DUARTE , Max

Nous abordons dans cette thèse le développement d'une nouvelle génération de méthodes numériques pour la résolution des EDP évolutives qui modélisent des phénomènes multi-échelles en temps et en espace issus de divers domaines applicatifs. En conséquence, il s'agit de développer des méthodes qui garantissent la précision des résultats via...

Nous abordons dans cette thèse le développement d'une nouvelle génération de méthodes numériques pour la résolution des EDP évolutives qui modélisent des phénomènes multi-échelles en temps et en espace issus de divers domaines applicatifs. En conséquence, il s'agit de développer des méthodes qui garantissent la précision des résultats via...

Nous abordons le développement d'une nouvelle génération de méthodes numériques pour la résolution des EDP évolutives qui modélisent des phénomènes multi-échelles en temps et en espace issus de divers domaines applicatifs. La raideur associée à ce type de problème, que ce soit via le terme source chimique qui présente un large spectre...

In this paper, we investigate the coupling between operator splitting techniques and a time parallelization scheme, the parareal algorithm, as a numerical strategy for the simulation of reaction-diffusion equations modeling multi-scale reaction waves. This type of problems induces peculiar difficulties and potentially large stiffness which stem...

Operator splitting techniques were originally introduced with the main objective of saving computational costs. A multi-physics problem is thus split in subproblems of different nature with a significant reduction of the algorithmic complexity and computational requirements of the numerical solvers. Nevertheless, splitting errors are introduced...

Nous abordons le développement d'une nouvelle génération de méthodes numériques pour la résolution des EDP évolutives qui modélisent des phénomènes multi-échelles en temps et en espace issus de divers domaines applicatifs. La raideur associée à ce type de problème, que ce soit via le terme source chimique qui présente un large spectre...

The simulation of the interaction of two simultaneously propagating air streamers of the same polarity is presented. A parametric study has been carried out using an accurate numerical method which ensures a time-space error control of the solution. For initial separation of both streamers smaller or comparable to the longest characteristic...

We develop a numerical strategy to solve multi-dimensional Poisson equations on dynamically adapted grids for evolutionary problems disclosing propagating fronts. The method is an extension of the multiresolution finite volume scheme used to solve hyperbolic and parabolic time-dependent PDEs. Such an approach guarantees a numerical solution of...

We present a new resolution strategy for multi-scale reaction waves based on adaptive time operator splitting and space adaptive multiresolution, in the context of localized and stiff reaction fronts. The main goal is to perform computationally efficient simulations of the dynamics of multi-scale phenomena under study, considering large...

In this work we are concerned with the the numerical simulation of flames issued from combustion applications with a time-space adaptive technique. This study is carried out in a classical context of laminar flames interacting with vortex structures including self-ignition processes of reactive mixtures. Hydrodynamics are decoupled from...

In this work we are concerned with the the numerical simulation of flames issued from combustion applications with a time-space adaptive technique. This study is carried out in a classical context of laminar flames interacting with vortex structures including self-ignition processes of reactive mixtures. Hydrodynamics are decoupled from...

This paper presents a new computational strategy for the simulation of combustion fronts based on adaptive time operator splitting and spatial multiresolution. High-order and dedicated one-step solvers compose the splitting scheme for the reaction, diffusion, and convection subproblems, to independently cope with their inherent numerical...

This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady problems. The strategy considers a second order Strang method and another lower order embedded splitting scheme...

This paper presents a new resolution strategy for multi-scale streamer discharge simulations based on a second order time adaptive integration and space adaptive multiresolution. A classical fluid model is used to describe plasma discharges, considering drift-diffusion equations and the computation of electric field. The proposed numerical...

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 non-asymptotic regime. The non-asymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated...

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...

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 non-asymptotic regime. The non-asymptotic regime is often attained in practice when the splitting time step is much larger than some of the scales associated...

In silico research in medicine is thought to reduce the need for expensive clinical trials under the condition of reliable mathematical models and accurate and efficient numerical methods. In the present work, we tackle the numerical simulation of reaction-diffusion equations modeling human ischemic stroke. This problem induces peculiar...

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...

In this paper, we tackle the numerical simulation of reaction-diffusion equations modeling multiscale reaction waves. This type of problems induces peculiar diffculties 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...

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...