Asymptotic-preserving schemes for multiscale physical problems

S ** - Acta Numerica, 2022‏ - cambridge.org
We present the asymptotic transitions from microscopic to macroscopic physics, their
computational challenges and the asymptotic-preserving (AP) strategies to compute …

Hypocoercivity based sensitivity analysis and spectral convergence of the stochastic Galerkin approximation to collisional kinetic equations with multiple scales and …

L Liu, S ** - Multiscale Modeling & Simulation, 2018‏ - SIAM
In this paper we provide a general framework to study a general class of linear and
nonlinear kinetic equations with random uncertainties from the initial data or collision …

Uncertainty quantification for kinetic equations

J Hu, S ** - Uncertainty quantification for hyperbolic and kinetic …, 2017‏ - Springer
Kinetic equations contain uncertainties in their collision kernels or scattering coefficients,
initial or boundary data, forcing terms, geometry, etc. Quantifying the uncertainties in kinetic …

Uniform spectral convergence of the stochastic Galerkin method for the linear semiconductor Boltzmann equation with random inputs and diffusive scalings

L Liu - arxiv preprint arxiv:1706.04757, 2017‏ - arxiv.org
In this paper, we study the generalized polynomial chaos (gPC) based stochastic Galerkin
method for the linear semiconductor Boltzmann equation under diffusive scaling and with …

A stochastic asymptotic-preserving scheme for the bipolar semiconductor Boltzmann-Poisson system with random inputs and diffusive scalings

L Liu - Journal of Computational Physics, 2019‏ - Elsevier
In this paper, we study the bipolar Boltzmann-Poisson model, both for the deterministic
system and the system with uncertainties, with asymptotic behavior leading to the drift …

On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation

ES Daus, S **, L Liu - ESAIM: Mathematical Modelling and …, 2021‏ - esaim-m2an.org
In this paper the nonlinear multi-species Boltzmann equation with random uncertainty
coming from the initial data and collision kernel is studied. Well-posedness and long-time …

High Order IMEX Stochastic Galerkin Schemes for Linear Transport Equation with Random Inputs and Diffusive Scalings

Z Chen, L Mu - Communications on Applied Mathematics and …, 2024‏ - Springer
In this paper, we consider the high order method for solving the linear transport equations
under diffusive scaling and with random inputs. To tackle the randomness in the problem …