Laboratoire de Mathématiques Pures et Appliquées
Joseph Liouville

Séminaire et groupe de travail d’Approximation et Analyse matricielle

Le séminaire et groupe de travail d’algèbre réunit les membres de l’équipe Approximation (et toutes personnes intéressées). Responsable : Khalide Jbilou.

Evénements passés

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 23 juin 2017

    Marcos Raydan (Universidad Simón Bolívar)

    The Quadratic Finite Element Model Updating Problem (QFEMUP) concerns
    with updating a symmetric second-order finite element model so that it
    remains symmetric and the updated model reproduces a given set of
    desired eigenvalues and eigenvectors by replacing the corresponding
    ones from the original model. Taking advantage of the special
    structure of the constraint set, it is first shown that the QFEMUP can
    be formulated as a suitable constrained nonlinear programming
    problem. Using this formulation, we present and analyze two different
    methods based on successive optimizations. To avoid that spurious
    modes (eigenvectors) appear in the frequency range of interest
    (eigenvalues) after the model has been updated, additional constraints
    based on a quadratic Rayleigh quotient are dynamically included in the
    constraint set. The results of our numerical experiments on
    illustrative problems show that the algorithms work well in practice.

    Informations : 11:00 - 12:00 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 16 juin 2017

    Achraf Badahmane (ULCO)

    In some applications, we have to solve large linear saddle
    point problems with multiple right-hand sides. Instead of applying a
    standard iterative process to the solution of each saddle point
    problem indepentely, it’s more efficient to apply a global process. We
    use different techniques of preconditioning ( Diagonal preconditioner,
    Triangular preconditioner, P0 preconditioner ,.. ) to improve spectral
    proprieties of the saddle point matrix and to accelerate the

    Informations : 14:30 - 15:30 B014

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 2 juin 2017

    Yassine Kaouane (LMPA, ULCO)

    In this talk, we present two new approaches for model order reduction
    problem, with multiple inputs and multiple outputs (MIMO). The
    Adaptive Global Tangentiel Arlondi Algorithms (AGTAA), and the
    Adaptive Global Tangentiel Lanczos Algorithms (AGTLA).These methods
    are based on a generalization of the global Arnoldi and the global
    Laczos algorithms. The selection of the shifts and the tangent
    directions is done with an adaptive procedure. We give some algebraic
    properties for the global case. Finally, some numerical examples are
    presented to show the effectiveness of the proposed algorithms.

    Key words : Global, Arnoldi, Lanczos, Model reduction, Tangential directions.

    Informations : 14:30 - 15:30 B014, Mi-voix

  • Séminaire et groupe de travail d’Approximation et Analyse matricielle du 12 mai 2017

    Hassane Sadok (ULCO)

    Krylov subspace methods are widely used for the iterative solution of
    a large variety of linear systems of equations with one or several
    right hand sides or for solving nonsymmetric eigenvalue problems. The
    solution of linear systems of equations with several right-hand sides
    is considered. Approximate solutions are conveniently computed by
    block GMRES methods. We describe and study three variants of block
    GMRES. These methods are based on three implementations of the block
    Arnoldi method, which differ in their choice of inner product.. The
    Block GMRES is classically implemented by first applying the Arnoldi
    iteration as a block orthogonalization process to create a basis of
    the block Krylov space generated by the matrix of the system from the
    initial residual. Next, the method is solving a block least-squares
    problem, which is equivalent to solving several least squares problems
    implying the same Hessenberg matrix. These laters are usually solved
    by using a block updating procedure for the QR decomposition of the
    Hessenberg matrix based on Givens rotations. A more effective
    alternative was given by M. H. Gutknecht and T. Schmelzer which uses
    the Householder reflectors. We propose a new and simple implementation
    of the block GMRES algorithm, based on a generalization of Ayachour’s
    method given for the GMRES with a single right-hand side. Several
    numerical experiments are provided to illustrate the performance of
    the new implementation.

    Informations : 13:30 - 14:30 B014
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