Schwarz methods, Numer. Math., 63 (1992), pp. 521-539.