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- Max Duarte, Marc Massot, +4 authors Frédérique Laurent
- 2011

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reactive fronts,… (More)

- Stéphane Descombes, Thierry Dumont, Violaine Louvet, Marc Massot
- Int. J. Comput. Math.
- 2007

On the local and global errors of splitting approximations of reaction–diffusion equations with high spatial gradients Stéphane Descombes a , Thierry Dumont b , Violaine Louvet b & Marc Massot c a Unité de Mathématiques Pures et Appliquées, CNRS UMR 5669, Ecole Normale Supérieure de Lyon, 46 Allée d’Italie, 69364 Lyon Cedex, 07, France b Institut Camille… (More)

- Max Duarte, Marc Massot, +4 authors Frédérique Laurent
- SIAM J. Scientific Computing
- 2012

We tackle the numerical simulation of reaction-diffusion equations modeling multiscale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of steep spatial gradients in the reaction fronts,… (More)

Parameter estimation in non linear mixed effects models requires a large number of evaluations of the model to study. For ordinary differential equations, the overall computation time remains reasonable. However when the model itself is complex (for instance when it is a set of partial differential equations) it may be time consuming to evaluate it for a… (More)

- Max Duarte, Marc Massot, +4 authors Violaine Louvet
- CLEI Electron. J.
- 2011

We tackle the numerical simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem from the broad spectrum of temporal scales in the nonlinear chemical source term as well as from the presence of large spatial gradients in the reaction fronts,… (More)

- Stéphane Descombes, Max Duarte, Thierry Dumont, Frédérique Laurent, Violaine Louvet, Marc Massot
- SIAM J. Numerical Analysis
- 2014

In this paper we mathematically characterize through a Lie formalism the local errors induced by operator splitting when solving nonlinear reaction-diffusion equations, especially in the nonasymptotic regime. The nonasymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated with either… (More)

A new solver featuring time-space adaptation and error control has been recently introduced to tackle the numerical solution of stiff reaction-diffusion systems. Based on operator splitting, finite volume adaptive multiresolution and high order time integrators with specific stability properties for each operator, this strategy yields high computational… (More)

- Emmanuel Grenier, Marc Hoffmann, +4 authors Paul Vigneaux
- 2017

Many physical phenomena are modeled by parametrized PDEs. The poor knowledge on the involved parameters is often one of the numerous sources of uncertainties on these models. Some of these parameters can be estimated, with the use of real world data. The aim of this mini-symposium is to introduce some of the various tools from both statistical and numerical… (More)

- Emmanuel Grenier, Céline Helbert, Violaine Louvet, Adeline Samson, Paul Vigneaux, Paul Vigneauxa
- 2015

In this article we focus on parametrization of black box models from repeated measurements among several individuals (population parametrization). We introduce a variant of the SAEM algorithm, called KSAEM algorithm, which couples the standard SAEM algorithm with the dynamic construction of an approximate meta model. The costly evaluation of the genuine… (More)