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I have conducted research in hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics and wave propagations.

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(incomplete) Citation information from Web of Science

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Google Scholar Citation data

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Hyperbolic conservation laws

• Relaxation and Diffusion Enhanced Dispersive Waves (with J.G. Liu), Proceedings of Royal Society London A, 446 (1994), 555-563.
  
• The Relaxation Schemes for Systems of Conservation Laws in Arbitrary Space Dimensions (with Z.P. Xin), Communication on Pure and Applied Mathematics, 48 (1995), 235-276.
  
• Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms , J. Computational Physics, 122 (1995), 51-67.
  
• Numerical Integrations of Systems of Conservation Laws of Mixed Type, SIAM J. Applied Mathematics, 55 (1995), 1536-1551.
  
• Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms (with C.D. Levermore), J. Computational Physics 126 (1996), 449-467.
  
• A Convex Entropy for a Hyperbolic System with Relaxation , J. Differential Equations, 127, 95-107 (1996).
  
• The Effects of Numerical Viscosities I: Slowly Moving Shocks (with J.G. Liu), J. Computational Physics 126 (1996), 373-389.
  
• Modern Shock Capturing Methods for Conservation Laws, invited review paper for "Some New Directions in Science on Computers", eds. G. Bhanot, S.Y. Chen and P. Seiden, World Scientific, pp. 64-90, 1997.
  
• Diffusion Limit of a Hyperbolic System with Relaxation (with H.L. Liu), Methods and Applications of Analysis, 5, 317-334, 1998.
  
• A Diffusive Subcharacteristic Condition for Hyperbolic Systems with Diffusive Relaxation, (with H.L. Liu), Transport Theory and Statistical Physics 29, 583-593, 2000.
  
• Hyperbolic Systems with Supercharacteristic Relaxations and Roll Waves , (with M.A. Katsoulakis), SIAM J. Appl. Math. 61, 273-292, 2000 (electronic).
  
• Asymptotic and Numerical Approximations to Multiscale Hyperbolic and Transport Equations , to appear.
  
• Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms, (with H. Fan and Z.-H. Teng), J. Differential Equations, 168, 270-294, 2000.
  
• The Random Projection Method for Hyperbolic Systems with Stiff Reaction Terms , (with W.Z. Bao), J. Comp. Phys. 163, 216-248, 2000.
  
• On the Computation of Roll Waves , (with Y.J. Kim), Math. Model Num. Anal. 35, 463-480, 2001.
  
• A steady-state capturing method for hyperbolic systems with geometrical source terms , , Math. Model. Num. Anal. 35, 631-646, 2001.
  
• Error Estimates on the Random Projection Methods for Hyperbolic Systems with Stiff Reaction Terms , (with W.Z. Bao), Appl. Num. Math. 43, 315-333, 2002.
  
• Wave Patterns, Stability and Slow Motions in Inviscid and Viscous Hyperbolic Equations with Stiff Reaction Terms, , (with H.T. Fan and J. Miller), J. Diff. Eqn. 189, 267-291, 2003.
  
• Front Motion in Multi-Dimensional Viscous Conservation Laws with Stiff Source Terms Driven by Mean Curvature and Variation of Front Thickness (with H.T. Fan), Quarterly Appl Math. LXI (4), 701-721, 2003.
  
• Numerical Approximations of Pressureless and Isothermal Gas Dynamics, (with F. Bouchut and X.T. Li), SIAM J. Num. Anal. 41, 135-158, 2003.
  
• An efficient method for computing hyperbolic systems with geometrical source terms having concentrations, (with X. Wen), J. Comp. Math. 22, 230-249, 2004.
  
• Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations (with X. Wen), SIAM J. Sci. Comp. 26, 2079-2101, 2005 (electronic).
  
• Convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I: L^1 error estimates, (with Xin Wen), J. Comp. Math. 26, 1-22, 2008.
  
• $l^{1}$-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: a simple proof , (with P. Qi), preprint.
  
• On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations , (with Jingwei Hu), Kinetic and Related Models 4, 517-530, 2011.
  
• A Domain Decomposition Method for Semilinear Hyperbolic Systems with Two-scale Relaxations (with Jian-Guo Liu and Li Wang), Math. Comp., to appear.
  

Kinetic Theory

• The Discrete-Ordinate Method in Diffusive Regime (with C.D. Levermore), Transport Theory and Statistical Physics 20 (1991), 413-439.
  
• Fully-Discrete Numerical Transfer in Diffusive Regimes (with C.D. Levermore), Transport Theory and Statistical Physics 22 (1993), 739-791.
  
• Uniformly Accurate Schemes for Hyperbolic Systems with Relaxations (with R.E. Caflisch and G. Russo), SIAM J. Numerical Analysis 34, 246-281 (1997).
  
• Diffusive Relaxation Schemes for Discrete-Velocity Kinetic Equations (with L. Pareschi and G. Toscani), SIAM J. Numerical Analysis, 35, 2405-2439, 1998.
  
• The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: The Discrete-Ordinate Method (with F. Golse and C.D. Levermore), SIAM J. Numerical Analysis, 36, 1333-1369, 1999.
  
• Efficient Asymptotic-Preserving (AP) Schemes for Some Multiscale Kinetic Equations , SIAM J. Sci. Comp. 21, 441-454, 1999 (electronic).
  
• Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes, , (with L. Pareschi), J. Comp. Phys. 161, 312-330, 2000.
  
• Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations , (with L. Pareschi and G. Toscani), SIAM J. Num. Anal. 38, 913-936, 2000 (electronic).
  
• Regularization of the Burnett Equations via Relaxation , (with M. Slemrod), J. Stat. Phys. 103, 1009-1033, 2001.
  
• Regularization of the Burnett Equations for Fast Granular Flows via Relaxation , (with M. Slemrod), Physica D 150, 207-218, 2001.
  
• Asymptotic-Preserving (AP) Schemes for Multiscale Kinetic Equations: a Unified Approach , (with L. Pareschi), pp 573-582, in Hyperbolic Problems: Theory, Numerics, Applications, Ed. H. Freistuhler and G. Warnecke, Birkhauser-Verlag, Berlin, 2001.
  
• A Relaxation Scheme for Solving the Boltzmann Equation Based on the Chapman-Enskog Expansion (with L. Pareschi and M. Slemrod) , Acta Mathematicas Applicatae Sinica (English Series) 18, 37-62, 2002.
  
• A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem, (with F. Golse and C.D. Levermore), Math. Model Num. Anal., 37, 869-892, 2003.
  
• A smooth transition model between kinetic and diffusion equations, (with P. Degond), SIAM J. Num. Anal. 42, 2671 - 2687, 2005 (electronic)
  
• Numerical study of a domain decomposition method for a two-scale linear transport equation (with X. Yang, F. Golse, Z.Y. Huang), Networks and Heterogeneous Media 1(1), 143-166, 2006.
  
• A Smooth Transition Model Between Kinetic and Hydrodynamic Equations (with P. Degond and L. Mieussens), J. Comp. Phys. 209, 665-694, 2005.
  
• on a uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface (with Min Tang and Houde Han), Networks and Heterogeneous Media 4, 35-65, 2009.
  
• A micro-macro decomposition based asymptotic-preserving scheme for the multispecies Boltzmann equation , (with Yingzhe Shi), SIAM J. Sci. Comp. 31, 4580-4606, 2010.
  
• A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources , (with Francis Filbet), J. Comp. Phys. 229, 7625-7648, 2010.
  
• An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation , (with F. Filbet), J. Sci. Comp., 46, 204-224, 2011.
  
• A numerical scheme for the quantum Boltzmann equation with stiff collision terms , (with Francis Filbet and Jingwei Hu), Math. Model Num. Anal 46, 443-463, 2012.
  
• A class of asymmptotic-preserving schemes for the Fokker-Planck-Landau equation , (with Bokai Yan), J. Comp. Phys. 230, 6420-6437, 2011.
  
• Simulation of fluid-particles flows: heavy particles, flowing regime and asymptotic-preserving schemes, (with T. Goudon and Bokai Yan), Comm. Math. Sci. 10, 355-385, 2012.
  
• Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review. Lecture Notes for Summer School on ''Methods and Models of Kinetic Theory" (M&MKT), Porto Ercole (Grosseto, Italy), June 2010. Rivista di Matematica della Universite  di Parma, to appear.
  
• A numerical scheme for the quantum Fokker-Planck-Landau equation efficient in the fluid regime (with Jingwei Hu and Bokai Yan), Comm. Comp. Phys., to appear.
  
• Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows , (with T. Goudon, J.G. Liu and B. Yan), preprint.
  
• An asymptotic preserving scheme for the Vlasov-Poisson-Fokker-Planck system in the high field regime, (with Li Wang), Acta Mathematica Scientia 31, 2219-2232, 2011 (special issue in honor of Peter Lax's 85th birthday).
• A BGK-penalization asymptotic-preserving scheme for the multispecies Boltzmann equation, (with Qin Li), preprint.
• A successive penalty-based asymptotic-preserving scheme for kinetic equations , (with Bokai Yan), preprint.
• Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density, (with T. Goudon, Jian-Guo Liu and Bokai Yan), preprint.
  
  

Hamilton-Jacobi equations and front propagations

• Relaxation Approximations to Front Propagation (with M. Katsoulakis), Journal of Differential Equations 138, 380-387 (1997).
  
• Numerical Passage from Systems of Conservation Laws to Hamilton-Jacobi Equation, and a Relaxation Scheme (with Z.P. Xin), SIAM J. Numerical Analysis 35, 2385-2404, 1998.
  
• A Model for Front Evolution with a Non-Local Growth Rate , (with X.L. Wang and T.L. Starr), J. Material Research 14, No.10, 3829-3832, 1999.
  
• Relaxation Schemes for Curvature-Dependent Front Propagation , (with M. Katsoulakis and Z.P. Xin), Comm. Pure Appl. Math. 52, 1587-1615, 1999.
  
• Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration I: Two Space Dimension , (with X.L. Wang, T.L. Starr and X.F. Chen), J. Comp. Phys. 162, 467-482, 2000.
  
• Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration II: Two Dimensional Anisotropic Fronts (with X.L. Wang), J. Comp. Phys. 179, 557-577, 2002.
  
• Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration III: Three space Dimension, (with X.L. Wang), J. Comp. Phys. 186, 582-595, 2003.
  

Computational fluid dynamics

• Numerical Methods for Turbines Flow Mixed with Cold Air (with J. Shi, J.S. Li and P.Q. Wang), J. Aerodynamics, 4(4), 305-309 (1989), (in Chinese).
  
• Physical Symmetry and Lattice Symmetry in Lattice Boltzmann Method (with N. Cao, S.Y. Chen and D. Martinez), Physical Review E 55, 21 (1997).
  
• Application of Relaxation Scheme to Wave Propagation Simulation in Open-Channel Networks (with M.M. Aral and Y. Zhang), J. Hydraulic Engineering 124, 1125-1133, 1998.
  
• High-Order I-Stable Central Difference Schemes for Viscous Compressible Flows , (with W.Z. Bao), J. Comp. Math. 21, 101-112, 2003.
  
• Weakly Compressible High-Order I-Stable Central Difference Schemes for Incompressible Viscous Flows , (with W.Z. Bao), Comput. Methods Appl. Mech. Eng., 190, 5009-5026, 2001.
  
• The Random Projection Method for Stiff Detonation Waves , (with W.Z. Bao), SIAM J. Sci. Comp. 23, 1000-1026, 2001.
  
• The Random Projection Method for Stiff Multi-Species Detonation Capturing , (with W.Z. Bao), J. Comp. Phys. 178, 37-57, 2002.
  
• Mach-number uniform asymptotic-preserving gauge schemes for compressible flows (with Pierre Degond and Jian-Guo Liu), Bulletin of the Institute of Mathematics, Academia Sinica, New Series, 2, No. 4, 851-892, 2007.
  
• An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equation , (with Jeffrey Haack and Jian-Guo Liu), Commun. Comp. Phys. 12 (2012), pp. 955-980.
  

High frequency wave propagation and Semiclassical Limit

High Frequency Behavior of the Focusing Nonlinear Schroedinger Equation with Random Inhomogeneities , (with A. Fannjiang and G. Papanicolaou), SIAM J. Appl. Math. 63, 1328 - 1358, 2003 (electronic).
On Time-Splitting Spectral Approximations for the Schrodinger Equation in the Semiclassical Regime, (with W.Z. Bao and P. Markowich), J. Comp. Phys., 175, 487-524, 2002.
Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrodinger Equations in the Semi-Classical Regimes (with W.Z. Bao and P. Markowich), SIAM J. Sci. Comp.25, 27-64, 2003 (elctronic).
Multi-phase Computations of the Semiclassical Limit of the Schrodinger Equation and Related Problems: Whitham vs. Wigner, (with X.T. Li), Physica D 182, 46-85, 2003.
On Two Moment Systems for Computing Multiphase Semiclassical Limit of the Schrodinger Equation, (with L. Gosse and X.T. Li), Math. Models Meth. Appl. Sci. 13, No. 12, 1689-1723, 2003.
An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons, (with X.T. Li, J.G. Wohlbier and J.H. Booske), Phys Rev E 70, 016502, 2004.
A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations, (with S. Osher), Comm. Math. Sci. 1(3), 575-591, 2003.
Computing multivalued physical observables for the semiclassical limit of the Schrodinger equations, (with H.L. Liu, S. Osher and R. Tsai), J. Comp. Phys. 205, 222-241, 2005.
Numerical simulation of a generalized Zakharov system (with P.A. Markowich and C.X. Zheng), J. Comp. Phys. 201, 376-395, 2004.
A time-splitting spectral method for the generlized Zakharov system in multi-dimensions (with C.X. Zheng), J. Sci. Comp. 26, 127-149, 2006.
Eulerian calculations of electron overtaking in a traveling wave tube, (with J.G. Wohlbier and S. Sengele), Phys. of Plasmas 12, 023106, 2005.
A time-splitting spectral scheme for the Maxwell-Dirac system (with Z.Y. Huang, Peter A. Markowich, Christof Sparber and C.X. Zheng), J. Comp. Phys., 208, 761-789, 2005.
Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials (with X. Wen), Comm. Math. Sci. 3, 285-315, 2005.
Computing multi-valued physical observables for high frequency limit of symmetric hyperbolic systems (with H. Liu, S. Osher and R. Tsai), J. Comp. Phys. 210, 497-518, 2005.
Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds, (with X. Wen), J. Comp. Phys. 214, 672-697, 2006.
Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with partial transmissions and reflections (with X. Wen), SIAM J. Num. Anal. 44, 1801-1828, 2006.
The l^1-stability of a Hamiltonian-preserving scheme for the Liouville equation with discontinuous potentials (with X. Wen), J. Comp. Math. 27 (2009), pp. 45-67.
Computation of Transmissions and Reflections in Geometrical Optics via the Reduced Liouville Equation (with X. Wen), Wave Motion 43(8), 667-688, 2006.
A Hamiltonian-preserving scheme for high frequency elastic waves in heterogeneous media (with Xiaomei Liao), J. Hyperbolic Diff. Eqn. 3, No. 4, 741-777, 2006.
A Bloch decomposition based time-splitting pseudospectral method for quantum dynamics with periodic potentials (with Z.Y. Huang, P.A. Markowich and C. Sparber), SIAM J. Sci. Comp. 29, 515-538, 2007.
A Semiclassical Transport Model for Thin Quantum Barriers (with k. Novak), Multiscale Modeling and Simulation, 5(4), 1063-1086, 2006.
Computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit (with X. Liao and X. Yang), SIAM J. Sci. Comp., 30, 1992-2017, 2008.
Computational high frequency waves through curved interfaces via the Loiuville equation and Geometric Theory of Diffraction, (with Dongsheng Yin), J. Comp. Phys. 227, 6106-6139, 2008.
Computation of the semiclassical limit of the Schrodinger equation with phase shift by a level set method (with Xu Yang), J. Sci. Comp. 35, Nos. 2-3, 144-169, 2008.
A Semiclassical Transport Model for Two-Dimensional Thin Quantum Barriers (with K. Novak), J. Comp. Phys. 226, 1623-1644, 2007.
The Vlasov-Poisson equations as the semiclassical Limit of the Schrodinger-Poisson Equations: a numerical study (with Xiaomei Liao and Xu Yang), J. Hyperbolic Diff. Eqn. 5(3), 569-587, 2008.
Numerical simulation of the nonlinear Schrodinger equation with multi-dimensional periodic potentials (with Z.Y. Huang, P.A. Markowich and C. Sparber), SIAM Multiscale Modeling and Simulation 7, 539-564, 2008.
On the time-splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit (with P. Degond and Min Tang), SIAM J. Sci. Comp. 30, 2466-2487, 2008.
The l^1-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials (with Xin Wen), SIAM J. Num. Anal. 46, 2688-2714, 2008.
Recent computational methods for high frequency waves in heterogeneous media, , preprint.
A domain decomposition method for a two-scale transport equation with energy flux conserved at the interface, (with X. Yang and G.W. Yuan) , Kinetic and Related Models, 1, 65-84, 2008.
A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians , (with H. Wu and Z.Y. Huang), SIAM J. Sci. Comput. 31, 1303-1321, 2008.
On the Bloch decomposition based spectral method for wave propagation in periodic media , (with Z.Y. Huang, P.A. Markowich and C. Sparber ), Wave Motion 46, 15-28, 2009.
Computation of high frequency wave diffraction by a half plane via the Loiuville equation and Geometric Theory of Diffraction, (with Dongsheng Yin), Comm. Comput. Phys., 4, No. 5, 1106-1128, 2008.
Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations , (with H. Wu and X. Yang), Comm. Math. Sci. 6, 995-1020, 2008.
A coherent semiclassical transport model for pure-state quantum scattering , (with K. Novak) Comm. Math. Sci. 8, 253-275, 2010.
Bloch Decomposition-Based Gaussian Beam Method for the Schr\"odinger equation with Periodic Potentials , (with Hao Wu, Xu Yang and Zhongyi Huang) J. Comp. Phys. 229, 4869-4883, 2010.
A numerical study of the Gaussian beam methods for one-dimensional Schr\"odinger-Poisson equations , (with Hao Wu and Xu Yang), J. Comp. Math. 28, 261-272, 2010.
Semi-Eulerian and High Order Gaussian Beam Methods for the Schrodinger Equation in the Semiclassical Regime , (with Hao Wu and Xu Yang), Comm. Comp. Phys., 9, 668-687, 2011.
An Eulerian surface hopping method for the Schr\"{o}dinger equation with conical crossings , (with Peng Qi and Zhiwen Zhang), SIAM Multiscale Modeling & Simulation 9, 258-281, 2011.
A level set method for the semiclassical limit of the Schrodinger equation with discontinuous potentials , (with Dongming Wei, Richard Tsai and Xu Yang), J. Comp. Phys. 229, 7440-7455, 2010.
Computational High Frequency Wave Diffraction by a Corner via the Liouville equation and Geometric Theory of Diffraction , (with Dongsheng Yin), Kinetic and Related Models 4, 295-316, 2011.
On the random choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds , (with Jingwei Hu), preprint.
Mathematical and computational methods for semiclassical Schrodinger equations , (with P.A. Markowich and C. Sparber), Acta Numerica 20, 211-289, 2011.
A novel numerical method for the semiclassical limit of the Schrodinger equation and the Vlasov-Poisson equations, (with Dongming Wei, preprint.
A Hybrid Schr\"odinger/Gaussian Beam Solver for Quantum Barriers and Surface Hopping, (with Peng Qi), Kinetic and Related Models 4, 1097-1120, 2011.
Gaussian beam methods for the Dirac equation in the semi-classical regime, , (with Hao Wu, Zhongyi Huang, and Dongsheng Yin), Comm. Math. Sci., to appear.
Gaussian beam methods for the Schrodinger equation with discontinuous potentials, (with Dongming Wei and Dongsheng Yin), preprint.
The Gaussian beam method for the Wigner equation with discontinuous potentials, (with Dongsheng Yin and Min Tang), preprint.