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  • 1
    Digitale Medien
    Digitale Medien
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 36 (1993), S. 457-497 
    ISSN: 0029-5981
    Schlagwort(e): Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Mathematik , Technik allgemein
    Notizen: We investigate the effect of the ordering of the blocks of unknowns on the rate of convergence of a preconditioned non-linear GMRES algorithm, for solving the Navier-Stokes equations for compressible flows, using finite element methods on unstructured grids. The GMRES algorithm is preconditioned by an incomplete LDU block factorization of the Jacobian matrix associated with the non-linear problem to solve. We examine a wide range of ordering methods including minimum degree, (reverse) Cuthill-McKee and snake, and consider preconditionings without fill-in. We show empirically that there can be a significant difference in the number of iterations required by the preconditioned non-linear GMRES method and suggest a criterion for choosing a good ordering algorithm, according to the problem to solve.We also consider the effect of orderings when an incomplete factorization which allows some fill-in is performed. We consider the effect of automatically controlling the sparsity of the incomplete factorization through the level of fill-in.Finally, following the principal ideas of non-linear GMRES algorithm, we suggest other inexact Newton methods.
    Zusätzliches Material: 40 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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  • 2
    Digitale Medien
    Digitale Medien
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 19 (1994), S. 275-294 
    ISSN: 0271-2091
    Schlagwort(e): Navier-Stokes ; Fully-coupled solution ; Iterative solvers ; Finite-element methods ; Parallel algorithm ; Block diagonal preconditioning ; CFD ; Engineering ; Engineering General
    Quelle: Wiley InterScience Backfile Collection 1832-2000
    Thema: Maschinenbau
    Notizen: This paper presents the parallelization aspects of a solution method for the fully coupled 3D compressible Navier-Stokes equations. The algorithmic thrust of the approach, embedded in a finite element code NS3D, is the linearization of the governing equations through Newton methods, followed by a fully coupled solution of velocities and pressure at each non-linear iteration by preconditioned conjugate gradient-like iterative algorithms. For the matrix assembly, as well as for the linear equation solver, efficient coarse-grain parallel schemes have been developed for shared memory machines, as well as for networks of workstations, with a moderate number of processors. The parallel iterative schemes, in particular, circumvent some of the difficulties associated with domain decomposition methods, such as geometry bookkeeping and the sometimes drastic convergence slow-down of partitioned non-linear problems.
    Zusätzliches Material: 15 Ill.
    Materialart: Digitale Medien
    Bibliothek Standort Signatur Band/Heft/Jahr Verfügbarkeit
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