Overall Objectives
Research Program
Application Domains
New Results
- Multi-revolution composition methods for highly oscillatory differential equations
- Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise
- High order numerical approximation of the invariant measure of ergodic SDEs
- PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
- An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems
- Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
- Weak second order explicit stabilized methods for stiff stochastic differential equations
- Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
- Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field
- A dynamic multi-scale model for transient radiative transfer calculations
- Quasi-periodic solutions of the 2D Euler equation
- Optimization and parallelization of Emedge3D on shared memory architecture
- Vlasov on GPU (VOG Project)
- 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
- Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
- Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
- Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus
- Weak backward error analysis for overdamped Langevin equation
- Weak backward error analysis for Langevin equation
- Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme
- An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
- Asymptotic Preserving schemes for highly oscillatory Vlasov-Poisson equations
- Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
- On the controllability of quantum transport in an electronic nanostructure
- The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
- Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties
- Analysis of models for quantum transport of electrons in graphene layers
- Analysis of a large number of Markov chains competing for transitions
- Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems
- Existence of densities for the 3D Navier–Stokes equations driven by Gaussian noise
- Invariant measure of scalar first-order conservation laws with stochastic forcing
- Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
- Existence of densities for stable-like driven SDE's with Hölder continuous coefficients
- Ergodicity results for the stochastic Navier-Stokes equations: an introduction
- Weak truncation error estimates for elliptic PDEs with lognormal coefficients
- Optimized high-order splitting methods for some classes of parabolic equations
- Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds
Partnerships and Cooperations
Bibliography
Overall Objectives
Research Program
Application Domains
New Results
- Multi-revolution composition methods for highly oscillatory differential equations
- Weak second order multi-revolution composition methods for highly oscillatory stochastic differential equations with additive or multiplicative noise
- High order numerical approximation of the invariant measure of ergodic SDEs
- PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
- An offline-online homogenization strategy to solve quasilinear two-scale problems at the cost of one-scale problems
- Reduced basis finite element heterogeneous multiscale method for quasilinear elliptic homogenization problems
- Weak second order explicit stabilized methods for stiff stochastic differential equations
- Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
- Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field
- A dynamic multi-scale model for transient radiative transfer calculations
- Quasi-periodic solutions of the 2D Euler equation
- Optimization and parallelization of Emedge3D on shared memory architecture
- Vlasov on GPU (VOG Project)
- 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
- Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
- Asymptotic preserving schemes for the Klein-Gordon equation in the non-relativistic limit regime
- Sobolev stability of plane wave solutions to the cubic nonlinear Schrödinger equation on a torus
- Weak backward error analysis for overdamped Langevin equation
- Weak backward error analysis for Langevin equation
- Approximation of the invariant law of SPDEs: error analysis using a Poisson equation for a full-discretization scheme
- An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
- Asymptotic Preserving schemes for highly oscillatory Vlasov-Poisson equations
- Uniformly accurate numerical schemes for highly oscillatory Klein-Gordon and nonlinear Schrödinger equations
- On the controllability of quantum transport in an electronic nanostructure
- The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
- Solving highly-oscillatory NLS with SAM: numerical efficiency and geometric properties
- Analysis of models for quantum transport of electrons in graphene layers
- Analysis of a large number of Markov chains competing for transitions
- Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems
- Existence of densities for the 3D Navier–Stokes equations driven by Gaussian noise
- Invariant measure of scalar first-order conservation laws with stochastic forcing
- Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case
- Existence of densities for stable-like driven SDE's with Hölder continuous coefficients
- Ergodicity results for the stochastic Navier-Stokes equations: an introduction
- Weak truncation error estimates for elliptic PDEs with lognormal coefficients
- Optimized high-order splitting methods for some classes of parabolic equations
- Higher-Order Averaging, Formal Series and Numerical Integration III: Error Bounds
Partnerships and Cooperations
Bibliography
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