Groupe de travail approximation et analyse matricielle
Le groupe de travail d’algèbre réunit les membres de l’équipe Approximation (et toutes personnes intéressées). Responsable : Khalide Jbilou.
Achraf Badahmane (ULCO-LMPA)
The preconditioned global MINRESInformations : 11:00 - 12:00 B014
In this talk, we propose the preconditioned global MINRES as a new strategy to solve problems $AX=B$ with several right-hand sides.
The preconditioner is obtained by replacing the block (2,2) by another block of the matrix A.
We apply the global MINRES method for this problem with several right hand sides and we give new convergence results and analyze the eigenvalue-distribution and the eigenvectors of the preconditioner.
Finally, numerical results show that our preconditioned global MINRES method, is very efficient for solving problem with several right hand sides.
Yassine Kaouane (ULCO)
An adaptive block tangential method for multi-input multi-output dynamical systems.Informations : 11:00 - 12:00 Salle B014
We present a new approach for model order reduction in large-scale dynamical systems, with multiple inputs and multiple outputs (MIMO). This approach will be named : Adaptive Block Tangential Arnoldi Algorithm (ABTAA) and is based on interpolation via block tangential Krylov subspaces requiring the selection of shifts and tangent directions via an adaptive procedure. We give some algebraic properties and present some numerical examples to show the effectiveness of the proposed method.
Groupe de travail approximation et analyse matricielle du 30 juin 2017A. Messaoudi (ENS, Université Mohammed VI, Rabat)
New algoritm for computing the interpolation polynomialsInformations : 11:00 - 12:00 B014
Le résumé est diponible ici pdf
Groupe de travail approximation et analyse matricielle du 23 juin 2017Marcos Raydan (Universidad Simón Bolívar)
Constrained optimization schemes for avoiding resonance in large structuresInformations : 11:00 - 12:00 B014
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.
Groupe de travail approximation et analyse matricielle du 16 juin 2017Achraf Badahmane (ULCO)
Saddle point problemsInformations : 14:30 - 15:30 B014
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
Groupe de travail approximation et analyse matricielle du 2 juin 2017Yassine Kaouane (LMPA, ULCO)
Adaptive tangential Computational Krylov subspaces methods for model reduction in large-scale dynamical systemsInformations : 14:30 - 15:30 B014, Mi-voix
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.
Groupe de travail approximation et analyse matricielle du 12 mai 2017Hassane Sadok (ULCO)
Convergence properties and implementations of Block Krylov subspaces methodsInformations : 13:30 - 14:30 B014
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.