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  • 1
    Electronic Resource
    Electronic Resource
    GMRES acceleration of iterative implicit finite element solvers for compressible Euler and Navier-Stokes equations (1995)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 20 (1995), S. 957-967 
    Details
    ISSN: 0271-2091
    Keywords: Newton ; GMRES ; descent direction ; local preconditioner ; dynamic sizing ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Implicit iterative schemes based on linearized and non-linear Newton methods are discussed, with resolution of a matrix subsystem or a matrix-free method by preconditioned GMRES algorithms. The defaults of convergence due to the locality of Newton algorithms can be partially overcome by using stabilizing descent techniques, restarting and global strategies such as line search backtracking procedures, or by tuning the iterations once the approximate Jacobians are closer to the exact ones. Comparison with a more conventional relaxation method and their implementation on parallel architectures are discussed.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650200816
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    NEWTON-GMRES ALGORITHM APPLIED TO COMPRESSIBLE FLOWS (1996)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 23 (1996), S. 177-190 
    Details
    ISSN: 0271-2091
    Keywords: non-linear problem ; approximate Jacobian ; convergence ; iterative linear solver ; restarting ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: This paper addresses the resolution of non-linear problems arising from an implicit time discretization in CFD problems. We study the convergence of the Newton-GMRES algorithm with a Jacobian approximated by a finite difference scheme and with restarting in GMRES. In our numerical experiments we observe, as predicted by the theory, the impact of the matrix-free approximations. A second-order scheme clearly improves the convergence in the Newton process.
    Additional Material: 9 Tab.
    Type of Medium: Electronic Resource
    Library Location Call Number Volume/Issue/Year Availability
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    Paper (German National Licenses)
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