Le travail de cette thèse a porté sur plusieurs problèmes d'homogénéisation d'équations elliptiques linéaires dans un cadre de coefficients oscillants non périodiques. Les classes de coefficients considérées sont supposées modéliser des géométries périodiques perturbées par des défauts de différentes natures. L'objectif de ces problèmes est d'expli...
We propose and analyse a parallel method, both in the time and space directions, that couples the Parareal algorithm with the Optimized Schwarz waveform relaxation (OSWR) method, with only few OSWR iterations in the fine propagator and with a simple coarse propagator deduced from the Backward Euler method. The analysis of this coupled method is pre...
We provide a comprehensive study of the convergence of the forward-backward algorithm under suitable geometric conditions, such as conditioning or Łojasiewicz properties. These geometrical notions are usually local by nature, and may fail to describe the fine geometry of objective functions relevant in inverse problems and signal processing, that h...
We study a stochastic first order primal-dual method for solving convex-concave saddle point problems over real reflexive Banach spaces using Bregman divergences and relative smoothness assumptions, in which we allow for stochastic error in the computation of gradient terms within the algorithm. We show ergodic convergence in expectation of the Lag...
Many modern applications rely on solving optimization problems (e.g., computational biology, mechanics, finance), establishing optimization methods as crucial tools in many scientific fields. Providing guarantees on the (hopefully good) behaviors of these methods is therefore of significant interest. A standard way of analyzing optimization algorit...
Many modern applications rely on solving optimization problems (e.g., computational biology, mechanics, finance), establishing optimization methods as crucial tools in many scientific fields. Providing guarantees on the (hopefully good) behaviors of these methods is therefore of significant interest. A standard way of analyzing optimization algorit...
Published in Journal of Mathematical Fluid Mechanics
This paper is devoted to the theoretical and numerical analysis of the heat transport problem through a viscous and incompressible fluid in a Hele–Shaw geometry. This model corresponds to a bi-dimensional system derived from the 3D-Navier–Stokes equations coupled with an advection-diffusion equation for the heat transport. We analyze the existence ...
Published in Journal of Scientific Computing
This article analyses the convergence of the Lie–Trotter splitting scheme for the stochastic Manakov equation, a system arising in the study of pulse propagation in randomly birefringent optical fibers. First, we prove that the strong order of the numerical approximation is 1/2 if the nonlinear term in the system is globally Lipschitz. Then, we sho...
The Frank-Wolfe algorithms, a.k.a. conditional gradient algorithms, solve constrained optimization problems. They break down a non-linear problem into a series of linear minimization on the constraint set. This contributes to their recent revival in many applied domains, in particular those involving large-scale optimization problems. In this disse...
