Balancing domain decomposition for problems with large jumps in coefficients

Mathematics of Computation

Volumn 65, Issue 216, 1996, Pages 1387-1401

  Mandel, Jan ^a   Brezina, Marian ^a  

^a UNIVERSITY OF COLORADO   (United States)

Author keywords

Discontinuous coefficients; Domain decomposition; Second order elliptic boundary value problems; Two level iterative methods

Indexed keywords

EID: 0030518529     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-96-00757-0     Document Type: Article

References (27)

1. S. Ashby, T. A. Manteuffel, and P. E. Saylor, A taxonomy for conjugate gradient methods, SIAM J. Numer. Anal., 27 (1990), pp. 1542-1568. MR 91i:65062
2. J.-F. Bourgat, R. Glowinski, P. Le Tallec, and M. Vidrascu, Variational formulation and algorithm for trace operator in domain decomposition calculations. in Domain Decomposition Methods, T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA, 1989. MR 90b:65198
3. J. H. Bramble, J. E. Pasciak, and A. H. Schatz, The construction of preconditioners for elliptic problems by sub structuring, I, Math. Comp., 47 (1986), pp. 103-134. MR 87m:65174
4. _, An iterative method for elliptic problems on regions partitioned into substructures, Math. Comp., 46 (1986), pp. 361-369. MR 88a:65123
5. _, The construction of preconditioners for elliptic problems by substructuring, IV, Math. Comp., 53 (1989), pp. 1-24. MR 89m:65098
6. T. F. Chan, Analysis of preconditioners for domain decomposition, SIAM J. Numer. Anal., 24 (1987), pp. 382-390. MR 88e:65033
7. T. F. Chan and T. P. Mathew, The interface probing technique in domain decomposition, SIAM J. on Matrix Analysis and Applications, 13 (1992), pp. 212-238. MR 92i:65183
8. P. G. Ciarlet, The Finite Element Method for Elliptic Problems, North-Holland, Amsterdam, 1978. MR 58:25001
9. L. Cowsar, J. Mandel, and M. F. Wheeler, Balancing domain decomposition for mixed finite elements. Math. Comp., 64 (1995), pp. 989-1015. MR 95j:65161
10. Y.-H. De Roeck, Résolution sur Ordinateurs Multi-Processeurs de Problème d'Elasticité par Décomposition de Domaines, PhD thesis, Université Paris IX Daupine, 1991.
11. Y.-H. De Roeck and P. Le Tallec, Analysis and test of a local domain decomposition preconditioner, in Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, Y. Kuznetsov, G. Meurant, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA, 1991. CMP 91:12
12. M. Dryja, A method of domain decomposition for 3-D finite element elliptic problems, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., SIAM, Philadelphia, PA, 1988. MR 90b:65200
13. M. Dryja and O. B. Widlund, Towards a unified theory of domain decomposition algorithms for elliptic problems, in Third International Symposium on Domain Decomposition Methods for Partial Differential Equations, held in Houston, Texas, March 20-22, 1989, T. Chan, R. Glowinski, J. Périaux, and O. Widlund, eds., SIAM, Philadelphia, PA, 1990. MR 91m:65294
14. _, Additive Schwarz methods for elliptic finite element problems in three dimensions, in Fifth International Symposium on Domain Decomposition Methods for Partial Differential Equations, T. F. Chan, D. E. Keyes, G. A. Meurant, J. S. Scroggs, and R. G. Voigt, eds., SIAM, Philadelphia, PA, 1992. MR 93j:65201
15. _, Domain decomposition algorithms with small overlap, SIAM J. Sci.Comput., 15 (1994), pp. 604-620. MR 95d:65102
16. _, Schwarz methods of Neumann-Neumann type for three-dimensional elliptic finite element problems, Comm. Pure Appl. Math, 48 (1995), pp. 121-155. CMP 95:09
17. R. Glowinski and M. F. Wheeler, Domain decomposition and mixed finite element methods for elliptic problems, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., SIAM, Philadelphia, PA, 1988. MR 90a:65237
18. D. E. Keyes and W. D. Gropp, A comparison of domain decomposition techniques for elliptic partial differential equations and their parallel implementation, SIAM J. Sci. Stat. Comput., 8 (1987), pp. s166-s202. MR 88g:65101
19. P. Le Tallec, J. Mandel, and M. Vidrascu, Balancing domain decomposition for plates, in Domain Decomposition Methods in Scientific and Engineering Computing, D. E. Keyes and J. Xu, eds., American Mathematical Society, Providence, RI, 1994, pp. 515-524. Proceedings of the 7th International Symposium on Domain Decomposition Methods, Penn State, November 1993. MR 95j:73080
20. J. Mandel, Balancing domain decomposition, Comm. in Numerical Methods in Engrg., 9 (1993), pp. 233-241. MR 94b:65158
21. J. Mandel and M. Brezina, Balancing domain decomposition: Theory and computations in two and three dimensions, UCD/CCM Report 2, Center for Computational Mathematics, University of Colorado at Denver, November 1993.
22. J. Mandel, S. McCormick, and R. Bank, Variational multigrid theory, in Multigrid Methods, S. F. McCormick, ed., SIAM, Philadephia, 1987, ch. 5, pp. 131-177. CMP 21:05
23. M. Sarkis, Two-level Schwarz methods for nonconforming finite elements and discontinuous coefficients, in Proceedings of the Sixth Copper Mountain Conference on Multigrid Methods, Volume 2, N. D. Melson, T. A. Manteuffel, and S. F. McCormick, eds., no. 3224, Hampton VA, 1993, NASA, pp. 543-566.
24. Scientific Computing Associates, CLAM User's Guide; The Computational Linear Algebra Machine, Version 2.00, New Haven, CT, 1990.
25. B. F. Smith, A domain decomposition algorithm for elliptic problems in three dimensions, Numer. Math., 60 (1991), pp. 219-234. MR 92m:65159
26. O. B. Widlund, An extension theorem for finite element spaces with three applications, in Numerical Techniques in Continuum Mechanics, W. Hackbusch and K. Witsch, eds., Braunschweig/Wiesbaden, 1987, Notes on Numerical Fluid Mechanics, v. 16, Friedr. Vieweg und Sohn, pp. 110-122. Proceedings of the Second GAMM-Seminar, Kiel, January, 1986.
27. _, Iterative sub structuring methods: Algorithms and theory jor elliptic problems in the plane, in First International Symposium on Domain Decomposition Methods for Partial Differential Equations, R. Glowinski, G. H. Golub, G. A. Meurant, and J. Périaux, eds., SIAM, Philadelphia, PA, 1988. MR 90c:65138