4 papers
Asymptotic-preserving semi-Lagrangian discontinuous Galerkin schemes for the Boltzmann equation
Xiaofeng Cai, Zhen Hao, Liu Liu +1
In this work, we present an asymptotic-preserving semi-Lagrangian discontinuous Galerkin scheme for the Boltzmann equation that effectively handles multi-scale transport phenomena.…
Hypocoercivity for the Linear Semiconductor Boltzmann Equation with Boundaries and Uncertainties
Hongxu Chen, Liu Liu, Jiayu Wan
In this paper, we establish hypocoercivity for the semiconductor Boltzmann equation with the presence of an external electrical potential under the Maxwell boundary condition. We w…
Machine learning-based moment closure model for the linear Boltzmann equation with uncertainties
Juntao Huang, Liu Liu, Kunlun Qi +1
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving cl…
Error estimates of asymptotic-preserving neural networks in approximating stochastic linearized Boltzmann equation
Jiayu Wan, Liu Liu
In this paper, we construct an asymptotic-preserving neural networks (APNNs) [21] for the linearized Boltzmann equation in the acoustic scaling and with uncertain parameters. Utili…