m
• E

F Nous contacter

0

# Documents  65M06 | enregistrements trouvés : 42

O

P Q

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Numerical methods for mean field games - Lecture 2: Monotone finite difference schemes Achdou, Yves | CIRM H

Post-edited

Research School;Computer Science;Control Theory and Optimization;Partial Differential Equations;Numerical Analysis and Scientific Computing

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Inhomogeneities and temperature effects in Bose-Einstein condensates de Bouard, Anne | CIRM H

Post-edited

Research talks;Partial Differential Equations;Probability and Statistics;Numerical Analysis and Scientific Computing

We will review in this talk some mathematical results concerning stochastic models used by physicist to describe BEC in the presence of fluctuations (that may arise from inhomogeneities in the confinement parameters), or BEC at finite temperature. The results describe the effect of those fluctuations on the structures - e.g. vortices - which are present in the deterministic model, or the convergence to equilibrium in the models at finite temperature. We will also describe the numerical methods which have been developed for those models in the framework of the ANR project Becasim. These are joint works with Reika Fukuizumi, Arnaud Debussche, and Romain Poncet. We will review in this talk some mathematical results concerning stochastic models used by physicist to describe BEC in the presence of fluctuations (that may arise from inhomogeneities in the confinement parameters), or BEC at finite temperature. The results describe the effect of those fluctuations on the structures - e.g. vortices - which are present in the deterministic model, or the convergence to equilibrium in the models at finite ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Hyperbolic systems of balance laws :lectures given at the C.I.M.E. summer school held in Cetraro#July 14-21 Bressan, Alberto ; Serre, Denis ; Williams, Mark ; Zumbrun, Kevin ; Marcati, Pierangelo | Springer 2007

Congrès

- 346 p.
ISBN 978-3-540-72186-4

Lecture notes in mathematics , 1911

Localisation : Collection 1er étage

EDP # lois de conservation hyperboliques # viscosité de disparition # onde # profils discrets de choc # choc visqueux # linéarisation # fonction de Evans # déterminants de Lopatinski

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Hyperbolic problems :theory, numerics, applicationsproceedings of the XIth international conference on...#July, 17-21 Benzoni-Gavage, Sylvie ; Serre, Denis | Springer-Verlag 2008

Congrès

- 1123 p.
ISBN 978-3-540-75711-5

Localisation : Colloque 1er étage (LYON)

EDP # mécanique des fluides # équations hyperboliques # lois de conservation # singularités # EDP pour la relativité # généralisation de maillage # méthode numérique

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Finite-difference methods theory and applications cfdm98. vol. 3Proceedings of the 2nd international conference on ... | National Academy of Sciences of Belarus 1998

Congrès

ISBN 978-985-6499-06-0

Localisation : Colloque 1er étage (BELA)

EDP # analyse numérique # modèle mathématique # méthode de différence finie # physique mathématique # problème aux limites de type multi-dimensionnel # problème de stabilité des méthodes numériques # problème à la frontière

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Finite-difference methods theory and applications cfdm98. vol. 2Proceedings of the 2nd international conference on ... | National Academy of Sciences of Belarus 1998

Congrès

ISBN 978-985-6499-05-3

Localisation : Colloque 1er étage (BELA)

EDP # analyse numérique # modèle mathématique # méthode de différence finie # physique mathématique # problème aux limites de type multi-dimensionnel # problème de stabilité des méthodes numériques # problème à la frontière

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Finite-difference methods theory and applications CFDM98. Vol. 1proceedings of the 2nd international conference on ... | National Academy of Sciences of Belarus 1998

Congrès

ISBN 978-985-6499-04-6

Localisation : Colloque 1er étage (BELA)

EDP # analyse numérique # modèle mathématique # méthode de différence finie # physique mathématique # problème aux limites de type multi-dimensionnel # problème de stabilité des méthodes numériques # problème à la frontière

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Computer algebra in scientific computing casc'99Proceedings of the second workshop on computer algebra in scientific computing, munich, may 31-june 4, 1999 Ganzha Victor G. ; Mayr, Ernst W. ; Vorozhtsov Evgenii V. | Springer-Verlag 1999

Congrès

ISBN 978-3-540-66047-7

Localisation : Disparu

algèbre commutatif # algèbre de calcul # analyse numérique # calcul symbolique # corps # informatique théorique # intelligence artificielle # méthode de différence finie # polynomes # représentation de groupes # stabilité de Lyaponov # système expert # théorie de stabilité # équations différentielles avancées

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Numerical methods for mean field games - Lecture 3: Variational MFG and related algorithms for solving the discrete system of nonlinear equations Achdou, Yves | CIRM H

Multi angle

Research School;Computer Science;Control Theory and Optimization;Partial Differential Equations;Numerical Analysis and Scientific Computing

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Numerical methods for mean field games - Lecture 1: Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions Achdou, Yves | CIRM H

Multi angle

Research School;Computer Science;Control Theory and Optimization;Partial Differential Equations;Numerical Analysis and Scientific Computing

Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and computing, and the potential applications to economics and social sciences are numerous.
In the limit when $n \to +\infty$, a given agent feels the presence of the others through the statistical distribution of the states. Assuming that the perturbations of a single agent's strategy does not influence the statistical states distribution, the latter acts as a parameter in the control problem to be solved by each agent. When the dynamics of the agents are independent stochastic processes, MFGs naturally lead to a coupled system of two partial differential equations (PDEs for short), a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation.
The latter system of PDEs has closed form solutions in very few cases only. Therefore, numerical simulation are crucial in order to address applications. The present mini-course will be devoted to numerical methods that can be used to approximate the systems of PDEs.
The numerical schemes that will be presented rely basically on monotone approximations of the Hamiltonian and on a suitable weak formulation of the Fokker-Planck equation.
These schemes have several important features:

- The discrete problem has the same structure as the continous one, so existence, energy estimates, and possibly uniqueness can be obtained with the same kind of arguments

- Monotonicity guarantees the stability of the scheme: it is robust in the deterministic limit

- convergence to classical or weak solutions can be proved

Finally, there are particular cases named variational MFGS in which the system of PDEs can be seen as the optimality conditions of some optimal control problem driven by a PDE. In such cases, augmented Lagrangian methods can be used for solving the discrete nonlinear system. The mini-course will be orgamized as follows

1. Introduction to the system of PDEs and its interpretation. Uniqueness of classical solutions.

2. Monotone finite difference schemes

3. Examples of applications

4. Variational MFG and related algorithms for solving the discrete system of nonlinear equations
Recently, an important research activity on mean field games (MFGs for short) has been initiated by the pioneering works of Lasry and Lions: it aims at studying the asymptotic behavior of stochastic differential games (Nash equilibria) as the number $n$ of agents tends to infinity. The field is now rapidly growing in several directions, including stochastic optimal control, analysis of PDEs, calculus of variations, numerical analysis and ...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Mean field type control with congestion Laurière, Mathieu | CIRM H

Multi angle

Research talks;Control Theory and Optimization;Partial Differential Equations;Numerical Analysis and Scientific Computing

The theory of mean field type control (or control of MacKean-Vlasov) aims at describing the behaviour of a large number of agents using a common feedback control and interacting through some mean field term. The solution to this type of control problem can be seen as a collaborative optimum. We will present the system of partial differential equations (PDE) arising in this setting: a forward Fokker-Planck equation and a backward Hamilton-Jacobi-Bellman equation. They describe respectively the evolution of the distribution of the agents' states and the evolution of the value function. Since it comes from a control problem, this PDE system differs in general from the one arising in mean field games.
Recently, this kind of model has been applied to crowd dynamics. More precisely, in this talk we will be interested in modeling congestion effects: the agents move but try to avoid very crowded regions. One way to take into account such effects is to let the cost of displacement increase in the regions where the density of agents is large. The cost may depend on the density in a non-local or in a local way. We will present one class of models for each case and study the associated PDE systems. The first one has classical solutions whereas the second one has weak solutions. Numerical results based on the Newton algorithm and the Augmented Lagrangian method will be presented.
This is joint work with Yves Achdou.
The theory of mean field type control (or control of MacKean-Vlasov) aims at describing the behaviour of a large number of agents using a common feedback control and interacting through some mean field term. The solution to this type of control problem can be seen as a collaborative optimum. We will present the system of partial differential equations (PDE) arising in this setting: a forward Fokker-Planck equation and a backward Hamilto...

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Discontinuous Galerkin solver design on hybrid computers Helluy, Philippe | CIRM H

Multi angle

Research talks;Mathematical Physics;Numerical Analysis and Scientific Computing

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Diffusion redistanciation schemes, Willmore problem and red blood cells Maitre, Emmanuel | CIRM H

Multi angle

Research talks;Numerical Analysis and Scientific Computing;Partial Differential Equations;Mathematical Physics

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Viskositätsapproximationen und schwache lösungen für das system der eindimensionalen nichtlinearen elastizitätsgleichungen Göbel, Dieter | Rheinischen Friedrich-Wilhelms-Universität 1993

Ouvrage

- 89 p.

Bonner mathematische schriften , 0252

Localisation : Publication 1er étage

viscosité # exsitance de solutions # loi de conservation # équation de la mécanique # méthode des différences finies

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The gradient discretisation method Droniou, Jérôme ; Eymard, Robert ; Gallouët, Thierry ; Guichard, Cindy ; Herbin, Raphaèle | Springer;Société de Mathématiques Appliquées et Industrielles 2018

Ouvrage

- xxiv; 497 p.
ISBN 978-3-319-79041-1

Mathématiques & applications , 0082

Localisation : Collection 1er étage

méthode de discrétisation du gradient # schéma de gradients # équation aux dérivées partielles elliptiques # équation aux dérivées partielles paraboliques # analyse de convergence uniforme # théorème d'Aubin-Simon discret # convergence par compacité # estimation des erreurs

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## The finite element method in heat transfer analysis Lewis, R. W. ; Morgan, K. ; Hughes, Thomas J. R. ; Seetharamu, K. N. | John Wiley And Sons 1996

Ouvrage

- 278 p.
ISBN 978-0-471-93424-0

Localisation : Ouvrage RdC (Finite)

méthode des éléments finis # équation parabolique non-linéaire # équation de la chaleur # transfert de chaleur # méthode de Galerkin # problème de changement de phase # approximation

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Plasticity:mathematical theory and numerical analysis Han, Weimin ; Reddy, B. Daya | Springer 2013

Ouvrage

- xv; 421 p.
ISBN 978-1-4614-5939-2

Interdisciplinary applied mathematics , 0009

Localisation : Ouvrage RdC (HAN)

plasticité # analyse numérique # élastoplasticité # principe variationnel # petite déformation

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Plasma physics via computer simulation Birdsall, C. K. ; Langdon, A. B. | Institute of Physics Publishing 2002

Ouvrage

- 479 p.
ISBN 978-0-7503-0117-6

Plasma physics series

Localisation : ouvrage RdC (BIRD)

physique des plasmas # simulation informatique # plasma # analyse numérique # particule chargée # électromagnétisme # méthode PIC #

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Partial differential equations: modeling, analysis and numerical approximation Le Dret, Hervé ; Lucquin, Brigitte | Birkhäuser 2016

Ouvrage

- xi; 395 p.
ISBN 978-3-319-27065-4

International series of numerical mathematics , 0168

Localisation : Ouvrage RdC (LEDR)

équation différentielle partielle # équation différentielle elliptique # équation différentielle parabolique # équation différentielle hyperbolique # différence finie # méthode des volumes finis

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

## Parabolic quasilinear equations minimizing linear growth functionals Andreu-Vaillo, Fuensanta ; Caselles, Vicent ; Mazon, José M. | Birkhäuser 2004

Ouvrage

- 340 p.
ISBN 978-3-7643-6619-3

Progress in mathematics , 0223

Localisation : Collection 1er étage

équation non linéaire parabolique # EDP # semi-groupe d'opérateur non linéaire # méthode des différences finies # traitement d'image # minimisation de la variation totale # model mathématique

#### Filtrer

##### Codes MSC

Titres de périodiques et e-books électroniques (Depuis le CIRM)

Ressources Electroniques

Books & Print journals

Recherche avancée

0
Z