TONUS started in January 2014. It is a team of the Inria Nancy-Grand Est center. It is located in the mathematics institute (IRMA) of the university of Strasbourg.

The International Thermonuclear Experimental Reactor (ITER) is a large-scale scientific experiment that aims to demonstrate that it is possible to produce energy from fusion, by confining a very hot hydrogen plasma inside a toroidal chamber, called tokamak. In addition to physics and technology research, tokamak design also requires mathematical modeling and numerical simulations on supercomputers.

The objective of the TONUS project is to deal with such mathematical and computing
issues. We are mainly interested in kinetic and gyrokinetic simulations of
collisionless plasmas. In the TONUS project-team we are working on the development of new
numerical methods devoted to such simulations. We investigate several
classical plasma models, study new reduced models and new numerical
schemes adapted to these models.
We implement our methods in two software projects: Selalib

We have strong relations with the CEA-IRFM team and participate to the development of their gyrokinetic simulation software GYSELA. We are involved into two Inria Project Labs, respectively devoted to tokamak mathematical modeling and high performance computing on future exascale super-computers. We also collaborate with a small company in Strasbourg specialized in numerical software for applied electromagnetics.

Finally, our subjects of interest are at the interaction between mathematics, computer science, High Performance Computing, physics and practical applications.

The fundamental model for plasma physics is the coupled Vlasov-Maxwell kinetic model: the Vlasov equation describes the distribution function of particles (ions and electrons), while the Maxwell equations describe the electromagnetic field. In some applications, it may be necessary to take into account relativistic particles, which lead to consider the relativistic Vlasov equation, but generally, tokamak plasmas are supposed to be non relativistic. The particles distribution function depends on seven variables (three for space, three for velocity and one for time), which yields a huge amount of computations.

To these equations we must add several types of source terms and boundary conditions for representing the walls of the tokamak, the applied electromagnetic field that confines the plasma, fuel injection, collision effects, etc.

Tokamak plasmas possess particular features, which require developing specialized theoretical and numerical tools.

Because the magnetic field is strong, the particle trajectories have a very fast rotation around the magnetic field lines. A full resolution would require prohibitive amount of calculations. It is then necessary to develop models where the cyclotron frequency tends to infinity in order to obtain tractable calculations. The resulting model is called a gyrokinetic model. It allows us to reduce the dimensionality of the problem. Such models are implemented in GYSELA and Selalib. Those models require averaging of the acting fields during a rotation period along the trajectories of the particles. This averaging is called the gyroaverage and requires specific discretizations.

The tokamak and its magnetics fields present a very particular geometry. Some authors have proposed to return to the intrinsic geometrical versions of the Vlasov-Maxwell system in order to build better gyrokinetic models and adapted numerical schemes. This implies the use of sophisticated tools of differential geometry: differential forms, symplectic manifolds, and hamiltonian geometry.

In addition to theoretical modeling tools, it is necessary to develop numerical schemes adapted to kinetic and gyrokinetic models. Three kinds of methods are studied in TONUS: Particle-In-Cell (PIC) methods, semi-Lagrangian and fully Eulerian approaches.

In most phenomena where oscillations are present, we can establish a
three-model hierarchy:

The Strasbourg team has a long and recognized experience in numerical methods of Vlasov-type equations. We are specialized in both particle and phase space solvers for the Vlasov equation: Particle-in-Cell (PIC) methods and semi-Lagrangian methods. We also have a longstanding collaboration with the CEA of Cadarache for the development of the GYSELA software for gyrokinetic tokamak plasmas.

The Vlasov and the gyrokinetic models are partial differential equations that express the transport of the distribution function in the phase space. In the original Vlasov case, the phase space is the six-dimension position-velocity space. For the gyrokinetic model, the phase space is five-dimensional because we consider only the parallel velocity in the direction of the magnetic field and the gyrokinetic angular velocity instead of three velocity components.

A few years ago, Eric Sonnendrücker and his collaborators introduce a new family of methods for solving transport equations in the phase space. This family of methods are the semi-Lagrangian methods. The principle of these methods is to solve the equation on a grid of the phase space. The grid points are transported with the flow of the transport equation for a time step and interpolated back periodically onto the initial grid. The method is then a mix of particle Lagrangian methods and eulerian methods. The characteristics can be solved forward or backward in time leading to the Forward Semi-Lagrangian (FSL) or Backward Semi-Lagrangian (BSL) schemes. Conservative schemes based on this idea can be developed and are called Conservative Semi-Lagrangian (CSL).

GYSELA is a 5D full gyrokinetic code based on a classical backward semi-Lagrangian scheme (BSL) for the simulation of core turbulence that has been developed at CEA Cadarache in collaboration with our team . Although GYSELA was carefully developed to be conservative at lowest order, it is not exactly conservative, which might be an issue when the simulation is under-resolved, which always happens in turbulence simulations due to the formation of vortices which roll up.

Historically PIC methods have been very popular for solving the Vlasov equations. They allow solving the equations in the phase space at a relatively low cost. The main disadvantage of the method is that, due to its random aspect, it produces an important numerical noise that has to be controlled in some way, for instance by regularizations of the particles, or by divergence correction techniques in the Maxwell solver. We have a longstanding experience in PIC methods and we started implement them in Selalib. An important aspect is to adapt the method to new multicore computers. See the work by Crestetto and Helluy .

As already said, kinetic plasmas computer simulations are very intensive, because of the gyrokinetic turbulence. In some situations, it is possible to make assumptions on the shape of the distribution function that simplify the model. We obtain in this way a family of fluid or reduced models.

Assuming that the distribution function has a Maxwellian shape, for instance, we obtain the MagnetoHydroDynamic (MHD) model. It is physically valid only in some parts of the tokamak (at the edges for instance). The fluid model is generally obtained from the hypothesis that the collisions between particles are strong. Fine collision models are mainly investigated by other partners of the IPL (Inria Project Lab) FRATRES. In our approach we do not assume that the collisions are strong, but rather try to adapt the representation of the distribution function according to its shape, keeping the kinetic effects. The reduction is not necessarily a consequence of collisional effects. Indeed, even without collisions, the plasma may still relax to an equilibrium state over sufficiently long time scales (Landau damping effect). Recently, a team at the Plasma Physics Institut (IPP) in Garching has carried out a statistical analysis of the 5D distribution functions obtained from gyrokinetic tokamak simulations . They discovered that the fluctuations are much higher in the space directions than in the velocity directions (see Figure ).

This indicates that the approximation of the distribution function could require fewer data while still achieving a good representation, even in the collisionless regime.

Our approach is different from the fluid approximation. In what follows
we call this the “reduced model” approach. A reduced model is
a model where the explicit dependency on the velocity variable is
removed. In a more mathematical way, we consider that in some regions
of the plasma, it is possible to exhibit a (preferably small) set
of parameters

In this case it is sufficient to solve for

Several approaches are possible: waterbag approximations, velocity space transforms,
*etc.*

An experiment made in the 60's exhibits in a spectacular
way the reversible nature of the Vlasov equations. When two perturbations
are applied to a plasma at different times, at first the plasma seems
to damp and reach an equilibrium. But the information of the perturbations
is still here and “hidden” in the high frequency microscopic oscillations
of the distribution function. At a later time a resonance occurs and
the plasma produces an echo. The time at which the echo occurs can
be computed (see Villani

More practically, this experiment and its theoretical framework show that it is interesting to represent the distribution function by an expansion on an orthonormal basis of oscillating functions in the velocity variables. This representation allows a better control of the energy transfer between the low frequencies and the high frequencies in the velocity direction, and thus provides more relevant numerical methods. This kind of approach is studied for instance by Eliasson in with the Fourier expansion.

In long time scales, filamentation phenomena result in high frequency oscillations in velocity space that numerical schemes cannot resolve. For stability purposes, most numerical schemes contain dissipation mechanisms that may affect the precision of the finest oscillations that could be resolved.

Another trend in scientific computing is to optimize the computation time through adaptive modeling. This approach consists in applying the more efficient model locally, in the computational domain, according to an error indicator. In tokamak simulations, this kind of approach could be very efficient, if we are able to choose locally the best intermediate kinetic-fluid model as the computation runs. This field of research is very promising. It requires developing a clever hierarchy of models, rigorous error indicators, versatile software architecture, and algorithms adapted to new multicore computers.

As previously indicated, an efficient method for solving the reduced models is the Discontinuous Galerkin (DG) approach. It is possible to make it of arbitrary order. It requires limiters when it is applied to nonlinear PDEs occurring for instance in fluid mechanics. But the reduced models that we intent to write are essentially linear. The nonlinearity is concentrated in a few coupling source terms.

In addition, this method, when written in a special set of variables, called the entropy variables, has nice properties concerning the entropy dissipation of the model. It opens the door to constructing numerical schemes with good conservation properties and no entropy dissipation, as already used for other systems of PDEs , , , .

A precise resolution of the electromagnetic fields is essential for proper plasma simulation. Thus it is important to use efficient solvers for the Maxwell systems and its asymptotics: Poisson equation and magnetostatics.

The proper coupling of the electromagnetic solver with the Vlasov solver is also crucial for ensuring conservation properties and stability of the simulation.

Finally plasma physics implies very different time scales. It is thus very important to develop implicit Maxwell solvers and Asymptotic Preserving (AP) schemes in order to obtain good behavior on long time scales.

The coupling of the Maxwell equations to the Vlasov solver requires some precautions. The most important is to control the charge conservation errors, which are related to the divergence conditions on the electric and magnetic fields. We will generally use divergence correction tools for hyperbolic systems presented for instance in (and included references).

As already pointed out, in a tokamak, the plasma presents several different space and time scales. It is not possible in practice to solve the initial Vlasov-Maxwell model. It is first necessary to establish asymptotic models by letting some parameters (such as the Larmor frequency or the speed of light) tend to infinity. This is the case for the electromagnetic solver and this requires implementing implicit time solvers in order to efficiently capture the stationary state, the solution of the magnetic induction equation or the Poisson equation.

The search for alternative energy sources is a major issue for the future. Among others, controlled thermonuclear fusion in a hot hydrogen plasma is a promising possibility. The principle is to confine the plasma in a toroidal chamber, called a tokamak, and to attain the necessary temperatures to sustain nuclear fusion reactions. The International Thermonuclear Experimental Reactor (ITER) is a tokamak being constructed in Cadarache, France. This was the result of a joint decision by an international consortium made of the European Union, Canada, USA, Japan, Russia, South Korea, India and China. ITER is a huge project. As of today, the budget is estimated at 20 billion euros. The first plasma shot is planned for 2020 and the first deuterium-tritium operation for 2027.

Many technical and conceptual difficulties have to be overcome before the actual exploitation of fusion energy. Consequently, much research has been carried out around magnetically confined fusion. Among these studies, it is important to carry out computer simulations of the burning plasma. Thus, mathematicians and computer scientists are also needed in the design of ITER. The reliability and the precision of numerical simulations allow a better understanding of the physical phenomena and thus would lead to better designs. TONUS's main involvement is in such research.

The required temperatures to attain fusion are very high, of the order of a hundred million degrees. Thus it is imperative to prevent the plasma from touching the tokamak inner walls. This confinement is obtained thanks to intense magnetic fields. The magnetic field is created by poloidal coils, which generate the toroidal component of the field. The toroidal plasma current also induces a poloidal component of the magnetic field that twists the magnetic field lines. The twisting is very important for the stability of the plasma. The idea goes back to research by Tamm and Sakharov, two Russian physicists, in the 50's. Other devices are essential for the proper operation of the tokamak: divertor for collecting the escaping particles, microwave heating for reaching higher temperatures, fuel injector for sustaining the fusion reactions, toroidal coils for controlling instabilities, etc.

The software and numerical methods that we develop can also be applied to other fields of physics or of engineering.

For instance, we have a collaboration with the company AxesSim in Strasbourg for the development of efficient Discontinuous Galerkin (DG) solvers on hybrid computers. The applications is electromagnetic simulations for the conception of antenna, electronic devices or aircraft electromagnetic compatibility.

The acoustic conception of large rooms requires huge numerical simulations. It is not always possible to solve the full wave equation and many reduced acoustic models have been developed. A popular model consists in considering "acoustic" particles moving at the speed of sound. The resulting Partial Differential Equation (PDE) is very similar to the Vlasov equation. The same modeling is used in radiation theory. We have started to work on the reduction of the acoustic particles model and realized that our reduction approach perfectly applies to this situation. A new PhD with CEREMA (Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement) has started in October 2015 (thesis of Pierre Gerhard). The objective is to investigate the model reduction and to implement the resulting acoustic model in our DG solver.

We have launched the SCHNAPS project: http://

Solveur pour les lois de Conservation Hyperboliques Non-linéaires Appliqué aux PlasmaS

Scientific Description

It is clear now that future computers will be made of a collection of thousands of interconnected multicore processors. Globally, it appears as a classical distributed memory MIMD machine. But at a lower level, each of the multicore processors is itself made of a shared memory MIMD unit (a few classical CPU cores) and a SIMD unit (a GPU). When designing new algorithms, it is important to adapt them to this kind of architecture. Our philosophy will be to program our algorithms in such a way that they can be run efficiently on this kind of computers. Practically, we will use the MPI library for managing the coarse grain parallelism, while the OpenCL library will efficiently operate the fine grain parallelism.

We have invested for several years until now into scientific computing on GPUs, using the open standard OpenCL (Open Computing Language). We were recently awarded a prize in the international AMD OpenCL innovation challenge thanks to an OpenCL two-dimensional Vlasov-Maxwell solver that fully runs on a GPU. OpenCL is a very interesting tool because it is an open standard now available on almost all brands of multicore processors and GPUs. The same parallel program can run on a GPU or a multicore processor without modification. OpenCL programs are quite complicated to construct. For instance it is difficult to distribute efficiently the computation or memory operations on the different available accelerators. StarPU http://

Because of the envisaged applications, which may be either academic or commercial, it is necessary to conceive a modular framework. The heart of the library is made of generic parallel algorithms for solving conservation laws. The parallelism can be both fine-grained (oriented towards GPUs and multicore processors) and coarse-grained (oriented towards GPU clusters). The separate modules allow managing the meshes and some specific applications. With our partner AxesSim, we also develop a C++ specific version of SCHNAPS for electromagnetic applications.

Functional Description

SCHNAPS is a generic Discontinuous Galerkin solver, written in C, based on the OpenCL, MPI and StarPU frameworks.

Partner: AxesSim

Contact: Philippe Helluy

SEmi-LAgrangian LIBrary

Keywords: Plasma physics - Semi-Lagrangian method - PIC - Parallel computing - Plasma turbulence

Scientific Description

The objective of the Selalib project (SEmi-LAgrangian LIBrary) is to develop a well-designed, organized and documented library implementing several numerical methods for kinetic models of plasma physics. Its ultimate goal is to produce gyrokinetic simulations.

Another objective of the library is to provide to physicists easy-to-use gyrokinetic solvers, based on the semi-Lagrangian techniques developed by Eric Sonnendrücker and his collaborators in the past CALVI project. The new models and schemes from TONUS are also intended to be incorporated into Selalib.

Functional Description

Selalib is a collection of modules conceived to aid in the development of plasma physics simulations, particularly in the study of turbulence in fusion plasmas. Selalib offers basic capabilities from general and mathematical utilities and modules to aid in parallelization, up to pre-packaged simulations.

Partners: Max Planck Institute - Garching - IRMA, Université de Strasbourg - IRMAR, Université Rennes 1 - LJLL, Université Paris 6

Contact: Michel Mehrenberger

Scientific description:

The JOREK code is one of the most important MHD codes in Europe. This code written 15 years ago allows to simulate the MHD instabilities which appear in the TOKAMAK. Using this code the physicist has obtained some important results. However to run larger and more complex test cases it is necessary to evolve the numerical methods used.

In 2014, the DJANGO code has been created, the aim of this code is double: have a numerical library to implement, test and validate new numerical methods for MHD, fluid mechanics and Electromagnetic equations in the finite element context and prepare the future new JOREK code. This code is a 2D-3D code based on implicit time schemes and IsoGeometric (B-Splines, Bezier curves) for the spatial discretization.

Functional description:

DJANGO is a finite element implicit solver written in Fortran 2003 with a Basic MPI framework. The code is coupled with the PETSC library for the linear solvers and the code CAID (A. Ratnani) for the mesh.

Authors:

Ahmed Ratnani (Max Planck Institut of Plasma Physic, Garching, Germany), Boniface NKonga (University of Nice and Inria Sophia-Antipolis, France), Emmanuel Franck (Inria Nancy Grand Est, TONUS Team)

Contributors:

Laura Mendoza, Mustafa Gaja (PhD), Jalal Lakhlili, Celine Caldini-Queiros, Matthias, Hoelzl, Eric Sonnendrücker (Max Planck Institut of Plasma Physic, Garching, Germany), Ayoub Iaagoubi (ADT), Hervé Guillard (University of Nice and Inria Sophia-Antipolis, France), Virginie Grandgirard, Guillaume Latu (CEA Cadarache, France)

Year 2015:

The year 2015 is an important year for the JOREK code. Indeed, after the year 2014 where the IsoParametric (Bezier curves) finite element approach in 2D have been implemented for basic elliptic equations, in 2015 we have extended the code for more complex problems. Now the code can treat some hyperbolic, parabolic and elliptic models with different approaches (IsoParametric/IsoGeometric approach, Splines for triangle) in 2D and 3D by tensor product. The compilation of the code is more stable and some regression test cases have been added. To finish, two realistic MHD models (which come from to the JOREK code) have been implemented and must be validated. The Year 2016 will be the year of the first physical and realistic results.

The aim of the following works is to study the dynamics of charged particles under the influence of a strong magnetic field by numerically solving in an efficient way the Vlasov-Poisson and guiding center models.

First, we work on the development of the time-stepping method introduced in , in two directions: improve the accuracy of the algorithm and adapt the algorithm for general configuration of magnetic field.

Second, by using appropriate data structures, we implement an efficient (from the memory access point of view) Particle-In-Cell method which enables simulations with a large number of particles. Thus, we present in numerical results for classical one-dimensional Landau damping and two-dimensional Kelvin-Helmholtz test cases. The implementation also relies on a standard hybrid MPI/OpenMP parallelization. Code performance is assessed by the observed speedup and attained memory bandwidth. A convergence result is also illustrated by comparing the numerical solution of a four-dimensional Vlasov-Poisson system against the one for the guiding center model.

We continue to investigate kinetic models for simulating the heat load on the divertor plates during transient events as edge-localised modes (ELMs). Our previous work deals with Vlasov-Poisson equations for two particle species for the dynamics of their transport parallel to the magnetic field. We started to improve this model by adding an equation for the evolution in time of the perpendicular temperatures. These equations take also into account the collisions between species which may play a role over long times. The first numerical results are encouraging, showing different features with respect to the older (simpler) model when computing total particles and energy fluxes on the divertor plates.

We study the semi-Lagrangian method on curvilinear grids , . The classical backward semi-Lagrangian method preserves constant states but is not mass conservative. Natural reconstruction of the field permits nevertheless to have at least first order in time conservation of mass, even if the spatial error is large. Interpolation is performed with classical cubic splines and also cubic Hermite interpolation with arbitrary reconstruction order of the derivatives. High odd order reconstruction of the derivatives is shown to be a good ersatz of cubic splines which do not behave very well as time step tends to zero. A conservative semi-Lagrangian scheme is then described; here conservation of mass is automatically satisfied and constant states are shown to be preserved up to first order in time.

Semi-Lagrangian guiding center simulations are performed on sinusoidal perturbations of cartesian grids, and on deformed polar grids with different boundary conditions. Key ingredients are: the use of a B-spline finite element solver for the Poisson equation and the classical backward semi-Lagrangian method (BSL) for the advection. We are able to reproduce standard Kelvin-Helmholtz and diocotron instability tests on such grids. When the perturbation leads to a strong distorted mesh, we observe that the solution differs if one takes standard numerical parameters that are used in the cartesian reference case. We can recover good results together with correct mass conservation, by diminishing the time step.

The method of "velocity space transformations" allows to obtain an interesting discretization of the Kinetic equations like Vlasov-Poisson or Vlasov Maxwell equations as has been proved in the works of P. Helluy, L. Navoret and N. Pham. During this year, we have begun to extend this method to the collisional case using the entropy variable to write a general collisional operator. To treat all the regimes (small or large collisional regime), asymptotic preserving schemes (stability and convergence independent of the collisional frequency) have been designed. However, this method admits some numerical difficulties if we use the physical entropy to construct the collisional operator. Now we propose to use modified entropy, which has good numerical properties and gives limit regime close to the real one in the low Mach context. If this new approach gives interesting results, we will study the adaptivity of the velocity discrete basis which would allow to treat the collisional and non-collisional regimes with the same method.

The Viscous-resistive MHD model used to simulate the instabilities is a multi-scale models with fast waves. In this context, it is not possible to use full explicit time schemes. However the classical implicit schemes are not usable directly since the matrices are ill-conditioned. For this reason it is necessary to use a preconditioning method. During this year we have studied a method called "physic based preconditioning" for the wave equations which consists to approximate the solution by suitable smaller and simpler systems. The results are very good. After this, we have extended this method to the Linearized Euler equation. During this new study, we have found additional difficulties which appear in some regimes. Two methods to treat this problem will be tested in 2016. We have also implemented a version of this preconditioning for the reduced MHD models of JOREK. The first results are positive. To finish, we have begun a collaboration with S. Serra-Capizzano to study at the theoretical level the physic based preconditioning and propose new preconditioning for each sub-systems of the Physic-Based PC efficient in all the physics regimes and for an arbitrary order.

We have also developed an implicit solver for the transport equation based on the upwind nature of the DG numerical flux. This solver will be used for solving Vlasov models or fluid models thanks to the Lattice-Boltzmann methodology. We have obtained recently a SPPEXA support (http://

This work have begun at the end of 2015. It is organized around a PhD: Mustafa Gaja supervised by E. Sonnendrücker, A. Ratnani and E. Franck at the Max-Planck Institute of Plasma Physic. The aim of this work is to design and study compatible finite element method (finite element method which preserve the DeRham sequence and the inclusion between the functional space) for B-Splines. This method will allow to discretize efficiently the Maxwell equations, the MHD model and some operators as curl-curl or grad-div vectorial operators which appear in the physic-based PC. For now, we have begun to study the finite element discretization of vectorial operators which appears in the linearized Euler equations and in the physic-based PC associated.

This work is devoted to study the aligned interpolation method in semi-Lagrangian codes. The scheme is presented and algorithms used implementing the scheme are given. A theoretical justification of the method is given with convergence estimates in the simplified context of 2D constant advection, assuming stability of the scheme. The stability is here studied numerically, letting the formal proof as an open problem. The solution is successfully applied in the gyrokinetic context: first in a simplified case in cylindrical geometry and then in toroidal geometry. In the first case, the solutions provided by simulations based on the scheme are in accordance with linear dispersion analysis; in the second case, numerical simulations produced by the Gysela code are presented, simulation based on the standard scheme are compared to those based on the new aligned scheme. This work will lead to a project of paper, which will be submitted in 2016.

We are involved in a common project with the company AxesSim in Strasbourg. The objective is to help to the development of a commercial software for the numerical simulation of electromagnetic phenomena. The applications are directed towards antenna design and electromagnetic compatibility. This project was partly supported by DGA through "RAPID" (régime d'appui à l'innovation duale) funds. The CIFRE PhD of Thomas Strub is part of this project. Another CIFRE PhD has started in AxesSim on the same kind of subjects in March 2015 (Bruno Weber). The new project is devoted to the use of runtime system in order to optimize DG solvers applied to electromagnetism. The resulting software will be applied to the numerical simulation of connected devices for clothes or medicine. The project is supported by the "Banque Public d'Investissemnt" (BPI) and coordinated by the Thales company.

The thesis of Pierre Gerhard devoted to numerical simulation of room acoustics is supported by the Alsace region. It is a joint project with CEREMA (Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement) in Strasbourg.

ANR project GYPSI (2010-2015), https://

ANR project ”PEPPSI” in Programme Blanc SIMI 9 – Sciences de l’ingénierie (Edition 2012) started in 2013.

The TONUS project belongs to the IPL FRATRES and there was an annual meeting, on 15-16 October 2015, with talks of Emmanuel Franck, Philippe Helluy, Sever Adrian Hirstoaga, Michel Mehrenberger.

The TONUS and HIEPACS project have obtained the financial support of the PhD thesis of Nicolas Bouzat thanks to the IPL C2S@exa. Nicolas Bouzat works at CEA Cadarache and is supervised locally by Guillaume Latu; the PhD advisors are Michel Mehrenberger and Jean Roman.

GENCI projet : t2015067387 "Simulation numérique des plasmas par des méthodes semi-lagrangiennes et eulériennes adaptées" 800 000 scalar computing hours on CURIE_standard (January 2015-February 2016); use: 300 000 heures.

GENCI projet : t2016067580 "Simulation numérique des plasmas par des méthodes semi-lagrangiennes et PIC adaptées" 450 000 scalar computing hours on CURIE_standard (January 2016-January 2017); coordinator: Michel Mehrenberger

Eurofusion Enabling Research Project ER15-IPP01 (1/2015-12/2017) "Verification and development of new algorithms for gyrokinetic codes" (Principal Investigator: Eric Sonnendrücker, Max-Planck Institute for Plasma Physics, Garching).

Eurofusion Enabling Research Project ER15-IPP05 (1/2015-12/2017) "Global non-linear MHD modeling in toroidal geometry of disruptions, edge localized modes, and techniques for their mitigation and suppression" (Principal Investigator: Matthias Hoelzl, Max-Planck Institute for Plasma Physics, Garching).

.

Michel Mehrenberger has a collaboration with Bedros Afeyan (Pleasanton, USA) to work on KEEN wave simulations.

ANR/SPPEXA "EXAMAG" is a joint French-German-Japanese project. Its goal is to develop efficient parallel MHD solvers for future exascale architectures. With our partners we plan to apply highly paralelized and hybrid solvers for plasma physics. One of our objective is to develop Lattice-Boltzmann MHD solvers based on high-order implicit Discontinous Galerkin methods using SCHNAPS and runtime systems such as StarPU.

Philippe Helluy is member of the editorial board of IJFV http://

Emmanuel Franck participates in reviewing for

ENUMATH 2015 Proceedings

Comptes Rendus Mathematique

Philippe Helluy participates in reviewing for

Mathematical reviews

ESAIM Procs

Computers and fluids

Computational physics paper

International Journal for Numerical Methods in Fluids

SINUM

Computer Physics Communications

Journal of Mechanical Science and Technology

Sever Adrian Hirstoaga participates in reviewing for

Discrete and Continuous Dynamical Systems-Series S

ESAIM Procs.

Michel Mehrenberger participates in reviewing for

Electronic Journal of Qualitative Theory of Differential Equations (EJQTDE)

ESAIM Procs

SISC

Zeitschrift fuer Angewandte Mathematik und Physik (ZAMP)

Abstract and Applied Analysis (AAA)

Laurent Navoret participates in reviewing for

ESAIM Procs

J. Comp. Phys.

Emmanuel Franck was invited at

Congrès SMAI 2015", Mini-symposium "Numerical method for Plasma physic", Karellis, June 2015.

"Multi-scale Numerical Methods for the Vlasov Poisson system with strong magnetic field", http://

" Workshop JOREK ", Garching, May 2015.

Seminar Nantes, October 2015

Philippe Helluy was invited at:

Numkin 2015, Max Planck Institute for Plasma Physics, Munich, Germany, October 2015, http://

JLESC workshop, Barcelona, June 2015, http://

Forum ORAP, November 2015, http://

Sever Adrian Hirstoaga was invited at

the workshop Modeling and Numerical Methods for Hot Plasmas II, Bordeaux, October 12-14, 2015

the "Séminaire d'Analyse", IRMA Strasbourg, December 10, 2015.

Michel Mehrenberger was invited at

IFIP Nice June 30, 2015, Mini Symposium "Oscillation, Degeneracy and Controllability".

Laurent Navoret was invited at

Séminaire LAMA, Université de Savoie

Séminaire Calcul Stochastique, IRMA, Université de Strasbourg

Workshop "Collective dynamics of active particles, swimmers, motile cells", IMFT, Toulouse

Sever Adrian Hirstoaga, expertises for:

computational project proposal at the Swiss National Supercomputing Centre

Philippe Helluy, expertises for:

ANR

U.S. Army Research Office

Defence Institute of Advanced Technology (India)

Energy research call CNRS (France).

Michaël Gutnic is member of the National Commity for Scientific Research (from september 2012).

Philippe Helluy:

head of the "Modélisation et Contrôle" research team at IRMA Strasbourg,

chargé de mission calcul scientifique at CNRS.

Michel Mehrenberger is partly responsible of the seminar MOCO (MOdelisation et COntrôle, IRMA, Université de Strasbourg).

Licence: Michaël Gutnic, Mathématiques pour les sciences du vivant, 84h eq. TD, L1 Sciences du Vivant, Université de Strasbourg, France

Licence: Michaël Gutnic, Statistiques pour les biologistes, 117h eq. TD, L2 Sciences du Vivant, Université de Strasbourg, France

Licence: Philippe Helluy, Calcul scientifique, 54h eq. TD, L2 Maths, Université de Strasbourg, France

Licence: Michel Mehrenberger, Fonctions de plusieurs variables et analyse vectorielle, 30 h eq. TD, L2, Université de Strasbourg, France

Licence: Laurent Navoret, Calcul scientifique, 65 h eq. TD, L3, Université de Strasbourg, France

Licence: Laurent Navoret, Optimisation Non-Linéaire, 54h eq. TD, Cours et TD, L3 Maths-Eco, Université de Strasbourg, France

Master: Michaël Gutnic, Probabilités et Statistiques, 30h eq. TD, Formation d'ingénieur en informatique en apprentissage, Institut des Techniques d'Ingénieur de l'Industrie, Centre de Formation d'Apprentis de l'Industrie, Conservatoire national des arts et métiers, France.

Master: Philippe Helluy, Recherche opérationnelle, 45h eq. TD, ENSIIE, Université de Strasbourg, France

Master: Philippe Helluy, Contrôle Optimal, 26h eq. TD, M2, Université de Strasbourg, France

Master: Philippe Helluy, Méthode des volumes finis, 26h eq. TD, M2, Université de Strasbourg, France

Master: Philippe Helluy, Calcul scientifique, 10h eq. TD, M2 Agrégation, Université de Strasbourg, France

Master: Michel Mehrenberger, Cours avancé math fonda, 20 h eq. TD, M1, Université de Strasbourg, France

Master: Michel Mehrenberger, PIP certification Python, 13 h eq. TD, M1, Université de Strasbourg, France

Master: Laurent Navoret, PIP : certification python, 13h eq. TD, M1 Mathématiques, Université de Strasbourg, France.

Master: Laurent Navoret, Calcul scientifique, 54 h eq. TD, M2 Agrégation, Université de Strasbourg, France.

Master: Laurent Navoret, Correction de devoir, 26 h eq. TD, M2 Agrégation, Université de Strasbourg, France.

Master: Laurent Navoret, Basics in Maths, 24h eq. TD, Cours, M2 Cell Physics, Université de Strasbourg, France.

PhD : Thomas Strub, "Résolution des équations de Maxwell tridimensionnelles instationnaires sur architecture massivement multicoeur", Université de Strasbourg, March 2015, Advisor: Philippe Helluy.

PhD in progress: Thi Trang Nhung Pham, "Méthodes numériques pour Vlasov", October 2012, Advisors: Philippe Helluy, Laurent Navoret.

PhD in progress: Pierre Gerhard, "Résolution des modèles cinétiques. Application à l'acoustique du bâtiment.", October 2015, Advisor: Philippe Helluy, Laurent Navoret.

PhD in progress: Bruno Weber, "Optimisation de code Galerkin Discontinu sur ordinateur hybride. Application à la simulation numérique en électromagnétisme", March 2015, Advisor: Philippe Helluy.

PhD in progress: Nicolas Bouzat, "Fine grain algorithms and deployment methods for exascale codes", October 2015, Advisor: Michel Mehrenberger, Jean Roman, Guillaume Latu.

PhD in progress: Michel Massaro, "Méthodes numériques pour les plasmas sur architectures multicœurs", December 2012, Advisor: Philippe Helluy.

Michel Mehrenberger was invited member of the jury of the PhD of Fabien Rozar (CEA Cadarache).

Philippe Helluy, PhD defence of: Lauriane Schneider (Strasbourg), Rémi Chauvin (Toulouse).

Philippe Helluy participated to the redaction of an ONISEP brochure about the jobs related to Mathematics or computer sciences
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Michel Mehrenberger is in the IREM ("Instituts de recherche sur l?enseignement des mathématiques") team "Modélisation" for the year 2015-2016.