no. 2
On a parallel implementation of the mortar element method
ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 245-259. 
@article{M2AN_1999__33_2_245_0,
     author = {Abdoulaev, Gassav S. and Achdou, Yves and Kuznetsov, Yuri A. and Prud'homme, Christophe},
     title = {On a parallel implementation of the mortar element method},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {245--259},
     publisher = {EDP-Sciences},
     volume = {33},
     number = {2},
     year = {1999},
     mrnumber = {1700034},
     zbl = {0946.65111},
     language = {en},
     url = {http://www.numdam.org/item/M2AN_1999__33_2_245_0/}
}
TY  - JOUR
AU  - Abdoulaev, Gassav S.
AU  - Achdou, Yves
AU  - Kuznetsov, Yuri A.
AU  - Prud'homme, Christophe
TI  - On a parallel implementation of the mortar element method
JO  - ESAIM: Modélisation mathématique et analyse numérique
PY  - 1999
SP  - 245
EP  - 259
VL  - 33
IS  - 2
PB  - EDP-Sciences
UR  - http://www.numdam.org/item/M2AN_1999__33_2_245_0/
LA  - en
ID  - M2AN_1999__33_2_245_0
ER  - 
%0 Journal Article
%A Abdoulaev, Gassav S.
%A Achdou, Yves
%A Kuznetsov, Yuri A.
%A Prud'homme, Christophe
%T On a parallel implementation of the mortar element method
%J ESAIM: Modélisation mathématique et analyse numérique
%D 1999
%P 245-259
%V 33
%N 2
%I EDP-Sciences
%U http://www.numdam.org/item/M2AN_1999__33_2_245_0/
%G en
%F M2AN_1999__33_2_245_0
Abdoulaev, Gassav S.; Achdou, Yves; Kuznetsov, Yuri A.; Prud'homme, Christophe. On a parallel implementation of the mortar element method. ESAIM: Modélisation mathématique et analyse numérique, Tome 33 (1999) no. 2, pp. 245-259. http://www.numdam.org/item/M2AN_1999__33_2_245_0/

[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] 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] Y. Achdou and Yu.A. Kuznetsov, Substructuring preconditioners for finite element methods on nonmatching grids. East-West J. Numer. Math. 3 (1995) 1-28. | MR | Zbl

[4] Y. Achdou, Yu.A. Kuznetsov and O. Pironneau, Substructuring preconditioners for Q1 mortar element method. Numer. Math. 79 (1995) 419-449. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[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] F. Ben Belgacem, The mortar finite element method with Lagrange multipliers. Rapport interne MIP n° 94-1, University of Paul Sabatier, France (1994). | Zbl

[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] 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). | Zbl

[12] J. Bramble, J. Pasciak and J. Xu, Parallel multilevel preconditioners. Math. Comp. 31 (1990) 333-390. | MR | Zbl

[13] M. A. Casarin and O. B. Widlund, A hierarchical preconditioner for the mortar finite element method. ETNA 4 (1996) 75-88. | EuDML | MR | Zbl

[14] P. Ciarlet, The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978). | MR | Zbl

[15] E. G. D'Yakonov, Minimization of Computations: Asymptotically Optimal Algorithms (in Russian). Nauka, Moscow (1989). | MR

[16] C. Farhat and F.X. Roux, Implicit parallel processing in structural mechanics. Comput. Mech. Adv. 2 (1994) 1-124. | MR | Zbl

[17] D. E. Goldberg, Genetic algorithms in search, optimization and machine leaming. Addison Wesley (1989). | Zbl

[18] G. H. Golub and C. F. Van Loan, Matrix Computations. The Johns Hopkins University Press, Baltimore and London (1983). | MR | Zbl

[19] M. Griebel, Multilevel algorithms considered as iterative methods on semidefinite Systems. SIAM J. Sci. Comput. 15 (1994) 547-565. | MR | Zbl

[20] J. H. Holland, Adaptation in natural and artificial Systems. University of Michigan Press, Ann Arbor (1975). | MR | Zbl

[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] Yu. A Kuznetsov, Multigrid domain décomposition methods for elliptic problems. Comput Methods Appl. Mech. Eng. 75 (1989) 185-193. | MR | Zbl

[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. | MR | Zbl

[24] P. Le Tallec, T. Sassi and M. Vidrascu, Domain decomposition method with nonmatching grids. Proceedings of DDM 9 AMS(1994) 61-74. | MR | Zbl

[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). | Zbl

[26] R. S. Varga, Matrix Iterative Analysis. Prentice Hall, Englewood Cliffs (1961). | MR | Zbl

[27] X. Zhang, Multilevel Schwarz methods. Numer. Math. 63 (1992) 521-539. | EuDML | MR | Zbl