An additive Schwarz preconditioner for the FETI method

Numerische Mathematik

Volumn 94, Issue 1, 2003, Pages 1-31

  Brenner, Susanne C ^a  

^a UNIVERSITY OF SOUTH CAROLINA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0142087017     PISSN: 0029599X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002110200397     Document Type: Article

References (44)

1. M. Bhardwaj, D. Day, C. Farhat, M. Lesoinne, K. Pierson, D. Rixen: Application of the FETI method to ASCI problems-scalability results on 1000 processors and discussion of highly heterogeneous problems. Internat. J. Numer. Methods Engrg., 47, 513-535 (2000)
2. P. Bjørstad, J. Mandel: On the spectra of sums of orthogonal projections with applications to parallel computing. BIT, 31, 76-88 (1991)
3. Å. Björck: Numerical Methods for Least Squares Problems. SIAM, Philadelphia, 1996
4. J. H. Bramble, J. E. Pasciak, A. H. Schatz: The construction of preconditioners for elliptic problems by substructuring, I. Math. Comp., 47, 103-134 (1986)
5. S. C. Brenner, L.-Y. Sung: Discrete Sobolev and Poincaré inequalities via Fourier series. East-West J. Numer. Math., 8, 83-92 (2000)
6. F. Chan, T. P. Mathew: Domain decomposition algorithms. In A. Iserles, editor, Acta Numerica, pages 61-143. Cambridge University Press, Cambridge, 1994
7. M. Dryja, O. B. Widlund: An additive variant of the Schwarz alternating method in the case of many subregions. Technical Report 339, Department of Computer Science, Courant Institute, 1987
8. M. Dryja, O. B. Widlund: Some domain decomposition algorithms for elliptic problems. In L. Hayes and D. Kincaid, editors, Iterative Methods for Large Linear Systems, pages 273-291. Academic Press, San Diego, CA, 1989
9. M. Dryja, O. B. Widlund: Towards a unified theory of domain decomposition algorithms for elliptic problems. In T. Chan, R. Glowinski, J. Périaux, and O.B. Widlund, editors, Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 3-21. SIAM, Philadelphia, 1990
10. M. Dryja, O. B. Widlund: Additive Schwarz methods for elliptic finite element problems in three dimensions. In D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, and R.G. Voigt, editors, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 3-18. SIAM, Philadelphia, 1992
11. M. Dryja, O. B. Widlund: Schwarz methods of Neumann-Neumann type for three dimensional elliptic finite element problems. Comm. Pure Appl. Math., 48, 121-155 (1995)
12. C. Farhat: A Lagrange multiplier based divide and conquer finite element algorithm. J. Comput. Systems Engrg., 2, 149-156 (1991)
13. C. Farhat: A saddle-point principle domain decomposition method for the solution of solid mechanics problems. In D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, and R.G. Voigt, editors, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 271-292. SIAM, Philadelphia, 1992
14. C. Farhat, P.-S. Chen, J. Mandel: A scalable Lagrange multiplier based domain decomposition method for time-dependent problems. Internat. J. Numer. Methods Engrg., 38, 3831-3853 (1995)
15. C. Farhat, P.-S. Chen, J. Mandel, F.-X. Roux: The two-level FETI method - Part II: Extension to shell problems, parallel implementation and performance. Comput. Methods Appl. Mech. Engrg., 155, 153-180 (1998)
16. C. Farhat, M. Lesoinne, P. LeTallec, K. Pierson, and D. Rixen. FETI-DP: A dual-primal unified FETI method, Part I: A faster alternative to the two-level FETI method. Internat. J. Numer. Methods Engrg., 50, 1523-1544 (2001)
17. C. Farhat, J. Mandel: The two-level FETI method for static and dynamic plate problems- Part I: An optimal iterative solver for biharmonic systems. Comput. Methods Appl. Mech. Engrg., 155, 129-152 (1998)
18. C. Farhat, J. Mandel, F.-X. Roux: Optimal convergence properties of the FETI domain decomposition method. Comput. Methods Appl. Mech. Engrg., 115, 364-385 (1994)
19. C. Farhat, F.-X. Roux: A method of finite element tearing and interconnecting and its parallel solution algorithm. Internat. J. Numer. Methods Engrg., 32, 1205-1227 (1991)
20. C. Farhat, F.-X. Roux: An unconventional domain decomposition method for an efficient parallel solution of large-scale finite element systems. SIAM J. Sci. Statist. Comput., 13, 379-396 (1992)
21. C. Farhat, F.-X. Roux: Implicit parallel processing in structural mechanics. Comput. Mech. Adv., 2, 1-124 (1994)
22. G. H. Golub, C. F. Van Loan: Matrix Computations (second edition). The Johns Hopkins University Press, Baltimore, 1989
23. M. Griebel, P. Oswald: On the abstract theory of additive and multiplicative Schwarz algorithms. Numer. Math., 70, 163-180 (1995)
24. M. R. Justino, Jr., K. C. Park, C. A. Felippa: An algebraically partitioned FETI method for parallel structural analysis: performance evaluation. Internat. J. Numer. Methods Engrg., 40, 2739-2758 (1997)
25. A. Klawonn, O. B. Widlund: A domain decomposition method with Lagrange multipliers and inexact solvers for linear elasticity. SIAM J. Sci. Comput., 22, 1199-1219 (2000)
26. A. Klawonn, O. B. Widlund: FETI and Neumann-Neumann iterative substructuring methods: connections and new results. Comm. Pure Appl. Math., 54, 67-90 (2001)
27. P. LeTallec: Domain decomposition methods in computational mechanics. Comput. Mech. Adv., 1, 121-220 (1994)
28. P. LeTallec, J. Mandel, M. Vidrascu: Balancing domain decomposition for plates. In D.E. Keyes and J. Xu, editors, Domain Decomposition Methods in Scientific and Engineering Computing (Contemporary Mathematics 180), pages 515-524. American Mathematical Society, Providence, 1994
29. J. Mandel: Balancing domain decomposition. Comm. Numer. Methods Engrg., 9, 233-241 (1993)
30. J. Mandel, M. Brezina: Balancing domain decomposition for problems with large jumps in coefficients. Math. Comp., 65, 1387-1401 (1996)
31. J. Mandel, R. Tezaur: Convergence of a substructuring method with Lagrange multipliers. Numer. Math., 73, 473-487 (1996)
32. J. Mandel, R. Tezaur: On the convergence of a dual-primal substructuring method. Numer. Math., 88, 543-558 (2001)
33. J. Mandel, R. Tezaur, C. Farhat: A scalable substructuring method by Lagrange multipliers for plate bending problems. SIAM J. Numer. Anal., 36, 1370-1391 (1999)
34. K. C. Park, M. R. Justino, Jr., C. A. Felippa: An algebraically partitioned FETI method for parallel structural analysis: algorithm description. Internat. J. Numer. Methods Engrg., 40, 2717-2737 (1997)
35. D. J. Rixen, C. Farhat: A simple and efficient extension of a class of substructure based preconditioners to heterogeneous structural mechanics problems. Internat. J. Numer. Methods Engrg., 44, 489-516 (1999)
36. D. J. Rixen, C. Farhat: Preconditioning the FETI method for problems with intra-and inter-subdomain coefficient jumps. In P. Bjørstad, M. Espedal, and D. Keyes, editors, Proceedings of the Ninth International Conference on Domain Decomposition Methods in Science and Engineering, Bergen, Norway, June 1996, 472-479 (1999)
37. D. J. Rixen, C. Farhat, R. Tezaur, J. Mandel: Theoretical comparison of the FETI and algebraically partitioned FETI methods, and performance comparisons with a direct sparse solver. Internat. J. Numer. Methods Engrg., 46, 501-533 (1999)
38. Y. Saad: Iterative Methods. PWS Publishing Company, Boston, 1996
39. M. Sarkis: Two level Schwarz methods for nonconforming finite elements and discontinuous coefficients. In N.D. Melson, T.A. Manteuffel, and S.F. McCormick, editors, Sixth Copper Mountain Conference on Multigrid methods, pages 543-565. NASA Conference Publication 3224, Part 2, 1993
40. B. Smith, P. Bjørstad, W. Gropp: Domain Decomposition. Cambridge University Press, Cambridge, 1996
41. R. Tezaur: Analysis of Lagrange Multiplier Based Domain Decomposition. PhD thesis, University of Colorado at Denver, 1998
42. O. Widlund: Some Schwarz methods for symmetric and nonsymmetric elliptic problems. In D.E. Keyes, T.F. Chan, G. Meurant, J.S. Scroggs, and R.G. Voigt, editors, Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, pages 19-36. SIAM, Philadelphi, 1991
43. J. Xu: Iterative methods by space decomposition and subspace correction. SIAM Review, 34, 581-613 (1992)
44. X. Zhang: Studies in Domain Decomposition: Multilevel Methods and the Biharmonic Dirichlet Problem. PhD thesis, Courant Institute, 1991