Flexible GMRES with deflated restarting

L Giraud, S Gratton, X Pinel, X Vasseur - SIAM Journal on Scientific Computing, 2010 - SIAM
In many situations, it has been observed that significant convergence improvements can be
achieved in preconditioned Krylov subspace methods by enriching them with some spectral …

An improved two‐grid preconditioner for the solution of three‐dimensional Helmholtz problems in heterogeneous media

…, S Gratton, X Pinel, X Vasseur - … Linear Algebra with …, 2013 - Wiley Online Library
In this paper, we address the solution of three‐dimensional heterogeneous Helmholtz
problems discretized with second‐order finite difference methods with application to acoustic …

Flexible variants of block restarted GMRES methods with application to geophysics

…, S Gratton, J Langou, X Pinel, X Vasseur - SIAM Journal on Scientific …, 2012 - SIAM
In a wide number of applications in computational science and engineering the solution of
large linear systems of equations with several right-hand sides given at once is required. …

Revisiting the spectral analysis for high-order spectral discontinuous methods

J Vanharen, G Puigt, X Vasseur, JF Boussuge… - Journal of …, 2017 - Elsevier
The spectral analysis is a basic tool to characterise the behaviour of any convection scheme.
By nature, the solution projected onto the Fourier basis enables to estimate the dissipation …

A flexible generalized conjugate residual method with inner orthogonalization and deflated restarting

LM Carvalho, S Gratton, R Lago, X Vasseur - SIAM Journal on Matrix Analysis …, 2011 - SIAM
This work is concerned with the development and study of a minimum residual norm
subspace method based on the generalized conjugate residual method with inner …

A modified block flexible GMRES method with deflation at each iteration for the solution of non-Hermitian linear systems with multiple right-hand sides

H Calandra, S Gratton, R Lago, X Vasseur… - SIAM Journal on …, 2013 - SIAM
We propose a variant of the block GMRES method for the solution of linear systems of
equations with multiple right-hand sides. We investigate a deflation strategy to detect when a …

Time-parallel simulation of the decay of homogeneous turbulence using parareal with spatial coarsening

T Lunet, J Bodart, S Gratton, X Vasseur - Computing and Visualization in …, 2018 - Springer
Direct Numerical Simulation of turbulent flows is a computationally demanding problem that
requires efficient parallel algorithms. We investigate the applicability of the time-parallel …

Constrained regional recovery of continental water mass time-variations from GRACE-based geopotential anomalies over South America

…, F Frappart, R Biancale, S Gratton, X Vasseur… - Surveys in …, 2012 - Springer
We propose a “constrained” least-squares approach to estimate regional maps of equivalent-water
heights by inverting GRACE-based potential anomalies at satellite altitude. …

Modelling spatially correlated observation errors in variational data assimilation using a diffusion operator on an unstructured mesh

O Guillet, AT Weaver, X Vasseur… - Quarterly Journal of …, 2019 - Wiley Online Library
We propose a method for representing spatially correlated observation errors in variational
data assimilation. The method is based on the numerical solution of a diffusion equation, a …

Numerical approximation of port-Hamiltonian systems for hyperbolic or parabolic PDEs with boundary control

A Brugnoli, G Haine, A Serhani, X Vasseur - arXiv preprint arXiv …, 2020 - arxiv.org
We consider the design of structure-preserving discretization methods for the solution of
systems of boundary controlled Partial Differential Equations (PDEs) thanks to the port-…