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math.NA2026
A Fourier spectral method for the cutoff Boltzmann equation: Convergence analysis and numerical simulation
Yanzhi Gui, Ling-Bing He, Liu Liu
This work presents a novel Fourier spectral method for the cutoff spatially homogeneous Boltzmann equation with Maxwellian and hard potentials. We establish finite-time error estim…
math.NA2025
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.…
math.NA2025
Asymptotic-preserving and positivity-preserving discontinuous Galerkin method for the semiconductor Boltzmann equation in the diffusive scaling
Huan Ding, Liu Liu, Xinghui Zhong
In this paper, we develop an asymptotic-preserving and positivity-preserving discontinuous Galerkin (DG) method for solving the semiconductor Boltzmann equation in the diffusive sc…