Master 2: Analysis, modelling and simulation


Overview


Partial differential equations and analysis in general have undergone spectacular progress over the past few decades. At the same time, progress in numerical methods and improved computer performance have made numerical simulation an essential tool for industry and research. The aeronautical, space, automobile, nuclear power, electricity generation, and material synthesis industries use it extensively. Big research bodies also use numerical simulation to predict the behavior of complex systems.

Language of instruction: French
ECTS: 60
Oriented: Industry and research
Duration: 1 year
Courses Location: Ensta Paris and Université Paris Sud


Educational objectives


The AMS degree program aims to provide comprehensive training in mathematical and numerical analysis and simulation, combining more theoretical approaches with concrete developments (modeling and numerical simulation). Sound knowledge of mathematical equations (differential equations, partial differential equations) is required to use and develop numerical approximation methods. Knowledge of the phenomena for which these equations account is also required. Effective implementation of associated approximation algorithms is unimaginable without solid IT knowledge.


Program structure


• Calcul scientifique parallèle (SC), Ensta Paris, 7 ECTS, 60 h, Erell Jamelot, Axel Modave; Edouard Audit, Nicolas Kielbasiewicz
• Modélisation et simulation du transport de particules neutres (SC), Ensta Paris, 4 ECTS, 30 h, François Févotte, Gérald Samba
• Propagation des ondes dans les milieux périodiques (AEDP,SC), Ensta Paris, 4 ECTS, 30h, Sonia Fliss, Patrick Joly
• Résolution des problèmes de diffraction par équations intégrales (SC), Ensta Paris, 4 ECTS, 30h, Eliane Bécache, Stéphanie Chaillat-Loseille
• Complétion de données et identification dans les problèmes gouvernés par des EDPs (SC), Ensta Paris, 4 ECTS, 30h, Laurent Bourgeois, Philippe Moireau
• Hautes fréquences et fronts d’ondes (SC), Ensta Paris, 4 ECTS, 30h, Daniel Bouche, Hasnaa Zidani
• Propagation et diffraction dans les guides d’ondes (AEDP), Ensta Paris, 4 ECTS, 30h, Anne-Sophie Bonnet-Ben Dhia, Eric Lunéville
• Modèles mathématiques et leur discrétisation en électromagnétisme (AEDP,SC), Ensta Paris, 4 ECTS, 30h, Patrick Ciarlet, Maryna Kachanovska
• Modélisation des plasmas et des systèmes astrophysiques (SC), Ensta Paris, 4 ECTS, 30h, Guy Bonnaud, Stéphane Mathis, Jérôme Perez
• Outils mathématiques pour l’analyse des EDP (SC), UVSQ, 4 ECTS, 24h, Tahar Boulmezaoud
• Analyse théorique et numérique des systèmes hyperboliques 1 (AEDP, SC), UVSQ, 4 ECTS, 24h, Benjamin Graille
• Analyse théorique et numérique des systèmes hyperboliques 2 (AEDP, SC), UVSQ, 4 ECTS, 24h, Christophe Chalons
• Optimisation sans gradient (SC), UVSQ, 4 ECTS, 24h, Anne Auger, Laurent Dumas
• Introduction à la quantification d’incertitude (SC), UVSQ, 4 ECTS, 24h, Didier Lucor
• Volumes finis (SC), ENS Paris Saclay, 4 ECTS, 27h, Hafid Fikri
• Réduction de modèles et méthodes d’ordre élevé (SC), ENS Paris Saclay, 4 ECTS, 30h, Daniel Bouche, David Néron, Hasna Zidani
• Introduction à la théorie spectrale (AEDP), Univ. Paris Sud, 4 ECTS, 30h, Christian Gérard
• Analyse microlocale (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Stéphane Nonnenmacher
• Equations elliptiques linéaires et non linéaires (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Jean-François Babadjian
• Equations dispersives (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Frédéric Rousset
• Analyse des fluides parfaits incompressibles (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Daniel Han-Kwan
• Calcul des variations (AEDP), Univ. Paris Sud, 5 ECTS, 30h,Jean-François Babadjian
• Contrôle des EDO (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Frédéric Bonnans, Hasnaa Zidani
• Equations de Navier Stokes (AEDP), Univ. Paris Sud, 5 ECTS, 30h, Pierre-Gilles Lemarié, Stéphane Menozzi
• Homogénéisation (SC), X, 4 ECTS, 30h, François Alouges, Sonia Fliss
• Méthodes numériques avancées et calcul haute performance pour la simulation de phénomènes complexes (SC), X, 4 ECTS, 30h, Marc Massot
• Modélisation et simulation des écoulements de fluides dans la géosphère (SC), INSTN, 4 ECTS, 30h, Michel Kern, Emannuel Mouche
• Programmation hybride et multi-cœurs (SC), INSTN, 4 ECTS, 30h, Marc Tajchman
• Informatique scientifique approfondie (SC), INSTN, 4 ECTS, 30h, Christophe Labourdette
• Simulation numérique en physique des plasmas et en astrophysique (SC), INSTN, 4 ECTS, 30h, Jean Clerouin, Yves Pleysson, Stéphane Mathis
• Visualisation scientifique (SC), INSTN, 3 ECTS, 21h, Charles Gueunet, Tobias Isenberg, Julien Tierny


Laboratories involved



Career prospects


Anticipated openings are in industry and with research bodies requiring top-level scientists, engineers, and researchers able to develop mathematical theories, run physical phenomena modeling projects, master mathematical aspects of models, and solve problems in an industrial or research context. Partnerships with big research bodies such as CEA, IFPEN, ONERA and INRIA, as well as the world of industry, enable students to find a job that matches their training and enjoy the diversity of applied fields.


Institutional partners


UVSQ, Université Paris Sud
Université d’Evry,
Ecole Centrale Supelec,
INSTN,
ENS Paris Saclay (université Paris-Saclay)


Industrial partners


CEA
EDF
ONERA


Admissions


Application guidelines for a master’s program at IP Paris

Academic prerequisites

  • Completion of the 1st year of a master program (Master 1) in applied mathematics or mathematics, second year in engineering school with M1 level.

Language prerequisites

  • French

Application timeline

Deadlines for the Master application sessions are as follows:
– First session: February 28, 2020
– Second session: April 30, 2020
– Third Session (optional): June 30, 2020 (only if there are availabilities remaining after the 2 first sessions)
Applications not finalized for a session will automatically be carried over to the next session.

You shall receive an answer 2 months after the application deadline of the session.
You can check your application status by logging in your candidate space.


Tuition fees


National Master: Official tuition fees of the Ministry of Higher Education, Research and innovation (2019-2020, EU students: 243 euros / Non-EU students: 3770 euros)


Contact


Fliss Sonia, Mathématiques appliquées
Email
Profile
Université Paris Saclay : Laurent Dumas (AVSQ) and Frédéric Rousset (Universtité Paris Sud)