Numerical methods, applied analysis, and mathematical modeling for
conservation laws, kinetic theory, quantum mechanics, fluid dynamics, social science, and biology.
of inverse transport equation in diffusion scaling and Fokker-Planck
limit (with K. Chen and Q. Li), submitted. [arXiv:1708.03063].
An accurate front capturing scheme for tumor growth models with a free
boundary limit (with J.-G. Liu, M. Tang and Z. Zhou), submitted. [arXiv:1708.08395].
A new numerical approach to inverse transport equation with error analysis (with Q. Li and R. Shu), submitted. [arXiv:1708.01984].
Analysis and computation of some tumor growth models with nutrient:
from cell density models to free boundary dynamics (with J.-G. Liu, M.
Tang and Z. Zhou), submitted. [preprint].
asymptotic-preserving scheme for kinetic equation with anisotropic
scattering: heavy tail equilibrium and degenerate collision frequency
(with B. Yan), submitted. [preprint]
and simulations of particle-laden flow with surface tension (with A.
Mavromoustaki, J. Wong and A. L. Bertozzi), submitted. [preprint]
Stability of stationary inverse transport equation in diffusion scaling (with. K. Chen and Q. Li), Inverse Problems, to appear. [arXiv:1703.00097]
regularity for linear kinetic equations with random input based on
hypocoercivity (with Q. Li), SIAM J. Uncer. Quan., to appear. [arXiv: 1612.01219]
Positivity-preserving and asymptotic preserving method for 2D Keller-Segal equations (with J.-G. Liu and Z. Zhou), Math. Comp., to appear. [preprint]
Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and
Glimm front sampling for scalar hyperbolic conservation laws (with F.
Coquel, S. Jin and J.-G. Liu), Math. Comp., to appear. [preprint]
Implicit asymptotic preserving method for linear transport equation (with Q. Li), Comm. Comput. Phys. 22, issue 1, 157--181, 2017. [link]
numerical schemes for multiscale crowd dynamics with emotional
contagion (with M. Short and A. L. Bertozzi), Math. Models Methods Appl. Sci. 27, no. 1, 205--230, 2017. [link]
An asymptotic-preserving scheme for linear kinetic equation with fractional diffusion limit (with B. Yan), J. Comput. Phys. 312, 157--174, 2016. [link]
The ADI methods for two-dimensional nonlinear multidelay parabolic equations (with Q. Zhang, C. Zhang), J. Comp. Appl. Math. 306, 217--230, 2016.
An asymptotic-preserving scheme for the semiconductor Boltzmann
equation with two-scale collisions: a splitting approach (with J. W. Hu
and S. Jin), Kinetic and Related Models 8, 707-723, 2015. [link]
Rarefaction-singular shock solution for conserved volume gravity
driven particle-laden thin film (with A. Mavromoustaki, A. L. Bertozzi, G. Urdaneta and K. Huang), Phys. Fluids 27, 033301, 2015. [link]
An asymptotic-preserving scheme for the
semiconductor Boltzmann equation toward the energy-transport limit (with J. W. Hu), J. Comput. Phys. 281, 806 - 821, 2015. [link]
Contagion shocks in one dimension (with A. L. Bertozzi, J. Rosado, and M. Short), J. Stat. Phys. 3, Vol. 158, 647 - 664, 2015. [link]
Well-posedness and singular limit of a semilinear hyperbolic relaxation
system with a two-scale discontinuous relaxation rate (with F. Coquel,
S. Jin, and J. G. Liu), Arch. Rat. Mech. Anal. 214, 1051-1084, 2014. [link]
Shock solutions for high
concentration particle laden thin films (with A. L. Bertozzi), SIAM J. Appl.
Math., 74(2), 322 - 344, 2014. [link]
Asymptotic-preserving numerical schemes for the semiconductor Boltzmann
equation efficient in the high field regime (with S. Jin), SIAM J. Sci. Comp. 35, B799 - B819, 2013. [link]
A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations (with S. Jin and J. G. Liu), Math. Comp. 82, 749 -779, 2013. [link]
An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime (with S. Jin) Acta Mathematica Scientia 31, 2219-2232, 2011. Special issue in honor of Peter Lax's 85th birthday. [link]