High-order adaptive rank integrators for multi-scale linear kinetic transport equations in the hierarchical tucker format
In this paper, we present a new adaptive rank approximation technique for computing
solutions to the high-dimensional linear kinetic transport equation. The approach we …
solutions to the high-dimensional linear kinetic transport equation. The approach we …
Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations
In this article, we are interested in the asymptotic analysis of a finite volume scheme for one-
dimensional linear kinetic equations, with either a Fokker–Planck or linearized BGK collision …
dimensional linear kinetic equations, with either a Fokker–Planck or linearized BGK collision …
Monte Carlo gradient in optimization constrained by radiative transport equation
Can Monte Carlo (MC) solvers be directly used in gradient-based methods for PDE-
constrained optimization problems? In these problems, a gradient of the loss function is …
constrained optimization problems? In these problems, a gradient of the loss function is …
On a discrete framework of hypocoercivity for kinetic equations
A Blaustein, F Filbet - Mathematics of Computation, 2024 - ams.org
We propose and study a fully discrete finite volume scheme for the linear Vlasov-Fokker-
Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This …
Planck equation written as an hyperbolic system using Hermite polynomials in velocity. This …
The aw–rascle traffic model: Enskog-type kinetic derivation and generalisations
We study the derivation of second order macroscopic traffic models from kinetic descriptions.
In particular, we recover the celebrated Aw–Rascle model as the hydrodynamic limit of an …
In particular, we recover the celebrated Aw–Rascle model as the hydrodynamic limit of an …
On asymptotic preserving schemes for a class of stochastic differential equations in averaging and diffusion approximation regimes
CE Bréhier, S Rakotonirina-Ricquebourg - Multiscale Modeling & Simulation, 2022 - SIAM
We introduce and study a notion of asymptotic preserving schemes, related to convergence
in distribution, for a class of slow-fast stochastic differential equations. In some examples …
in distribution, for a class of slow-fast stochastic differential equations. In some examples …
A hybrid fluid-kinetic model for hydrogenic atoms in the plasma edge of tokamaks based on a micro-macro decomposition of the kinetic equation
Monte Carlo (MC) simulations of the full kinetic equation for the neutral particles in the
plasma edge become computationally costly for reactor-relevant regimes. To accelerate the …
plasma edge become computationally costly for reactor-relevant regimes. To accelerate the …
Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation
We develop a novel multilevel asymptotic-preserving Monte Carlo method, called Multilevel
Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport …
Kinetic-Diffusion Monte Carlo (ML-KDMC), for simulating the kinetic Boltzmann transport …
Kinetic‐diffusion asymptotic‐preserving Monte Carlo algorithms for plasma edge neutral simulation
B Mortier, M Baelmans… - Contributions to Plasma …, 2020 - Wiley Online Library
Abstract We developed novel Monte Carlo simulation strategies for the neutral model in
plasma edge simulations where both low‐collisional and high‐collisional regimes are …
plasma edge simulations where both low‐collisional and high‐collisional regimes are …
A multilevel Monte Carlo method for asymptotic-preserving particle schemes in the diffusive limit
Kinetic equations model distributions of particles in position-velocity phase space. Often,
one is interested in studying the long-time behavior of particles in high-collisional regimes in …
one is interested in studying the long-time behavior of particles in high-collisional regimes in …