ED Mathématiques et Informatique
Nonlinear domain decomposition methods: analysis and industrial applications
by El Mehdi ETTAOUCHI (Institut national de recherche en informatique et en automatique - Bordeaux - Sud-Ouest)
The defense will take place at 14h00 - amphi 2, bâtiment Azur d'EDF R&D Paris-Saclay 7 bd Gaspard Monge, 91120 Palaiseau
in front of the jury composed of
- Luc GIRAUD - Directeur de recherche - Inria - Directeur de these
- Victorita DOLEAN - Professeure - TU Eindhoven - Examinateur
- Nicole SPILLANE - Chargée de recherche - CNRS, CMAP - Examinateur
- Carola KRUSE - Chercheuse senior - CERFACS - CoDirecteur de these
- Pierre GOSSELET - Professeur - Université de Lille - Examinateur
- Augustin PARRET-FRéAUD - Ingénieur de recherche - Safran - Examinateur
- Martin GANDER - Professeur - Université de Genève - Rapporteur
- Félix KWOK - Professeur - Université Laval - Rapporteur
This thesis focuses on the design, analysis, and high performance implementation of parallel nonlinear solvers for large-scale discretizations of nonlinear partial differential equations. These problems yield large nonlinear systems whose cost is dominated by repeated linearizations and Krylov solves. Because linear domain decomposition cannot achieve perfect parallel efficiency at scale, its overhead is paid at every nonlinear iteration, motivating methods that act directly on the nonlinear convergence loop. We develop nonlinear domain decomposition preconditioners for the Newton method, with emphasis on RASPEN and its substructured variant SRASPEN. A theoretical analysis explains how nonlinear subdomain corrections condense the nonlinearity onto interface unknowns and improve the contraction properties of the induced Newton mapping. We then introduce nonlinear two-level preconditioning through an algebraic coarse correction computed by a nonlinear subspace iteration. We focus on a multiplicative approach and identify conditions on the coarse space that enhance favorable spectral properties of the initial two-level Jacobian. Practical constructions follow from local singular value problems posed on the interfaces of the overlapping subdomains, leading to error propagation and conditioning driven coarse spaces. A main outcome is a fully parallel implementation within the solver class of Code_Aster, assessed on fine discretizations and high levels of parallelism. The approach is validated primarily on unsaturated two-phase, two-component flow configurations in porous media, central to storage-scale thermo-hydro-mechanical simulations. As an additional case of interest, it is also evaluated on large-scale elasto-visco-plasticity simulations, confirming its ability to make simulations more robust and reduce the cost of computations.
ED Sciences Chimiques
From ionomer dispersions and carbon black suspensions to catalyst inks: formulation, structure and rheology for fuel cell electrodes manufacturing
by Jackie BURGHART (Laboratoire du Futur)
The defense will take place at 9h30 - Amphithéâtre F ENSEIRB-MATMECA 1 Avenue du Dr Albert Schweitzer 33402 Talence
in front of the jury composed of
- Yaocihuatl MEDINA-GONZALEZ - Directrice de recherche - Université de Bordeaux - Directeur de these
- Martine MEIRELES - Directrice de recherche - Université de Toulouse - Rapporteur
- Arnaud MORIN - Directeur de recherche - CEA-Liten - Rapporteur
- Stéphane CHEVALIER - Maître de conférences - Université de Bordeaux - Examinateur
Proton exchange membrane fuel cells are key technologies for the energy transition, particularly in the transport sector. The performance of these devices strongly depends on the quality of the electrodes, and especially on the catalytic layer, which is obtained by depositing a complex catalyst ink. Despite recent advances, the understanding of the links between formulation, multi-scale structuring, and rheology of catalyst ink remains incomplete, limiting the rational optimization of manufacturing processes. This thesis aims to elucidate the physicochemical mechanisms governing the structuring and rheological behavior of these inks. The approach is based on the progressive study of the main ink components: an ionomer and a carbon black, analyzed separately and then in combination in a range of solvent mixtures. Complementary structural characterization techniques (small-angle X-ray scattering, dynamic light scattering, cryo-transmission electron microscopy, microscopy, rheo-microscopy), adsorption studies, and rheological measurements were used to explore the influence of formulation parameters (solvent, concentration, ionomer / carbon black ratio, preparation protocols) on internal structuring and flow properties. The study of ionomer dispersions revealed the impact of solvent, concentration, and thermal treatment on the formation of aggregates and agglomerates, as well as on the dynamics of structuring, with direct consequences on viscosity. The adopted approach also showed, for carbon black suspensions, the role of solvent and concentration in the formation of percolating networks and the modulation of yield stress, as well as a strong sensitivity to shear history. The analysis of complete catalyst inks demonstrated that the addition of ionomer modulates the dispersion of carbon black and, above a certain threshold, controls the rheology of the system. Adsorption studies highlighted the dual role of the ionomer as both dispersant and continuous matrix, while a first exploration of drying kinetics opens perspectives on the link between formulation and deposition. This work stands out for its implementation of an integrative and multi-scale approach, combining in-depth analysis of the internal structuring and flow properties of the different ink components, studied separately and then together. This methodology enables a systematic connection between dispersion, aggregation, and interaction phenomena and the rheology of the inks, thus providing a new and comprehensive understanding of these systems. The knowledge acquired provides a foundation for rationalizing subsequent steps in the fabrication of catalytic layers and paves the way for future studies on the relationship between rheology, layer microstructure and electrochemical performance.