On a parallel implementation of the mortar element method

 Access to full text

 Full (PDF)

1. [1] G. S. Abdoulaev, Yu. A. Kuznetsov and O. Pironneau, The Numerical Implementation of the Domain Decomposition Method with Mortar Finite Elements for a 3D Problem, in Proc. of the 1st European Conf. on Numer. Math, and Advanced Appl. (Paris, September 1995). SMAI/GAMNI (to appear). 
2. [2] G.S. Abdoulaev, Y. Achdou, Yu.A. Kuznetsov, K.N. Lipnikov, J. Periaux and O. Pironneau, Finite element methods with nonmatching grids and applications, in Proc. of the Conf. on Applied Math, and Computer Science. Moscow University/INRIA(1997). 
3. [3] Y. Achdou and Yu.A. Kuznetsov, Substructuring preconditioners for finite element methods on nonmatching grids. East-West J. Numer. Math. 3 (1995) 1-28. Zbl0831.65115MR1331481
4. [4] Y. Achdou, Yu.A. Kuznetsov and O. Pironneau, Substructuring preconditioners for Q1 mortar element method. Numer. Math. 79 (1995) 419-449. Zbl0840.65122MR1355049
5. [5] Y. Achdou, Y. Maday and O.B. Widlund, Méthodes itératives de sous-structuration pour les éléments avec joints. Note CRAS, Paris, série I t 322 (1996) 185-190. Zbl0836.65118MR1373759
6. [6] Y. Achdou, Y. Maday and O.B. Widlund, Iterative substructuring preconditioners for mortar element methods in two dimensions. SIAM J. Numer. Anal. 36 (1999) 551-580. Zbl0931.65110MR1675257
7. [7] Y. Achdou and O. Pironneau, A fast solver for Navier-Stokes equations in the laminar regime using mortar finite element and boundary element methods. SIAM J. Numer. Anal. 32 (1995) 985-1016. Zbl0833.76032MR1342280
8. [8] F. Ben Belgacem, Discrétisations 3D nonconformes par la méthode de décomposition de domaines des éléments avec joints : analyse mathématique et mise en oeuvre pour le problème de Poisson. Ph.D. thesis, University of Pierre et Marie Curie, France.Note technique EDF, réf. HI72/93017 (1993). 
9. [9] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Rapport interne MIP n° 94-1, University of Paul Sabatier, France (1994). Zbl0944.65114
10. [10] F. Ben Belgacem and Y. Maday, The mortar element method for three dimensional finite elements. Rapport interne MIP n° 94-19, University of Paul Sabatier (1994). 
11. [11] C. Bernardi, Y. Maday and A. Patera, A new nonconforming approach to domain decomposition : the mortar element method, in Nonlinear Partial Differential Equations and Their Applications. H. Brezis, J.L. Lions Eds., Pitman, New York (1993). Zbl0797.65094
12. [12] J. Bramble, J. Pasciak and J. Xu, Parallel multilevel preconditioners. Math. Comp. 31 (1990) 333-390. Zbl0725.65095MR1023042
13. [13] M. A. Casarin and O. B. Widlund, A hierarchical preconditioner for the mortar finite element method. ETNA 4 (1996) 75-88. Zbl0870.65105MR1401446
14. [14] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). Zbl0383.65058MR520174
15. [15] E. G. D'yakonov, Minimization of Computations: Asymptotically Optimal Algorithms (in Russian). Nauka, Moscow (1989). MR1153409
16. [16] C. Farhat and F.X. Roux, Implicit parallel processing in structural mechanics. Comput. Mech. Adv. 2 (1994) 1-124. Zbl0805.73062MR1280753
17. [17] D. E. Goldberg, Genetic algorithms in search, optimization and machine leaming. Addison Wesley (1989). Zbl0721.68056
18. [18] G. H. Golub and C. F. Van Loan, Matrix Computations. The Johns Hopkins University Press, Baltimore and London (1983). Zbl0559.65011MR733103
19. [19] M. Griebel, Multilevel algorithms considered as iterative methods on semidefinite Systems. SIAM J. Sci. Comput. 15 (1994) 547-565. Zbl0818.65108MR1273151
20. [20] J. H. Holland, Adaptation in natural and artificial Systems. University of Michigan Press, Ann Arbor (1975). Zbl0317.68006MR441393
21. [21] Y. Iliash, T. Rossi and J. Toivanen, Two itérative methods for solving the Stokes problem. Tech. Report 2, University of Jyväskylä, Department of Mathematics, Laboratory of Scientific Computing (1993). 
22. [22] Yu. A Kuznetsov, Multigrid domain décomposition methods for elliptic problems. Comput Methods Appl. Mech. Eng. 75 (1989) 185-193. Zbl0692.65056MR1035752
23. [23] Yu. A Kuznetsov, Efficient itérative solvers for elliptic finite element problems on nonmatching grids.Russ. J. Numer. Anal.Math. Modelling 10 (1995) 187-211. Zbl0839.65031MR1343473
24. [24] P. Le Tallec, T. Sassi and M. Vidrascu, Domain decomposition method with nonmatching grids. Proceedings of DDM 9 AMS(1994) 61-74. Zbl0817.65110MR1312378
25. [25] G. I. Marchuk and Yu. A Kuznetsov, Méthodes itératives et fonctionnelles quadratiques, in Méthodes Mathématiques de L'Informatique - 4: Sur les Méthodes Numériques en Sciences, Physiques et Economiques. J.L. Lions, G.I. Marchuk Eds., Dunod, Paris (1974). Zbl0332.65040
26. [26] R. S. Varga, Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs (1961). Zbl0133.08602MR158502
27. [27] X. Zhang, Multilevel Schwarz methods. Numer. Math. 63 (1992) 521-539. Zbl0796.65129MR1189535