Overall Objectives
Scientific Foundations
Application Domains
New Results
- PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
- Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
- Weak second order explicit stabilized methods for stiff stochastic differential equations
- High weak order methods for stochastic differential equations based on modified equations
- Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
- Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis
- A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
- An Isogeometric Analysis Approach for the study of the gyrokinetic quasi-neutrality equation
- Guiding-center simulations on curvilinear meshes using semi-Lagrangian conservative methods
- Quasi-periodic solutions of the 2D Euler equation
- Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles
- Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field
- A dynamic multi-scale model for transient radiative transfer calculations
- Accuracy of unperturbed motion of particles in a gyrokinetic semi-Lagrangian code
- High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation
- A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem
- Asymptotic preserving schemes for highly oscillatory kinetic equation
- Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
- Orbital stability of spherical galactic models
- Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system
- Micro-macro schemes for kinetic equations including boundary layers
- Stroboscopic averaging for the nonlinear Schrödinger equation
- An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
- Analysis of a large number of Markov chains competing for transitions
- High frequency behavior of the Maxwell-Bloch mdel with relaxations: convergence to the Schrödinger-rate system
- Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion
- Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates
- Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems
- Optimized high-order splitting methods for some classes of parabolic equations
- A formal series approach to averaging: exponentially small error estimates
- Higher-order averaging, formal series and numerical integration II: the quasi-periodic case
- Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise
- Diffusion limit for a stochastic kinetic problem
- Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
- Weak backward error analysis for SDEs
- Convergence of stochastic gene networks to hybrid piecewise deterministic processes
- Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises
- Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
- Fast Weak-Kam Integrators
- Sparse spectral approximations for computing polynomial functionals
Partnerships and Cooperations
Bibliography
Overall Objectives
Scientific Foundations
Application Domains
New Results
- PIROCK: a swiss-knife partitioned implicit-explicit orthogonal Runge-Kutta Chebyshev integrator for stiff diffusion-advection-reaction problems with or without noise
- Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations
- Weak second order explicit stabilized methods for stiff stochastic differential equations
- High weak order methods for stochastic differential equations based on modified equations
- Analysis of the finite element heterogeneous multiscale method for nonmonotone elliptic homogenization problems
- Coupling heterogeneous multiscale FEM with Runge-Kutta methods for parabolic homogenization problems: a fully discrete space-time analysis
- A priori error estimates for finite element methods with numerical quadrature for nonmonotone nonlinear elliptic problems
- An Isogeometric Analysis Approach for the study of the gyrokinetic quasi-neutrality equation
- Guiding-center simulations on curvilinear meshes using semi-Lagrangian conservative methods
- Quasi-periodic solutions of the 2D Euler equation
- Kinetic/fluid micro-macro numerical schemes for Vlasov-Poisson-BGK equation using particles
- Two-Scale Macro-Micro decomposition of the Vlasov equation with a strong magnetic field
- A dynamic multi-scale model for transient radiative transfer calculations
- Accuracy of unperturbed motion of particles in a gyrokinetic semi-Lagrangian code
- High order Runge-Kutta-Nyström splitting methods for the Vlasov-Poisson equation
- A Discontinuous Galerkin semi-Lagrangian solver for the guiding-center problem
- Asymptotic preserving schemes for highly oscillatory kinetic equation
- Asymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
- Orbital stability of spherical galactic models
- Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system
- Micro-macro schemes for kinetic equations including boundary layers
- Stroboscopic averaging for the nonlinear Schrödinger equation
- An asymptotic preserving scheme based on a new formulation for NLS in the semiclassical limit
- Analysis of a large number of Markov chains competing for transitions
- High frequency behavior of the Maxwell-Bloch mdel with relaxations: convergence to the Schrödinger-rate system
- Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion
- Coexistence phenomena and global bifurcation structure in a chemostat-like model with species-dependent diffusion rates
- Markov Chains Competing for Transitions: Application to Large-Scale Distributed Systems
- Optimized high-order splitting methods for some classes of parabolic equations
- A formal series approach to averaging: exponentially small error estimates
- Higher-order averaging, formal series and numerical integration II: the quasi-periodic case
- Existence of densities for the 3D Navier-Stokes equations driven by Gaussian noise
- Diffusion limit for a stochastic kinetic problem
- Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
- Weak backward error analysis for SDEs
- Convergence of stochastic gene networks to hybrid piecewise deterministic processes
- Exponential mixing of the 3D stochastic Navier-Stokes equations driven by mildly degenerate noises
- Existence and stability of solitons for fully discrete approximations of the nonlinear Schrödinger equation
- Fast Weak-Kam Integrators
- Sparse spectral approximations for computing polynomial functionals
Partnerships and Cooperations
Bibliography
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