Presentation of the Workshop
In applications involving complex physics such as plasmas and nanotechnologies, the numerical simulation is a prediction tool used by every engineer or researcher, which supplements real experiments. The performance of a simulation relies not only on computational power, but also on the efficiency of the numerical method that has been implemented, which is itself strongly linked to the complexity of the underlying models.
The design of numerical schemes is also deeply dependent on the identification of the different scales present in the problem.
In many applications, several small and large scales are present. Many often, small scales have a strong impact on the cost of numerical simulations since, without using specific schemes, the meshes must resolve the smaller scale. Then building efficient numerical methods for the resolution of such multiscale problems is a challenging problem

This workshop is funded by the ANR project Moonrise, the Inria ANTIpODE team and the ENS-Rennes MUNIQ project, all essentially dealing with numerical methods for multi-scale PDES.
This meeting is organized by the Universities of Rennes and Toulouse and its aim is to bring together international experts and young researchers working on numerical methods for the resolution of multi-scale evolution problems involving stiff dissipations (phase transitions) or high oscillations. The target equations cover a broad spectrum: Schrödinger equations, kinetic equations with or without collisions (Boltzmann, Vlasov-Poisson or Vlasov-Maxwell type), but all including several small and large scales.
Recently, new numerical methods have been developed to bypass the difficulties induced by the presence of several scales. In particular, they avoid the huge computational cost of the standard methods in the stiff regime, while providing a consistent approximation of the limit problems.

However, some open problems still remain when dealing with complex and realistic models. The aim of this workshop is therefore to present emerging  techniques.

Confirmed Lecturers
1     - Assyr Abdulle, ANMC, EPFL Ecole Polytechnique Fédérale de Lausanne, Switzerland.
                   Title: "Bayesian numerical homogenization methods for multiscale inverse problems"
       - Mihai Bostan, Institut de Mathématiques de Marseille, Université Aix-Marseille, France.
       - Martin Campos-Pinto, Jacques-Louis Lions Laboratory, University Paris 6, UPMC, France.
       - Fernando Casas, Institut Universitari de Matemàtiques i Aplicacions de Castelló,Universitat Jaume I, Castellón, Spain.
                   Title: ”Splitting and composition methods with embedded error estimators”
5     - Anaïs Crestetto, Laboratoire de Mathématiques Jean Leray, Université de Nantes, France.
                   Title: "Particle Micro-Macro schemes for collisional kinetic equations in the diffusive scaling"
       - Bruno Despres, Jacques-Louis Lions Laboratory, University Paris 6, UPMC, France.
                   Title: "Trefftz methods for transport equations with boundary layers (with C. Buet and G. Morel)"
       - Giacomo Dimarco, Department of Mathematics and Computer Science, University of Ferrara, Italy.
       - Francis Filbet, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse, France.
       - Shi Jin, Department of Mathematics, University of Wisconsin, Madison, USA.
10   - Frédéric Lagoutière, Institut Camille Jordan, Université Claude Bernard Lyon 1, France
       - Qin Li, Department of Mathematics, University of Wisconsin, Madison, USA.
       - Christian Lubich, Mathematisches Institut, Universität Tübingen, Germany.
                  Title: "A low-rank projector-splitting integrator for the Vlasov-Poisson equation"
       - Maurizio Ottaviani, IRFM, Institut de Recherche sur la Fusion par confinement Magnétique, CEA Cadarache, France.
       - Lorenzo Pareschi, Department of Mathematics and Computer Science, University of Ferrara, Italy.
 15  - Katharina Schratz, Department of Mathematics, Karlsruhe Institute of Technology, Karlsruhe, Germany.
                   Title: "Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes''​
       - Nicolas Seguin, IRMAR (Institut de Recherche Mathématique de Rennes), University of Rennes 1, France.
       - Xiaofei Zhao, IRMAR (Institut de Recherche Mathématique de Rennes), University of Rennes 1, France.
  18 - Gerhard Wanner, former professor at the University of Geneva, Switzerland.


Organizing Comitee
Christophe Besse, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse 3, christophe.besse@math.univ-toulouse.fr
Philippe Chartier, INRIA Rennes Bretagne Atlantique, IRMAR (Institut de Recherche Mathématique de Rennes), University of Rennes 1, France,
                            philippe.chartier@inria.fr
Mohammed Lemou, CNRS, IRMAR (Institut de Recherche Mathématique de Rennes), University of Rennes 1, France,
                            mohammed.lemou@univ-rennes1.fr
Florian Méhats, IRMAR (Institut de Recherche Mathématique de Rennes), University of Rennes 1, France, florian.mehats@univ-rennes1.fr
Marie-Hélène Vignal, Institut de Mathématiques de Toulouse, Université Paul Sabatier, Toulouse 3, mhvignal@math.univ-toulouse.fr

Financial supports

    ANR project Moonrise, MOdels, Oscillations and NumeRIcal SchEmes, web site.

    Project MUNIQ, web site.                           Inria ANTIpODE team, web site.

web site.                                          web site.