A family of energy minimizing coarse spaces for overlapping schwarz preconditioners

Lecture Notes in Computational Science and Engineering

Volumn 60, Issue , 2008, Pages 247-254

  Dohrmann, Clark R ^a   Klawonn, Axel ^b   Widlund, Olof B ^c  

^a SANDIA NATIONAL LABORATORIES   (United States)

^b UNIVERSITY OF DUISBURG ESSEN   (Germany)

^c NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

CONDITION NUMBERS; ENERGY MINIMIZING; NUMERICAL EXAMPLE; OVERLAPPING SCHWARZ; PRECONDITIONERS; SUBDOMAIN BOUNDARY; SUBSTRUCTURING;

NUMBER THEORY;

DOMAIN DECOMPOSITION METHODS;

EID: 70349607199     PISSN: 14397358     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-3-540-75199-1_28     Document Type: Conference Paper

References (16)

1. M. Brezina and P. Vaněk. A black box iterative solver based on a two-level Schwarz method. Computing, 63:233-263, 1999.
2. C. R. Dohrmann. A preconditioner for substructuring based on constrained energy minimization. SIAM J. Sci. Comput., 25(1):246-258, 2003.
3. C. R. Dohrmann, A. Klawonn, and O. B. Widlund. Domain decomposition for less regular subdomains: Overlapping Schwarz in two dimensions. Technical Report TR2007-888, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, March 2007.
4. C. R. Dohrmann and O. B. Widlund. An overlapping Schwarz preconditioner for almost incompressible elasticity. In preparation, 2007.
5. M. Dryja, M. V. Sarkis, and O. B. Widlund. Multilevel Schwarz methods for elliptic problems with discontinuous coefficients in three dimensions. Numer. Math., 72(3):313-348, 1996.
6. M. Dryja, B. F. Smith, and O. B. Widlund. Schwarz analysis of iterative substructuring algorithms for elliptic problems in three dimensions. SIAM J. Numer. Anal., 31(6):1662-1694, 1994.
7. I. G. Graham, P. Lechner, and R. Scheichl. Domain decomposition for multiscale pdes. Technical report, Bath Institute for Complex Systems, 2006.
8. E. W. Jenkins, C. E. Kees, C. T. Kelley, and C. T. Miller. An aggregationbased domain decomposition preconditioner for groundwater flow. SIAM J. Sci. Comput., 23(2):430-441, 2001.
9. A. Klawonn, O. Rheinbach, and O. B. Widlund. An analysis of a FETI-DP algorithm on irregular subdomains in the plane. Technical Report TR2007-889, Department of Computer Science, Courant Institute of Mathematical Sciences, New York University, April 2007.
10. J. Mandel. Balancing domain decomposition. Comm. Numer. Methods Engrg., 9:233-241, 1993.
11. J. Mandel and C. R. Dohrmann. Convergence of a balancing domain decomposition by constraints and energy minimization. Numer. Linear Algebra Appl., 10(7):639-659, 2003.
12. M. Sarkis. Partition of unity coarse spaces and Schwarz methods with harmonic overlap. Lecture Notes in Computational Science and Engineering, 23:77-94, 2002.
13. M. Sarkis. Partition of unity coarse spaces: Enhanced versions, discontinuous coefficients and applications to elasticity. In I. Herrera, D. E. Keyes, O. B. Widlund, and R. Yates, editors, Fourteenth International Conference on Domain Decomposition Methods, 2003.
14. R. Scheichl and E. Vainikko. Additive Schwarz and aggregation-based coarsening for elliptic problems with highly variable coefficients. Technical report, Bath Institute for Complex Systems, 2006.
15. B. Smith, P. Bj∅rstad, and W. Gropp. Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press, 1996.
16. A. Toselli and O. Widlund. Domain Decomposition Methods - Algorithms and Theory. Springer Series in Computational Mathematics. Springer, 2005.