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
Liste des exposés de 2017
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Vendredi 30 juin 2017
A. Messaoudi (ENS, Université Mohammed VI, Rabat)
New algoritm for computing the interpolation polynomials
(⊕ résumé) 11:00 - 12:00 B014
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Vendredi 23 juin 2017
Marcos Raydan (Universidad Simón Bolívar)
Constrained optimization schemes for avoiding resonance in large structures
(⊕ résumé) 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.
11:00 - 12:00 B014
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Vendredi 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
convergence
14:30 - 15:30 B014
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Vendredi 2 juin 2017
Yassine Kaouane (LMPA, ULCO)
Adaptive tangential Computational Krylov subspaces methods for model reduction in large-scale dynamical systems
(⊕ résumé) 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.
14:30 - 15:30 B014, Mi-voix
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Vendredi 12 mai 2017
Hassane Sadok (ULCO)
Convergence properties and implementations of Block Krylov subspaces methods
(⊕ résumé) 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.
13:30 - 14:30 B014
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