Asymptotic-Preserving Monte Carlo Methods for Transport Equations in the Diffusive Limit

DOI10.1137/17M1140741zbMath1383.65130arXiv1707.09672OpenAlexW2739637503MaRDI QIDQ4603508

Giovanni Samaey, Giacomo Dimarco, Lorenzo Pareschi

Publication date: 21 February 2018

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.09672

zbMATH Keywords

Monte Carlo methodstransport equationsimplicit time discretizationasymptotic-preserving schemesdiffusion limit

Mathematics Subject Classification ID

Monte Carlo methods (65C05) Transport processes in time-dependent statistical mechanics (82C70) Probabilistic methods, particle methods, etc. for initial value and initial-boundary value problems involving PDEs (65M75) First-order hyperbolic equations (35L02)

Related Items (13)

Multilevel asymptotic-preserving Monte Carlo for kinetic-diffusive particle simulations of the Boltzmann-BGK equation ⋮ On Asymptotic Preserving Schemes for a Class of Stochastic Differential Equations in Averaging and Diffusion Approximation Regimes ⋮ A Kinetic-Diffusion Asymptotic-Preserving Monte Carlo Algorithm for the Boltzmann-BGK Model in the Diffusive Scaling ⋮ On a discrete framework of hypocoercivity for kinetic equations ⋮ Monte Carlo Gradient in Optimization Constrained by Radiative Transport Equation ⋮ On multilevel Monte Carlo methods for deterministic and uncertain hyperbolic systems ⋮ Accelerated Simulation of Boltzmann-BGK Equations near the Diffusive Limit with Asymptotic-Preserving Multilevel Monte Carlo ⋮ A Multilevel Monte Carlo Asymptotic-Preserving Particle Method for Kinetic Equations in the Diffusion Limit ⋮ Asymptotically complexity diminishing schemes (ACDS) for kinetic equations in the diffusive scaling ⋮ A multilevel Monte Carlo method for asymptotic-preserving particle schemes in the diffusive limit ⋮ Hypocoercivity and diffusion limit of a finite volume scheme for linear kinetic equations ⋮ The Aw-Rascle traffic model: Enskog-type kinetic derivation and generalisations ⋮ A hybrid fluid-kinetic model for hydrogenic atoms in the plasma edge of tokamaks based on a micro-macro decomposition of the kinetic equation

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