Project-Team:IPSO

Project-Team Ipso

Members

Overall Objectives

Research Program

Application Domains

New Results

Highlights of the Year
Multi-revolution composition methods for highly oscillatory differential equations
Multiscale schemes for the BGK-Vlasov-Poisson system in the quasi-neutral and fluid limits. Stability analysis and first order schemes
Asymptotic preserving scheme for a kinetic model describing incompressible fluids
Comparison of numerical solvers for anisotropic diffusion equations arising in plasma physics
Asymptotic-Preserving scheme based on a Finite Volume/Particle-In-Cell coupling for Boltzmann- BGK-like equations in the diffusion scaling
Hamiltonian splitting for the Vlasov-Maxwell equations
A hybrid transport-diffusion model for radiative transfer in absorbing and scattering media
Charge conserving grid based methods for the Vlasov-Maxwell equations
Improving conservation properties of a 5D gyrokinetic semi-Lagrangian code
Simulations of Kinetic Electrostatic Electron Nonlinear (KEEN) Waves with Variable Velocity Resolution Grids and High-Order Time-Splitting
Gyroaverage operator on polar mesh
A new fully two-dimensional conservative semi-Lagrangian method: applications on polar grids, from diocotron instability to ITG turbulence
Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
Models of dark matter halos based on statistical mechanics: II. The fermionic King model
Models of dark matter halos based on statistical mechanics: I. The classical King model
Analysis of models for quantum transport of electrons in graphene layers
Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime
Superconvergence of Strang splitting for NLS in Td
Strong confinement limit for the nonlinear Schrödinger equation constrained on a curve
The fermionic King model
Landau damping in Sobolev spaces for the Vlasov-HMF model
Collisions of vortex filament pairs
Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
Analysis of a large number of Markov chains competing for transitions
Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates
Global behavior of N competing species with strong diffusion: diffusion leads to exclusion
Randomized Message-Passing Test-and-Set
Existence of densities for the 3D Navier–Stokes equations driven by Gaussian noise
Diffusion limit for the radiative transfer equation perturbed by a Markovian process
Diffusion limit for the radiative transfer equation perturbed by a Wiener process

Partnerships and Cooperations

Dissemination

Bibliography

Inria | Raweb 2014 | Presentation of the Project-Team IPSO


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Section: New Results

Multi-revolution composition methods for highly oscillatory differential equations

In [22] , we introduce a new class of multi-revolution composition methods (MRCM) for the approximation of the $N$ th-iterate of a given near-identity map. When applied to the numerical integration of highly oscillatory systems of differential equations, the technique benefits from the properties of standard composition methods: it is intrinsically geometric and well-suited for Hamiltonian or divergence-free equations for instance. We prove error estimates with error constants that are independent of the oscillatory frequency. Numerical experiments, in particular for the nonlinear Schrödinger equation, illustrate the theoretical results, as well as the efficiency and versatility of the methods.

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