In this paper we develop high-order asymptotic-preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi, where asymptotic preserving exponential Runge-Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes work with high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen numbers ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas.
High order asymptotic-preserving schemes for the Boltzmann equation
Université de Toulouse（图卢兹大学；法国国家科学研究中心数学研究所）；UPS, INSA, UT1, UTM（费拉拉大学数学系和CMCS）；CNRS, UMR 5219；Institut de Mathématiques de Toulouse；Mathematics Department, University of Ferrara and CMCS
Structure-preserving neural networks for the regularized entropy-based closure of the Boltzmann moment system
Computer Science and Mathematics Division（计算机科学与数学分部）；Oak Ridge National Laboratory（橡树岭国家实验室）；Faculty of Mathematics（数学学院）；KIT（卡尔斯鲁厄理工学院）；University of Tennessee（田纳西大学）
Positivity preserving DG schemes for a Boltzmann - Poisson model of electrons in semiconductors in curvilinear momentum coordinates
TU Wien - Institute for Analysis and Scientific Computing（维也纳工业大学分析与科学计算研究所）；The University of Texas at Austin - Institute for Computational Engineering and Sciences & Department of Mathematics（德克萨斯大学奥斯汀分校计算工程与科学研究所及数学系）；Oak Ridge National Lab - Computational and Applied Mathematics Group（橡树岭国家实验室计算与应用数学组）
A linearly implicit energy-preserving exponential integrator for the nonlinear Klein-Gordon equation
在本文中，我们推广了最近的文章[SIAM J. Sci. Comput. 38（2016）A1876-A1895]，其现在通过进一步利用标量辅助变量方法的思想而变为线性隐式。与传统的指数型保能积分器相比，该方法只涉及常系数矩阵的线性系，而通常会导致非线性代数系统。以非线性Klein-Gordon方程为例，给出了具体的能量守恒格式，并通过数值实验验证了其高效性.
A bi-fidelity method for the multiscale Boltzmann equation with random parameters
本文利用文献[A]中发展的一种双精度随机配置方法研究了具有多维随机参数的多尺度Boltzmann方程。纳拉扬角Gittelson和D. Xiu，SIAM J. Sci.计算：36（2014）; X. Zhu，中国茶青冈A. Narayan和D. Xiu，SIAM J. Uncertain.数量，2（2014）]。通过选择可压缩Euler系统作为低保真模型，采用双保真SC方法，将低保真模型的计算效率与高保真（Boltzmann）模型的高精度结合起来。双保真度近似只需少量的保渐近解，就能很好地捕捉随机空间中玻尔兹曼方程解的宏观量.先验估计的精度之间的高保真度和双保真度的解决方案，以及收敛性分析。最后，我们提出了广泛的数值实验，以验证我们所提出的方法的效率和准确性。
High-order multi-structures-preserving exponential integrators for the derivative nonlinear Schrödinger equation
Faculty of Information Engineering and Automation, Kunming University of Science and Technology（昆明理工大学信息工程与自动化学院）；School of Statistics and Mathematics, Yunnan University of Finance and Economics（云南财经大学统计与数学学院）
A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems
Asymptotic preserving Implicit-Explicit Runge-Kutta methods for non linear kinetic equations
Université de Toulouse（图卢兹大学；法国国家科学研究中心数学研究所）；UPS, INSA, UT1, UTM（费拉拉大学数学系与CMCS）；CNRS, UMR 5219；Institut de Mathématiques de Toulouse；Mathematics Department, University of Ferrara and CMCS
An IMEX multi-level domain-decomposition method for the Boltzmann equation on unstructured meshes
Université Côte d’Azur（蔚蓝海岸大学）；CNRS（法国国家科学研究中心）；University of Ferrara（费拉拉大学）；Maxwell Institute for Mathematical Sciences（麦克斯韦数学科学研究所）；Heriot-Watt University（赫瑞瓦特大学）
