Inria
/
Raweb 2009
Presentation of the Project IPSO
Logo Inria
IPSO
Invariant Preserving Solvers
2009 Research Team Activity Report
Rennes - Bretagne-Atlantique
Area :
Applied Mathematics, Computation and Simulation
Theme : Computational models and simulation
Presentation of the Project-Team
- Activity Report in
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Members
Overall Objectives
An overview of geometric numerical integration
Overall objectives
Scientific Foundations
Structure-preserving numerical schemes for solving ordinary differential equations
Highly-oscillatory systems
Geometric schemes for the Schrödinger equation
High-frequency limit of the Helmholtz equation
From the Schrödinger equation to Boltzmann-like equations
Spatial approximation for solving ODEs
Application Domains
Laser physics
Molecular Dynamics
New Results
A Fast Multipole Method for Geometric Numerical Integrations of Hamiltonian Systems
Composing B-series of integrators and vector fields
Resonances in long time integration of semi-linear Hamiltonian PDEs.
Quasi invariant modified Sobolev norms for semi-linear reversible PDEs.
Modified energy for split-step methods applied to the linear Schrödinger equation.
Birkhoff normal form for splitting methods applied semi linear Hamiltonian PDEs. Part II: Abstract splitting
A probabilistic approach of high-dimensional least-squares approximations
Computing semi-classical quantum dynamics with Hagedorn wavepackets
Conservative stochastic differential equations: Mathematical and numerical analysis
Analysis of splitting methods for reaction-diffusion problems using stochastic calculus
Weak approximation of stochastic partial differential equations: the nonlinear case
Long-time behavior in scalar conservation laws
Soliton dynamics for the Korteweg-de Vries equation with multiplicative homogeneous noise
Weak order for the discretization of the stochastic heat equation
Hybrid stochastic simplifications for multiscale gene networks
Moments analysis in Markov reward models.
The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire.
An averaging technique for highly-oscillatory Hamiltonian problems.
Propagation of Gevrey regularity over long times for the fully discrete Lie Trotter splitting scheme applied to the linear Schrödinger equation.
Splitting methods with complex times for parabolic equations
Higher-order averaging, formal series and numerical integration
An algebraic theory of order
Other Grants and Activities
National Grants
Dissemination
Program committees, editorial Boards and organization of conferences
INRIA and University committees
Teaching
Participation in conferences
International exchanges
Bibliography
Major publications
Publications of the year
References in notes
