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Abstract: . We present a new Neumann-Neumann type preconditioner of large scale linear systems arising from plate and shell problems. The advantage of the new method is a smaller coarse space than those of earlier method of the authors; this improves parallel scalability. A new abstract framework for Neumann-Neumann preconditioners is used to prove almost optimal convergence properties of the method. The convergence estimates are independent of the number of subdomains, coefficient jumps between... (Update)
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...bending finite element satisfy the following approximate parametric variational principle recently formulated in [20] Assumption 3. 13 ([19, 20]) We consider finite elements with displacements and rotations at the vertices only, and assume that there exist constants c 1 0, c...
.... have been shown to perform similarly to the case of conforming nite elements; cf. 3, 14] for iterative substructuring methods, [15, 37, 38] for Neumann Neumann algorithms, and [36, 48] for the FETI method. For other studies of preconditioners for the mortar method, see [13]...
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9: The construction of preconditioners for elliptic problems by substructuring (context) - Bramble, Pasciak et al. - 1986
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BibTeX entry: (Update)
P. Le Tallec, Neumann-Neumann domain decomposition algorithms for solving 2D elliptic problems with nonmatching grids, East-West J. Numer. Math., 1 (1993), pp. 129--146. http://citeseer.ist.psu.edu/letallec97neumannneumann.html More
@article{ letallec98neumannneumann,
author = "Patrick Le Tallec and Jan Mandel and Marina Vidrascu",
title = "A {Neumann-Neumann} Domain Decomposition Algorithm for Solving Plate and Shell Problems",
journal = "SIAM Journal on Numerical Analysis",
volume = "35",
number = "2",
pages = "836--867",
year = "1998",
url = "citeseer.ist.psu.edu/letallec97neumannneumann.html" }
Citations (may not include all citations):2441 John Hopkins University Press (context) - Golub, Van Loan et al. - 1989
233 The construction of preconditioners for elliptic problems by.. (context) - Bramble, Pasciak et al. - 1986
70 Basic error estimates for elliptic problems (context) - Ciarlet - 1989
55 Balancing domain decomposition - Mandel - 1993
53 Schwarz methods of Neumann-Neumann type for threedimensional.. - Dryja, Widlund - 1995
49 Optimal convergence properties of the FETI domain decomposit.. (context) - Farhat, Mandel et al. - 1994
47 Balancing domain decomposition for mixed finite elements - Cowsar, Mandel et al. - 1995
46 Domain decomposition methods in computational mechanics (context) - Le Tallec - 1994
40 Implicit parallel processing in structural mechanics (context) - Farhat, Roux - 1994
31 Convergence of a substructuring method with Lagrange multipl.. - Mandel, Tezaur - 1996
30 A method of domain decomposition for 3-D finite element prob.. (context) - Dryja - 1988
29 Variational formulation and algorithm for trace operator in .. (context) - Bourgat, Glowinski et al. - 1989
27 Balancing domain decomposition: Theory and computations in t.. (context) - Mandel, Brezina - 1993
20 A scalable substructuring method by Lagrange multipliers for.. - Mandel, Tezaur et al.
17 Analysis and test of a local domain decomposition preconditi.. (context) - De Roeck, Le Tallec - 1991
16 Lagrange multiplier based divide and conquer finite element .. (context) - Farhat - 1991
16 Two-level Schwarz methods for nonconforming finite elements .. - Sarkis - 1993
12 Parallel domain decomposition solver for adaptive hp finite .. - Oden, patra et al. - 1994
6 A study of three-node triangular bending element (context) - Batoz, Bathe et al. - 1980
6 A survey of parametrized variational principles and applicat.. (context) - Felippa - 1994
4 On drilling degrees of freedom (context) - Brezzi, Hughes - 1994
3 The Finite Element Method in Thin Shell Theory (context) - Bernadou, Boisserie - 1982
3 A triangular membrane element with rotational degrees of fre.. (context) - Bergan, Felippa - 1985
2 Singular Integrals and Defferentiability Properties of Funct.. (context) - Stein - 1970
2 Transonic computations by a multidomain technique with poten.. (context) - Morice - 1989
2 Finite element with drilling degrees of freedom (context) - Brezzi, Hughes et al. - 1989
2 The Poincar'e-Steklov's operators and the domain decompositi.. (context) - Aghoskov, Lebedev - 1985
2 el'ements finis pour les probl`emes de coques minces (context) - Bernadou - 1994
2 A domain decomposed solver for nonlinear elasticity (context) - De Roeck, Le Tallec et al. - 1992
2 Finite element approximation of a geometrically exact shell .. (context) - Le Tallec, Carrive-Bedouani et al. - 1995
1 Center for Computational Mathematics (context) - multiplier, decomposition et al. - 1995
1 Mathematics of Computation (context) - decomposition, with et al. - 1996
1 ele de Koiter pour une coque peu r (context) - Blouza, Le Dret et al. - 1994
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Documents on the same site (http://www-math.cudenver.edu/~jmandel/papers/): More
Balancing Domain Decomposition for Plates - Le Tallec, Mandel, Vidrascu (1994) (Correct)
Convergence of a Substructuring Method with Lagrange Multipliers - Mandel, Tezaur (1995) (Correct)
A Scalable Substructuring Method By Lagrange Multipliers.. - Mandel, Tezaur, Farhat (1998) (Correct)
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