Il résume les principaux résultats de ce travail et fournit un aperçu de certaines idées présentées ,
, At some point you stop being a student and you start being a scientist
Episode 124 -In Search of Reality: A Conversation with Sean Carroll, Waking Up Podcast with Sam Harris, 2018. ,
D. spinodal decomposition, IUPAC Compendium of Chemical Terminology, vol.1669, 1997. ,
Lithium-ion batteries and materials, Springer Handbook of Electrochemical Energy, chapter 15, pp.449-494, 2017. ,
, Numerical Linear Algebra (Texts in Applied Mathematics)
, , 2007.
, com/Numerical-Linear-Algebra-Applied-Mathematics/dp/0387341595?SubscriptionId= 0JYN1NVW651KCA56C102&tag=techkie-20&linkCode=xm2&camp=2025&creative=165953&
Fully-implicit time-marching aeroelastic solutions, 32nd Aerospace Sciences Meeting and Exhibit, p.56, 1994. ,
A new unconditionally stable fractional step method for non-linear coupled thermomechanical problems, International Journal for Numerical Methods in Engineering, vol.35, issue.4, pp.737-766, 1992. ,
, Owe Axelsson. Iterative Solution Methods, 1994.
Block recursive lu preconditioners for the thermally coupled incompressible inductionless mhd problem, Journal of Computational Physics, vol.274, pp.562-591, 2014. ,
On the convergence of a relaxation method with natural constraints on the elliptic operator, USSR Computational Mathematics and Mathematical Physics, vol.6, issue.5, pp.101-135, 1966. ,
Dimensional changes normal to the direction of diffusion, Journal of Applied Physics, vol.23, issue.9, pp.953-956, 1952. ,
Effect of grain boundaries upon pore formation and dimensional changes during diffusion, Acta Metallurgica, vol.3, issue.2, pp.170-177, 1955. ,
Additive intentity. From MathWorld-A Wolfram Web Resource ,
Additive intentity. From MathWorld-A Wolfram Web Resource ,
Preconditioning techniques for large linear systems: A survey, Journal of Computational Physics, vol.182, issue.2, pp.418-477, 2002. ,
, Variational Principles of Continuum Mechanics: II. Applications. Interaction of Mechanics and Mathematics, 2009.
Finite Element Simulation of Heat Transfer, 2010. ,
Thermoelasticity and irreversible thermodynamics, Journal of Applied Physics, vol.27, issue.3, pp.240-253, 1956. ,
URL : https://hal.archives-ouvertes.fr/hal-01368671
A monolithical fluid-structure interaction algorithm applied to the piston problem, Computer Methods in Applied Mechanics and Engineering, vol.167, issue.3, pp.369-391, 1998. ,
Contribution to algorithmic strategies for solving coupled thermo-mechanical problems by an energy-consistent variational approach, 2012. ,
URL : https://hal.archives-ouvertes.fr/tel-00827159
, , pp.107-161
, , 2011.
Convex Optimization. Berichteüber verteilte messysteme. Cambridge University Press, 2004. ,
Multi-level adaptive solutions to boundary-value problems, Mathematics of Computation, vol.31, issue.138, pp.333-333, 1977. ,
Reactive flow in large-deformation electrodes of lithium-ion batteries, International Journal of Applied Mechanics, vol.04, issue.03, p.1250023, 2012. ,
Reactive flow in solids, Journal of the Mechanics and Physics of Solids, vol.61, issue.1, pp.61-77, 2013. ,
, The Mathematical Theory of Finite Element Methods. Texts in Applied Mathematics, 2013.
, A Multigrid Tutorial, Second Edition. Society for Industrial and Applied Mathematics, 2000.
Applied mathematics at the u.s. department of energy: Past, present and a view to the future, 2008. ,
Convergence theory of nonlinear newton-krylov algorithms, SIAM Journal on Optimization, vol.4, issue.2, pp.297-330, 1994. ,
Etude du comportement du Nucleus pulposusà l'aide d'un modèle couplant grandes déformations et diffusion, 2014. ,
Measurement and modeling of the mechanical and electrochemical response of amorphous si thin film electrodes during cyclic lithiation, Journal of the Mechanics and Physics of Solids, vol.62, pp.276-294, 2014. ,
Thermodynamics and an Introduction to Thermostatistics, 1985. ,
Two calculation procedures for steady, three-dimensional flows with recirculation, Proceedings of the Third International Conference on Numerical Methods in Fluid Mechanics, pp.60-68, 1973. ,
Origin of compressive residual stress in polycrystalline thin films, Phys. Rev. Lett, vol.88, p.156103, 2002. ,
, Matrix Preconditioning Techniques and Applications. Cambridge Monographs on Applied and Computational Mathematics, 2005.
Diffusion with a chemical concentration gradient, vol.4, 2005. ,
, Methods of Mathematical Physics, vol.001, 1989.
The Mathematics of Diffusion, 1979. ,
Teko: a block preconditioning capability with concrete example applications in Navier-Stokes and MHD, SIAM J. Sci. Comput, vol.38, issue.5, pp.307-331, 2016. ,
Mathematical modelling of ionic transport in the electrolyte of liion batteries, Electrochimica Acta, vol.53, issue.17, pp.5569-5578, 2008. ,
A monolithic computational approach to thermo-structure interaction, International Journal for Numerical Methods in Engineering, vol.95, issue.13, pp.1053-1078, 2013. ,
A survey of direct methods for sparse linear systems, Acta Numerica, vol.25, pp.383-566, 2016. ,
Non-equilibrium Thermodynamics, 1984. ,
, Computational Methods for Plasticity: Theory and Applications, 2011.
Variational principles are a powerful tool also for formulating field theories, pp.1-15, 2011. ,
Waves and imaging-class notes -18, vol.325, 2015. ,
Inexact newton methods, SIAM Journal on Numerical Analysis, vol.19, issue.2, pp.400-408, 1982. ,
, Newton Methods for Nonlinear Problems: Affine Invariance and Adaptive Algorithms. Springer Series in Computational Mathematics, 2005.
The electroneutrality approximation in electrochemistry, Journal of Solid State Electrochemistry, vol.15, issue.7, pp.1335-1345, 2011. ,
, Finite Element Methods for Flow Problems. Finite Element Methods for Flow Problems, 2003.
Determination of Transport Parameters of Binary Electrolyte Solutions for the Use in Numerical Simulations. Dissertation, 2017. ,
Über die von der molekularkinetischen theorie der wärme geforderte bewegung von in ruhenden flüssigkeiten suspendierten teilchen, Annalen der Physik, vol.322, issue.8, pp.549-560, 1905. ,
Partial Differential Equations. Graduate studies in mathematics, 1998. ,
A monolithic, mortar-based interface coupling and solution scheme for finite element simulations of lithium-ion cells, International Journal for Numerical Methods in Engineering, 2017. ,
The speed of convergence of one iterative process, USSR Computational Mathematics and Mathematical Physics, vol.4, issue.3, pp.227-235, 1964. ,
Partitioned analysis of coupled mechanical systems, S0045782500003911. Advances in Computational Methods for Fluid-Structure Interaction, vol.190, pp.3247-3270, 2001. ,
The Feynman Lectures on Physics, volume I, 1963. ,
V. on liquid diffusion, Philosophical Magazine Series, vol.4, issue.63, pp.30-39 ,
The Method of Weighted Residuals and Variational Principles, Classics in Applied Mathematics. Society for Industrial and Applied Mathematics, 19104. ,
The artificial added mass effect in sequential staggered fluid-structure interaction algorithms, vol.01, 2006. ,
Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows, Computer Methods in Applied Mechanics and Engineering, vol.196, issue.7, pp.1278-1293, 2007. ,
The theory of newton's method, Journal of Computational and Applied Mathematics, vol.124, issue.1, pp.25-44, 2000. ,
A variational derivation of the thermodynamics of a moist atmosphere with rain process and its pseudoincompressible approximation, Geophysical & Astrophysical Fluid Dynamics, vol.01, p.2019 ,
Truly monolithic algebraic multigrid for fluid-structure interaction, International Journal for Numerical Methods in Engineering, vol.85, issue.8, pp.987-1016, 2010. ,
A brief introduction to krylov space methods for solving linear systems, Frontiers of Computational Science, pp.53-62, 2007. ,
On the relation between the principle of maximum dissipation and inelastic evolution given by dissipation potentials, Proc. R. Soc. A, vol.464, pp.117-132, 2008. ,
Sur les matériaux standard généralisés, Journal de Mécanique, vol.14, pp.39-63, 1975. ,
Methods of Conjugate Gradients for Solving Linear Systems, Journal of Research of the National Bureau of Standards, vol.49, issue.6, pp.409-436, 1952. ,
Playa: Highperformance programmable linear algebra, Sci. Program, vol.20, issue.3, pp.257-273, 2012. ,
The idea behind krylov methods, The American Mathematical Monthly, vol.105, issue.10, pp.889-899, 1998. ,
Quasi-newton methods, motivation and theory, SIAM Review, vol.19, issue.1, pp.46-89, 1977. ,
URL : https://hal.archives-ouvertes.fr/hal-01495720
Charge neutrality in electrolytic solutions and the liquid junction potential, The Journal of Physical Chemistry, vol.78, issue.20, pp.2060-2064, 1974. ,
Chemical potential-a quantity in search of recognition, European Journal of Physics, vol.27, issue.2, pp.353-371, 2006. ,
Physical Chemistry from a Different Angle: Introducing Chemical Equilibrium, Kinetics and Electrochemistry by Numerous Experiments, 2015. ,
A theory for stress-driven interfacial damage upon cationic-selective oxidation of alloys, Journal of the Mechanics and Physics of Solids, vol.56, issue.12, pp.3392-3415, 2008. ,
Multiphysics simulations: Challenges and opportunities, International Journal of High Performance Computing Applications, vol.27, pp.4-83, 2013. ,
High capacity, power density and cycling stability of silicon li-ion battery anodes with a few layer black phosphorus additive, Sustainable Energy & Fuels, vol.3, issue.1, pp.245-250, 2019. ,
Rates of Diffusion of Copper and Zinc in Alpha Brass, 1938. ,
, Ionic Transport Processes: in Electrochemistry and Membrane Science, 2008.
The Variational Principles of Mechanics, vol.4, 1949. ,
A linear theory of thermochemical equilibrium of solids under stress, Acta Metall, vol.21, issue.8, pp.1051-1063, 1973. ,
Thermodynamic consistent transport theory of li-ion batteries, Journal of Power Sources, vol.196, issue.6, pp.3296-3302, 2011. ,
The theory of everything, Proceedings of the National Academy of Sciences, vol.97, pp.28-31, 2000. ,
Introduction to Nanoscience, 2009. ,
Quasi-newton preconditioners for the inexact newton method. ETNA. Electronic Transactions on Numerical Analysis, vol.23, pp.76-87, 2006. ,
AztecOO User Guide. United States. Department of Energy, 2004. ,
A new staggered algorithm for thermomechanical coupled problems, International Journal of Solids and Structures, pp.42-58, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01697274
A temporal consistent monolithic approach to fluid-structure interaction enabling single field predictors, SIAM Journal on Scientific Computing, vol.37, issue.1, p.2015 ,
Entropic thermoelasticity at finite strains. aspects of the formulation and numerical implementation, Computer Methods in Applied Mechanics and Engineering, vol.120, issue.3, pp.243-269, 1995. ,
Formulation and numerical exploitation of mixed variational principles for coupled problems of cahn-hilliard-type and standard diffusion in elastic solids, International Journal for Numerical Methods in Engineering, vol.99, issue.10, pp.737-762, 2014. ,
A multi-field incremental variational framework for gradient-extended standard dissipative solids, Journal of the Mechanics and Physics of Solids, vol.59, issue.4, pp.898-923, 2011. ,
Plastic creep flow effects in the diffusive cavitation of grain boundaries, Acta Metall, vol.28, issue.10, pp.1315-1332, 1980. ,
Die elektromotorische wirksamkeit der jonen, Zeitschrift für physikalische Chemie, vol.4, pp.129-181, 1889. ,
Electrochemical Systems, 2004. ,
The role of electric field in pore formation during aluminum anodization, Electrochimica Acta, vol.56, issue.11, pp.4044-4051, 2011. ,
Reciprocal relations in irreversible processes. i, Phys. Rev, vol.37, pp.405-426, 1931. ,
Theories and problems of liquid diffusion, Annals of the New York Academy of Sciences, vol.46, pp.241-265, 1945. ,
The variational formulation of viscoplastic constitutive updates, Computer Methods in Applied Mechanics and Engineering, vol.171, issue.3, pp.419-444, 1999. ,
URL : https://hal.archives-ouvertes.fr/hal-01007379
Solution of sparse indefinite systems of linear equations, SIAM Journal on Numerical Analysis, vol.12, issue.4, pp.617-629, 1975. ,
Time-discretized variational formulation of non-smooth frictional contact, 2001. ,
A model for the sintering and coarsening of rows of spherical particles, Mechanics of Materials, vol.31, pp.43-61, 1999. ,
Concurrent electromigration and creep in lead-free solder, Journal of Applied Physics, vol.110, issue.8, p.83716, 2011. ,
Ueber die potentialdifferenz zwischen zwei verdünnten lösungen binärer electrolyte, Annalen der Physik, vol.276, issue.8, pp.561-576, 1890. ,
Modeling and simulation of lithium-ion batteries from a systems engineering perspective, Journal of the Electrochemical Society, vol.159, issue.3, pp.31-45, 2012. ,
The deborah number, Physics Today, vol.17, issue.1, pp.62-62, 1964. ,
The approximate arithmetical solution by finite differences of physical problems involving differential equations, with an application to the stresses in a masonry dam, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.210, pp.307-357, 1911. ,
GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM Journal on Scientific and Statistical Computing, vol.7, issue.3, pp.856-869, 1986. ,
Iterative Methods for Sparse Linear Systems, Society for Industrial and Applied Mathematics, 2003. ,
Robust algebraic preconditioners with IFPACK 3.0, 2005. ,
On the design of interfaces to sparse direct solvers. submitted, 2006. ,
Amesos: A set of general interfaces to sparse direct solver libraries, Proceedings of PARA'06 Conference, 2006. ,
Governing equations for a two-scale analysis of li-ion battery cells, International Journal of Solids and Structures, vol.59, pp.90-109, 2015. ,
Lithium batteries: Status, prospects and future, Journal of Power Sources, vol.195, issue.9, pp.2419-2430, 2010. ,
Addison-Wesley principles of physics series, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics, 1975. ,
An introduction to the conjugate gradient method without the agonizing pain, 1994. ,
, Computational Inelasticity. Interdisciplinary Applied Mathematics, 2000.
Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation, Computer Methods in Applied Mechanics and Engineering, vol.98, issue.1, pp.41-104, 1992. ,
Monolithic discretization of linear thermoelasticity problems via adaptive multimesh hp-fem, Fourth International Conference on Advanced COmputational Methods in Engineering, vol.234, pp.2350-2357, 2008. ,
Consistent incremental approximation of dissipation pseudo-potentials in the variational formulation of thermo-mechanical constitutive updates, Mechanics Research Communications, vol.38, issue.4, pp.315-319, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00768511
Study and validation of a variational theory of thermo-mechanical coupling in finite visco-plasticity, International Journal of Solids and Structures, vol.47, issue.5, pp.705-715, 2010. ,
Calculus. Cengage Learning, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-00554549
Computational Science and Engineering, 2007. ,
An Analysis of the Finite Element Method, 2008. ,
A continuum theory that couples creep and self-diffusion, J. Appl. Mech, pp.646-651, 2004. ,
Stresses induced in alloys by selective oxidation, Acta Materialia, vol.51, issue.4, pp.959-974, 2003. ,
Vacancy-driven stress relaxation in layers, Acta Materialia, vol.57, issue.16, pp.4649-4657, 2009. ,
On diffusion-controlled evolution of closed solid-state thermodynamic systems at constant temperature and pressure, Phil. Mag. B, vol.64, issue.6, pp.749-759, 1991. ,
Modelling of fluid-structure interactions with the space-time finite elements: Solution techniques, International Journal for Numerical Methods in Fluids, vol.54, issue.6-8, pp.855-900, 2007. ,
On the rumpling mechanism in nickel-aluminide coatings: Part ii: characterization of surface undulations and bond coat swelling, Acta Materialia, vol.52, issue.17, pp.5129-5141, 2004. ,
, , pp.0-1, 2000.
Thermo-chemo-mechanics of ASR expansion in concrete structures, Journal of Engineering Mechanics, vol.126, issue.3, pp.233-242, 2000. ,
URL : https://hal.archives-ouvertes.fr/hal-00586622
Iterative methods for concave programming, Studies in Linear and Non-linear Programming, Stanford mathematical studies in the social sciences, 1958. ,
Iterative Krylov Methods for Large Linear Systems, Cambridge Monographs on Applied and Computational Mathematics, 2003. ,
Thermo-mechanical coupling strategies in elastic-plastic problems, Continuum Mechanics and Thermodynamics, vol.29, issue.2, pp.373-383, 2017. ,
Unified computational framework for the efficient solution of n-field coupled problems with monolithic schemes, Computer Methods in Applied Mechanics and Engineering, vol.310, pp.335-366, 2016. ,
, Matrix preconditioning techniques and applications. by k. chen, vol.550, pp.442-443, 2005.
, Preconditioning. Acta Numerica, vol.24, pp.329-376, 2015.
Geometric multigrid with applications to computational fluid dynamics, VII: Partial Differential Equations, vol.128, pp.311-334, 2000. ,
An Introduction to Aqueous Electrolyte Solutions, 2007. ,
Nonaqueous liquid electrolytes for lithium-based rechargeable batteries, Chemical Reviews, vol.104, issue.10, pp.4303-4418, 2004. ,
A variational formulation of the coupled thermo-mechanical boundaryvalue problem for general dissipative solids, Journal of the Mechanics and Physics of Solids, vol.54, issue.2, pp.401-424, 2006. ,
URL : https://hal.archives-ouvertes.fr/hal-01004967
The newton and halley methods for complex roots, The American Mathematical Monthly, vol.105, issue.9, pp.806-818, 1998. ,
Lithium salts for advanced lithium batteries: Li-metal, li-o2, and li-s, Energy Environ. Sci, vol.8, 1905. ,
Preconditioned krylov subspace methods for solving nonsymmetric matrices from cfd applications, Computer Methods in Applied Mechanics and Engineering, vol.189, issue.3, pp.825-840, 2000. ,
Some extremum principles in irreversible thermodynamics with applications to continuum mechanics, Progress in Solid Mechanics, vol.4, p.127, 1963. ,
, AMG algebraic multigrid strategy, vol.24, p.149
, BC boundary conditions, vol.36, p.37
, BGS block Gauss-Seidel, vol.24, p.25
, CoV Calculus of Variations, vol.12, p.15
, ENC ElectroNeutrality condition, vol.83, p.99
, FEM Finite Element Method, vol.113, p.148
, FSI Fluid Structure Interaction, vol.25, p.149
, GMG geometric multigrid strategy, vol.27, p.31
, GMRES General Minimum Residual, vol.26
, IC initial conditions, pp.36-38
, , vol.23, p.30
, IVD intervertebral disc, vol.5, p.6
, , p.28
, MG multigrid strategy, vol.27, p.32
, MINRES Minimum Residual, vol.26
, PDE Partial Differential Equation, vol.8, pp.54-57
, RHS right hand side, vol.37, p.127