__Numerical methods in general setting:__

- Low rank structure of hyperbolic systems

*Sparse+Low-energy decomposition for viscous conservation laws*

with Thomas Y. Hou and Hayden Schaeffer, J. Comput. Phys.

*Computing conservation laws with L1 minimization: existence, uniqueness and error analysis*

with Anne Gelb and Xiao Hou, submitted, J. Sci. Comput.

- Low rank structure of elliptic equations

*Randomized sampling for basis functions construction in generalized finite element methods*

with Ke Chen, Jianfeng Lu and Steve Wright, submitted

*Random Sampling and Efficient Algorithms for Multiscale PDEs*

with Ke Chen, Jianfeng Lu and Steve Wright, submitted

__Uncertainties__

- Elliptic type

*Exploring the locally low dimensional structure in solving random elliptic PDEs*

with Thomas Y. Hou and Pengchuan Zhang, accepted, SIAM-Multiscale Model. Simul.

*A sparse decomposition of low rank symmetric positive semi-definite matrices*

with Thomas Y. Hou and Pengchuan Zhang, accepted, SIAM-Multiscale Model. Simul.

- Hyperbolic type

*Uniform regularity for linear kinetic equations with random input based on hypocoercivity*

with Li Wang, SIAM-UQ

*Galerkin Method for Stationary Radiative Transfer Equations with Uncertain Coefficients*

with Xinghui Zhong, Journal of Scientific Computing

*On quantifying uncertainties for the linearized BGK kinetic equation*

with Christian Klingenberg and Marlies Pirner, Proc. 16th Int’l Conf. on Hyperbolic Problems

*Polynomial interpolation of Burgers' equation with randomness*

with Jian-Guo Liu and Ruiwen Shu, submitted to SIAM-UQ

- Information Theory

*Understanding and Predicting Nonlinear Turbulent Dynamical Systems with Information Theory*

with Nan Chen, Xiao Hou and Yingda Li, Atmosphere

__Kinetic theory__

- Boundary layer analysis

*A convergent method for linear half-space kinetic equations*

with Jianfeng Lu and Weiran Sun, finally appeared, ESAIM: M2AN

*Half-space Kinetic Equations with General Boundary Conditions*

with Jianfeng Lu and Weiran Sun, Math Comp

*Diffusion approximations of linear transport equations: asymptotics and numerics*

with Jianfeng Lu and Weiran Sun, J. Comput. Phys.

*Validity and regularization of classical half-space equations*

with Jianfeng Lu and Weiran Sun, J. Stat. Phys.

*A numerical method for coupling the BGK model and Euler equation through the linearized Knudsen layer*

with Hongxu Chen and Jianfeng Lu, revision, J. Comput. Phys. - Inverse problem

*Stability of Stationary Inverse Transport Equation in Diffusion Scaling*

with Ke Chen and Li Wang, Inverse Problems

*A numerical approach to inverse transport equation with error analysis*

with Ruiwen Shu and Li Wang, accepted to SIAM-NA

*Stability of Inverse Transport Equation in Diffusion Scaling and Fokker-Planck limit*

with Ke Chen and Li Wang, accepted by SIAM-AM

*Online learning in optical tomography: a stochastic approach*

with Ke Chen and Jian-Guo Liu, Inverse Problems

*Inverse problems for the stationary transport equation in the diffusion scaling*

with Ru-Yu Lai and Gunther Uhlmann, submitted

*Two-level Markov chain Monte Carlo methods for the inverse radiative transfer equation*

with Kit Newton, Entropy

*Diffusive optical tomography in the Bayesian framework*

with Kit Newton and Andew Stuart, submitted

- Homogenization

*An asymptotic preserving method for transport equations with oscillatory scattering coefficients*

with Jianfeng Lu, SIAM-MMS

*Generalized multiscale finite element method for the steady state linear Boltzmann equa- tion*

with Eric Chung, Yalchin Efendiev and Yanbo Li, submitted, SIAM-MMS

- Asymptotic preserving methods

*A BGK-penalization based asymptotic-preserving scheme for the multi-species Boltzmann equation*

with: Shi Jin, Numer. Methods Partial Diﬀerential Equations

*Exponential Runge–Kutta for the inhomogeneous Boltzmann equations with high order of accuracy*

with Lorenzo Pareschi, J. Comput. Phys.

*Exponential Runge-Kutta based AP scheme for multi-species Boltzmann equation*

with Xu Yang, Commun. Comput. Phys.

*Asymptotic-preserving exponential methods for the quantum Boltzmann equation with high-order accuracy*

with Jingwei Hu and Lorenzo Pareschi, J. Sci. Comput.

*Numerical methods for plasma physics in collisional regimes*

with Giacomo Dimarco, Lorenzo Pareschi and Bokai Yan, invited review, J. Plasma Physics

*Implicit Asymptotic Preserving Method for Linear Transport Equations*

with Li Wang, accepted, Commun. Comput. Phys.

*Asymptotic-Preserving Schemes for Multiscale Hyperbolic and Kinetic Equations" for the book "Handbook on Numerical Methods for Hyperbolic Problems*

with Jingwei Hu and Shi Jin, invited review, Handbook on Numerical Methods for Hyperbolic Problems

__Quantum system with crossing energies__

*Semiclassical models for Schrodinger equations with periodic potentials and band-crossings*

with Lihui Chai and Shi Jin, Kinet. Relat. Models

*Semiclassical model for the surface hopping problem, multiband Wigner approach and domain decomposition method*

with Lihui Chai, Shi Jin and Omar Morandi, SIAM-Multiscale Model. Simul.

__Thesis:__

*Modeling and Computational Methods for Multi-scale Quantum Dynamics and Kinetic Equations*