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  • 1
    Electronic Resource
    Electronic Resource
    Two-level domain decomposition preconditioning for the p-version finite element method in three dimensionsThis research was partially sponsored by the National Science Foundation under grant DMS-8704169. This paper was presented at the Fourth Copper Mountain Conference on Multigrid Methods, Copper Mountain, Colorado, U.S.A., April 9-14, 1989 (1990)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 29 (1990), S. 1095-1108 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: This paper presents a flexible approach to domain decomposition preconditioning for problems expressed in terms of local stiffness matrices of subdomains. Evaluation of the preconditioner requires fully parallelizable local computations and the solution of a global auxiliary problem with few variables per subdomain. Convergence factors can be bounded using properties of the local stiffness matrices only. The method is applied to the p-version finite element method for three-dimensional elasticity. We treat each element as a subdomain and compute explicit convergence bounds.
    Additional Material: 5 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620290513
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Balancing domain decomposition (1993)
    Chichester : Wiley-Blackwell
    Communications in Numerical Methods in Engineering 9 (1993), S. 233-241 
    Details
    ISSN: 1069-8299
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: The Neumann-Neumann algorithm is known to be an efficient domain decomposition preconditioner with unstructured subdomains for iterative solution of finite-element discretizations of difficult problems with strongly discontinuous coefficients (De Roeck and Le Tallec, 1991). However, this algorithm suffers from the need to solve in each iteration an inconsistent singular problem for every subdomain, and its convergence deteriorates with increasing number of subdomains due to the lack of a coarse problem to propagate the error globally. We show that the equilibrium conditions for the singular problems on subdomains lead to a simple and natural construction of a coarse problem. The construction is purely algebraic and applies also to systems such as those that arise in elasticity. A convergence bound independent of the number of subdomains is proved and results of computational tests are reported.
    Additional Material: 1 Tab.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1640090307
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  • 3
    Electronic Resource
    Electronic Resource
    A scalable Lagrange multiplier based domain decomposition method for time-dependent problems (1995)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 38 (1995), S. 3831-3853 
    Details
    ISSN: 0029-5981
    Keywords: domain decomposition ; dynamics ; nonlinear ; parallel processing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Notes: We present a new efficient and scalable domain decomposition method for solving implicitly linear and non-linear time-dependent problems in computational mechanics. The method is derived by adding a coarse problem to the recently proposed transient FETI substructuring algorithm in order to propagate the error globally and accelerate convergence. It is proved that in the limit for large time steps, the new method converges toward the FETI algorithm for time-independent problems. Computational results confirm that the optimal convergence properties of the time-independent FETI method are preserved in the time-dependent case. We employ an iterative scheme for solving efficiently the coarse problem on massively parallel processors, and demonstrate the effective scalability of the new transient FETI method with the large-scale finite element dynamic analysis on the Paragon XP/S and IBM SP2 systems of several diffraction grating finite element structural models. We also show that this new domain decomposition method outperforms the popular direct skyline solver. The coarse problem presented herein is applicable and beneficial to a large class of Lagrange multiplier based substructuring algorithms for time-dependent problems, including the fictitious domain decomposition method.
    Additional Material: 3 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620382207
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  • 4
    Electronic Resource
    Electronic Resource
    Preface (1992)
    New York, NY [u.a.] : Wiley-Blackwell
    Communications in Applied Numerical Methods 8 (1992), S. 561-561 
    Details
    ISSN: 0748-8025
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/cnm.1630080902
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    Paper (German National Licenses)
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