Statistical estimation of roundoff errors and condition numbers

Disponible dans les fichiers attachés à ce documen

Varying the s in Your s-step GMRES

International audienceKrylov subspace methods are commonly used iterative methods for solving large sparse linear systems, however they suffer from communication bottlenecks on parallel computers.Therefore, $s$-step methods have been developed where the Krylov subspace is built block by block, so that $s$ matrix-vector multiplications can be done before orthonormalizing the block. Then Communication-Avoiding algorithms can be used for both kernels.This paper introduces a new variation on $s$-step GMRES in order to reduce the number of iterations necessary to ensure convergence, with a small overhead in the number of communications. Namely, we develop a $s$-step GMRES algorithm, where the block size is variable and increases gradually. Our numerical experiments show a good agreement with our analysis of condition numbers and demonstrate the efficiency of our variable $s$-step approach

On the Performance of Various Adaptive Preconditioned GMRES Strategies

This paper compares the performance on linear systems of equations of three similar adaptive accelerating strategies for restarted GMRES. The underlying idea is to adaptively use spectral information gathered from the Arnoldi process. The first strategy retains approximations to some eigenvectors from the previous restart and adds them to the Krylov subspace. The second strategy uses also approximated eigenvectors to define a preconditioner at each restart. This paper designs a third new strategy which combines elements of both previous approaches. Numerical results show that this new method is both more efficient and more robust

Des pollutions suivies à la trace par Jocelyne Erhel et Jean-Raynald de Dreuzy. Des déchets à vie longue, entretien avec Jérôme Jaffré, propos recueillis par Dominique Chouchan.

National audienceL'accès à l'eau potable est un privilège si l'on songe qu'un milliard d'humains en est encore dépourvu. Les recherches visent à produire les connaissances susceptibles d'aider à réduire la dégradation des nappes phréatiques

Characterizations of Solutions in Geochemistry: Existence, Uniqueness and Precipitation Diagram

International audienceIn this paper, we study the properties of a geochemical model involving aqueous and precipitation-dissolution reactions at a local equilibrium in a diluted solution. This model can be derived from the minimization of the free Gibbs energy subject to linear constraints. By using logarithmic variables, we define another minimization problem subject to different linear constraints with reduced size. The new objective function is strictly convex, so that uniqueness is straightforward. Moreover, existence conditions are directly related to the totals, which are the parameters in the mass balance equation. These results allow us to define a partition of the totals into mineral states, where a given subset of minerals are present. This precipitation diagram is inspired from thermodynamic diagrams where a phase depends on physical parameters. Using the polynomial structure of the problem, we provide characterizations and an algorithm to compute the precipitation diagram. Numerical computations on some examples illustrate this approach

Impact of fractures on diffusion dominated reactive transport in porous media: application to the study of a radioactive waste storage

International audienceImpact of fractures on diffusion dominated reactive transport in porous media: application to the study of a radioactive waste storag