I have conducted research in hyperbolic conservation laws, kinetic theory, Hamilton-Jacobi equations and front propagations, computational fluid dynamics, high frequency wave propagations, semiclassical limit in quantum dynamics, and uncertainty quantification.

(incomplete) Citation information from Web of Science

Google Scholar Citation data

Honors, Awards and Fellowships

Invited Lectures

Former Ph.D. students

Editorships

Committees

**In refereed journals****Submitted**

[186] J. Carrillo, Shi Jin, Lei Li and Yuhua Zhu,

*A consensus-based global optimization method for high dimensional machine learning problems,*

[185] Esther Daus, Shi Jin and Liu Liu,

*On the multi-species Boltzmann equation with uncertainty and its stochastic Galerkin approximation,*

[184] Shi Jin and Ruiwen Shu,

*Collective dynamics of opposing groups with stochastic communication,*

[183] F. Golse, Shi Jin and T. Paul,

*On the Convergence of Time Splitting Methods for Quantum Dynamics in the Semiclassical Regime,*

[182] Xin Liu, Xi Chen, Shi Jin, Alexander Kurganov, and Hui Yu,

*Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System,*

[181] Shi Jin, Liu Liu, Giovanni Russo and Zhennan Zhou,

*Gaussian wave packet transform based numerical scheme for the semi-classical Schrodinger equation with random inputs,*

[180] Seung-Yeal Ha, Shi Jin, Jinwook Jung and Woojoo Shim,

*A local sensitivity analysis for the hydrodynamic Cucker-Smale model with random inputs,*

[179] Zhiyan Ding, Seung-Yeal Ha and Shi Jin,

*A local sensitivity analysis in Landau Damping for the kinetic Kuramoto equation with random inputs,*

[178] Seung-Yeal Ha, Shi Jin, and Jinwook Jung,

*Local sensitivity analysis for the Kuramoto model with random inputs in a large coupling regime,*preprint.

[177] N. Crouseilles, S. Jin, M. Lemou and F. Mehats,

*A micro-macro method for a kinetic graphene model in one-space dimension*, preprint.

[176] N. Crouseilles, Shi Jin, M. Lemou and Liu Liu,

*Nonlinear Geometric Optics Based Multiscale Stochastic Galerkin Methods for Highly Oscillatory Transport Equations with Random Inputs,*

[175] Alina Chertock, Shi Jin and Alexander Kurganov,

*A well-balanced operator splitting based stochastic Galerkin method for the one-dimensional Saint-Venant system with uncertainty**,*Preprint.

[174] Alina Chertock, Shi Jin and Alexander Kurganov,

*An operator splitting based stochastic Galerkin method for the one-dimensional compressible Euler equations with uncertainty**,*Preprint.

**Accepted**[173] I. Gamba, Shi Jin and Liu Liu,

*Asymptotic-preserving schemes for two-species binary collisional kinetic system with disparate masses I: time discretization and asymptotic analysis,*

[172] Anton Arnold, Shi Jin and Tobias Wohrer,

*Sharp Decay Estimates in Local Sensitivity Analysis for Evolution Equations with Uncertainties: from ODEs to Linear Kinetic Equations,*

[171] Di Fang, Shi Jin, P.A. Markowich and B. Perthame,

*Implicit and Semi-implicit Numerical Schemes for the Gradient Flow of the Formation of Biological Transport Networks,*

[170] Shi Jin, Lei Li and Jian-Guo Liu,

*Random Batch Methods (RBM) for interacting particle systems*

[169] Jingwei Hu, Shi Jin, and Ruiwen Shu,

*On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime,*

**2019**[168] Di Fang, Seung-yeal Ha and Shi Jin,

*Emergent behaviors of the Cucker-Smale emsemble under attractive-repulsive couplings and Rayleigh frictions,*

[167] Shi Jin and Ruiwen Shu,

*A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty,*

[166] Zhiyan Ding and Shi Jin,

*Random regularity of a nonlinear Landau Damping solution for the Vlasov-Poisson equations with random inputs,*

[165] Yingda Li and Shi Jin,

*Local sensitivity analysis and spectral convergence of the stochastic Galerkin method for discrete-velocity Boltzmann equations with multi-scales and random inputs,*

[164] E.S. Daus, Shi Jin and Liu Liu,

*Spectral convergence of the stochastic Galerkin approximation to the Boltzmann equation with multiple scales and large random perturbation in the collision kernel,*

[163] Seung-Yeal Ha, Shi Jin, and Jinwook Jung,

*A local sensitivity analysis for the kinetic Kuramoto model with random inputs,*Networks and Heterogeneous Media 14, 317-340, 2019.

[162] Ruiwen Shu and Shi Jin,

*A study of Landau damping with random initial inputs,*J. Diff. Eqn., 266, 1922-1945, 2019.

[161] I. Gamba, Shi Jin and Liu Liu,

*Micro-macro decomposition based asymptotic-preserving numerical schemes and numerical moments conservation for collisional nonlinear kinetic equations,*

**2018**[160] Shi Jin, Hanqing Lu and Lorenzo Pareschi,

*A High Order Stochastic Asymptotic Preserving Scheme for Chemotaxis Kinetic Models with Random Inputs,*

[159] Ruiwen Shu and Shi Jin,

*Uniform regularity in the random space and spectral accuracy of the stochastic Galerkin method for a kinetic-fluid two-phase flow model with random initial inputs in the light particle regime,*

[158] Jingwei Hu, Shi Jin and Ruiwen Shu,

*A stochastic Galerkin method for the Fokker-Planck-Landau equation with random uncertainties,*

[157] Seung-Yeal Ha, Shi Jin, and Jinwook Jung,

*A local sensitivity analysis for the kinetic Cucker-Smale model with random inputs,*J. Diff. Eqn. 265, 3618-3649, 2018.

[156] Shi Jin and Minh-Binh Tran,

*Quantum hydrodynamic approximations to the finite temperature trapped Bose gases,*

[155] Shi Jin,

*Mathematical Analysis and Numerical Methods for Multiscale Kinetic Equations with Uncertainties,*

[154] Liu Liu and Shi Jin,

*Hypocoercivity based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs,*[153] Di Fang, Shi Jin and Christof Sparber,

*An efficient time-splitting method for the Ehrenfest dynamics,*

[152] Lihui Chai, Shi Jin and P.A. Markowich,

*A hybrid method for computing the Schrodinger equations with periodic potential with band-crossings in the momentum space**,*Comm. Comp. Phys. 24, 989-1020, 2018. (a special issue in honor of the 80th birthday of Prof. Houde Han).

[151] Shi Jin and Yuhua Zhu,

*Hypocoercivity and Uniform Regularity for the Vlasov-Poisson-Fokker-Planck System with Uncertainty and Multiple Scales,*

[150] Seung-Yeal Ha and Shi Jin,

*Local sensitivity analysis for the Cucker-Smale model with random inputs,*

[149] Shi Jin, Hanqing Lu and Lorenzo Pareschi,

*Efficient stochastic Asymptotic-preserving IMEX methods for transport equations with diffusive scalings and random inputs,*

[148] Frederic Coquel, Shi Jin, Jian-Guo Liu and Li Wang,

*Entropic sub-cell shock capturing schemes via Jin-Xin relaxation and Glimm front sampling for scalar hyperbolic conservation laws**,*Math. Comp. 87, 1083-1126, 2018

[147] Shi Jin and Zheng Ma,*The discrete stochastic Galerkin method for hyperbolic equations with non-smooth and random coefficeints,*

**2017**[146] Jingwei Hu and Shi Jin,

**Uncertainty Quantification for Kinetic Equations,**

[145] Shi Jin, Jian-Guo Liu and Zheng Ma, Uniform spectral convergence of the stochastic Galerkin method for the linear transport equations with random inputs in diffusive regime and a micro-macro decomposition based asymptotic preserving method, , Research in Math. Sci.,(a special issue in honor of the 70th birthday of Bjorn Engquist), 4:15, 2017. DOI 10.1186/s40687-017-0105-1. (

**(inaugural) Best Article Award**, Research in the Mathematical Sciences)

[144] Yuhua Zhu and Shi Jin,

*The Vlasov-Poisson-Fokker-Planck system with uncertainty and a one-dimensional asymptotic-preserving method**,*SIAM Multiscale Model. Simul., 15, 1502-1529, 2017.

[143] Nicolas Crouseilles, Shi Jin and Mohammed Lemou,

*Nonlinear geometric optics method based multi-scale numerical schemes for a class of highly-oscillatory transport equations**,*Math. Model Methods Applied Sci., 27, 2031-2070, 2017.

[142] Ruiwen Shu, Jingwei Hu and Shi Jin,

*A Stochastic Galerkin Method for the Boltzmann Equation with multi-dimensional random inputs using sparse wavelet bases,*

[141] Shi Jin and Ruiwen Shu,*A stochastic Asymptotic-Preserving scheme for a kinetic-fluid model for disperse two-phase flows with uncertainty**,*J. Comp. Phys., 335, 905-924, 2017.

[140] Shi Jin and Hanqing Lu,

*An Asymptotic-Preserving Stochastic Galerkin Method for the Radiative Heat Transfer Equations with Random Inputs and Diffusive Scalings**,*J. Comp. Phys., 334, 182-206, 2017.[139] Shi Jin and Liu Liu,

*An Asymptotic-Preserving Stochastic Galerkin Method for the Semiconductor Boltzmann Equation with Random Inputs and Diffusive Scalings*

[138] Jingwwei Hu, Shi Jin and Qin Li,

*Asymptotic-Preserving schemes for multiscale hyperbolic and kinetic equations**,*Handbook of Numerical Methods for Hyperbolic Problems, (ed. by R. Abgrall and C.-W. Shu), North Holland/Elsevier, Vol 18, 103-129, 2017.

[137] Ali Faraj and Shi Jin,

*The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene**,*Comm. Comp. Phys., 21, 313-357, 2017.

[136] Shi Jin, C. Sparber and Zhennan Zhou,

*On the classical limit of a time-dependent self-consistent field system: analysis and computation,*

**2016**[135] Jingwei Hu and Shi Jin,

*A stochastic Galerkin method for the Boltzmann equation with uncertainty**,*J. Comp. Phys. 315, 150-168, 2016.

[134] Shi Jin, Dongbin Xiu and Xueyu Zhu,

*A well-balanced stochastic Galerkin method for scalar hyperbolic balance laws with random inputs**,*J. Sci. Comp., 67, 1198-1218, 2016.

[133] Kerstin Kupper, Martin Frank and Shi Jin,

*An asymptotic-preserving 2-D staggered grid method for multiscale transport equations,**,*SIAM J. Num. Anal., 54, 440-461, 2016.

[132] Bin Zhang, Hong Liu and Shi Jin,

*An Asymptotic Preserving Monte Carlo Method for the Multispecies Boltzmann Equation**,*J. Comp. Phys. 305, 575-588, 2016.

**2015**[131] Shi Jin,

*Schrodinger equation: Computation,*

[130] Jingwei Hu, Shi Jin, and Dongbin Xiu,

*A stochastic Galerkin method for Hamilton-Jacobi equations with uncertainty,**,*SIAM J. Sci. Comput. 37, A2246-A2269, 2015.

[129] Jingwei Hu, Shi Jin, and Li Wang,

*An asymptotic-preserving scheme for the semiconductor Boltzmann equation with two-scale collisions: a splitting approach,**,*Kinetic and Related Models 8, 707-723, 2015.

[128] L. Jefferis and S. Jin,

*A Gaussian Beam Method for High Frequency Solution of Symmetric Hyperbolic Systems with Polarized Waves,*

[127] Shi Jin, Dongbin Xiu and Xueyu Zhu,

*Asymptotic-preserving methods for hyperbolic and transport equations with random inputs and diffusive scalings,**,*J. Comp. Phys. 289, 35-52, 2015.

[126] L. Jefferis and Shi Jin,*Computing high frequency solutions of symmetric hyperbolic systems with polarized waves,*

[125] Lihui Chai, Shi Jin, Qin Li and Omar Morandi,

*A multi-band semi-classical model for surface hopping quantum dynamics,**,*SIAM Multiscale Modeling and Simulation, 13, 205-230, 2015.

**2014**[124] F. Coquel, S. Jin, J.-G. Liu and Li Wang,

*Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate,*

[123] W. Ren, H. Liu and S. Jin,

*An Asymptotic-Preserving Monte Carlo Method for the Boltzmann Equation,**,*J. Comp. Phys. 276, 380-404, 2014.

[122] T. Goudon, S. Jin, Jian-Guo Liu, and Bokai Yan,

*Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density**,*, International Journal for Numerical Methods in Fluids 75, 81-102, 2014.

[121] S. Jin, D. Wei and D. Yin,

*Gaussian beam methods for the Schrodinger equation with discontinuous potentials**,*J. Comp. Appl. Math. 265, 199-219, 2014 (a special issue in honor of Prof. Benyu Guo's 70th birthday).

**2013**[120] S. Jin and Z. Zhou,

*A semi-Lagrangian time splitting method for the Schrodinger equation with vector potentials,*

[119] S. Jin and P. Qi,

*$l^{1}$-error estimates on the immersed interface upwind scheme for linear convection equations with piecewise constant coefficients: a simple proof*

[118] Jingwei Hu and Shi Jin,

*On the quasi-random choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds*

[117] Dongsheng Yin, Min Tang and Shi Jin,

*The Gaussian beam method for the Wigner equation with discontinuous potentials**,*Inverse Problems and Imaging 7, 1051-1074, 2013 (a special issue in honor of the 60th birthday of Tony Chan).

[116] Shi Jin and Li Wang,

*Asymptotic-preserving numerical schemes for the semiconductor Boltzmann equation efficient in the high field regime,*

[115] Lihui Chai, Shi Jin, and Qin Li,

*Semiclassical Models for the Schrodinger Equation with Periodic Potentials and Band Crossings,*

[114] T. Goudon, S. Jin, J.G. Liu and B. Yan

*Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows**,*J. Comp. Phys. 246, 145-164, 2013.

[113] Bokai Yan and Shi Jin,

*A successive penalty-based asymptotic-preserving scheme for kinetic equations**,*SIAM J. Sci. Comput. 35, A150-A172, 2013.

[112] Shi Jin and Qin Li,

*A BGK-penalization asymptotic-preserving scheme for the multispecies Boltzmann equation**,*(with Qin Li), Numerical Methods for Partial Differential Equations, 29, 1056-1080, 2013.

[111] Shi Jin, Jian-Guo Liu and Li Wang

*A Domain Decomposition Method for Semilinear Hyperbolic Systems with Two-scale Relaxations*, Math. Comp. 82, 749-779, 2013.

**2012**[110] S. Jin and D. Wei,

*A particle method for the semiclassical limit of the Schrodinger equation and the Vlasov-Poisson equations,*, SIAM J. Num. Anal. 50, 3259-3279, 2012.

[109]

*Gaussian beam methods for the Dirac equation in the semi-classical regime,**,*(with Hao Wu, Zhongyi Huang, and Dongsheng Yin), Comm. Math. Sci. 10, 1301-1315, 2012.

[108]

*A numerical scheme for the quantum Fokker-Planck-Landau equation efficient in the fluid regime*(with Jingwei Hu and Bokai Yan), Commn. Comp. Phys. 12, 1541-1561, 2012.

[107]

*Asymptotic preserving (AP) schemes for multiscale kinetic and hyperbolic equations: a review.*

[106]

*An all-speed asymptotic-preserving method for the isentropic Euler and Navier-Stokes equation*

[105]

*A numerical scheme for the quantum Boltzmann equation with stiff collision terms*

[104]

*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.

**2011**[103]

*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).

[102]

*A Hybrid Schrodinger/Gaussian Beam Solver for Quantum Barriers and Surface Hopping,*

[101]

*A class of asymmptotic-preserving schemes for the Fokker-Planck-Landau equation*

[100]

**Mathematical and computational methods for semiclassical Schrodinger equations**

[99]

*On Kinetic Flux Vector Splitting Schemes for Quantum Euler Equations*

[98]

*An Eulerian surface hopping method for the Schr\"{o}dinger equation with conical crossings*

[97]

*Computational High Frequency Wave Diffraction by a Corner via the Liouville equation and Geometric Theory of Diffraction*

[96]

*An asymptotic preserving scheme for the ES-BGK model of the Boltzmann equation*

[95]

*Semi-Eulerian and High Order Gaussian Beam Methods for the Schrodinger Equation in the Semiclassical Regime*

**2010**[94]

*A class of asymptotic preserving schemes for kinetic equations and related problems with stiff sources***( On the list of the most cited papers of J. Comp. Phys. published since 2010) (No. 8 by Sept 2015) .**

[93]

*A level set method for the semiclassical limit of the Schrodinger equation with discontinuous potentials*

[92]

*Bloch Decomposition-Based Gaussian Beam Method for the Schr\"odinger equation with Periodic Potentials*

[91]

*A micro-macro decomposition based asymptotic-preserving scheme for the multispecies Boltzmann equation*

[90]

*A numerical study of the Gaussian beam methods for one-dimensional Schr\"odinger-Poisson equations*

[89]

*A coherent semiclassical transport model for pure-state quantum scattering*

**2009**[88]

*Recent computational methods for high frequency waves in heterogeneous media,*

[87]

*Numerical methods for hyperbolic systems with singular coefficients: well-balanced scheme, Hamiltonian preservation, and beyond,*

[86]

*On a uniformly second order numerical method for the one-dimensional discrete-ordinate transport equation and its diffusion limit with interface*

[85]

*The l^1-stability of a Hamiltonian-preserving scheme for the Liouville equation with discontinuous potentials*

[84]

*On the Bloch decomposition based spectral method for wave propagation in periodic media*

**2008**[83]

*A Hybrid Phase-Flow Method for Hamiltonian Systems with Discontinuous Hamiltonians*

[82]

*Gaussian beam methods for the Schrodinger equation in the semi-classical regime: Lagrangian and Eulerian formulations*

[81]

*On the time-splitting spectral method for the complex Ginzburg-Landau equation in the large time and space scale limit*

[80]

*The Vlasov-Poisson equations as the semiclassical Limit of the Schrodinger-Poisson Equations: a numerical study*

[79]

*The l^1-error estimates for a Hamiltonian-preserving scheme for the Liouville equation with piecewise constant potentials*

[78]

*Computation of the semiclassical limit of the Schrodinger equation with phase shift by a level set method*

[77]

*Computation of high frequency wave diffraction by a half plane via the Loiuville equation and Geometric Theory of Diffraction,*

[76]

*Numerical simulation of the nonlinear Schrodinger equation with multi-dimensional periodic potentials*

[75]

*Computational high frequency waves through curved interfaces via the Loiuville equation and Geometric Theory of Diffraction,*

[74]

*Computation of interface reflection and regular or diffuse transmission of the planar symmetric radiative transfer equation with isotropic scattering and its diffusion limit*

[73]

*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.

[72]

*Convergence of an immersed interface upwind scheme for linear advection equations with piecewise constant coefficients I: L^1-error estimates*

**2007**[71]

*Mach-number uniform asymptotic-preserving gauge schemes for compressible flows*

[70]

*A Semiclassical Transport Model for Two-Dimensional Thin Quantum Barriers*

[69]

*A Bloch decomposition based time-splitting pseudospectral method for quantum dynamics with periodic potentials*

**2006**[68]

*A Hamiltonian-preserving scheme for high frequency elastic waves in heterogeneous media*

[67]

*Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with partial transmissions and reflections*

[66]

*A Semiclassical Transport Model for Thin Quantum Barriers*

[65]

*Computation of Transmissions and Reflections in Geometrical Optics via the Reduced Liouville Equation*

[64]

*Hamiltonian-preserving schemes for the Liouville equation of geometrical optics with discontinuous local wave speeds,*

[63]

*A time-splitting spectral method for the generlized Zakharov system in multi-dimensions*

[62]

*Numerical study of a domain decomposition method for a two-scale linear transport equation*

**2005**[61]

*Computing multi-valued physical observables for high frequency limit of symmetric hyperbolic systems*

[60]

*Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having concentrations*

[59]

*Hamiltonian-preserving schemes for the Liouville equation with discontinuous potentials*

[58]

*A Smooth Transition Model Between Kinetic and Hydrodynamic Equations*

[57]

*A time-splitting spectral scheme for the Maxwell-Dirac system*

[56]

*A smooth transition model between kinetic and diffusion equations,*

[55]

*Computing multivalued physical observables for the semiclassical limit of the Schrodinger equations,*

[54]

*Eulerian calculations of electron overtaking and multi-valued solutions in a traveling wave tube,*

**2004**[53]

*Numerical simulation of a generalized Zakharov system*

[52]

*An Eulerian method for computing multi-valued solutions of the Euler-Poisson equations and applications to wave breaking in klystrons,*

[51]

*An efficient method for computing hyperbolic systems with geometrical source terms having concentrations,*

**2003**[50]

*On Two Moment Systems for Computing Multiphase Semiclassical Limits of the Schrodinger Equation,*

[49]

*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.

[48]

*A Domain Decomposition Analysis for a Two-Scale Linear Transport Problem,*

[47]

*A level set method for the computation of multivalued solutions to quasi-linear hyperbolic PDEs and Hamilton-Jacobi equations,*

[46]

*Numerical Study of Time-Splitting Spectral Discretizations of Nonlinear Schrodinger Equations in the Semi-clasical Regimes*(with W.Z. Bao and P. Markowich), SIAM J. Sci. Comp. 25, 27-64, 2003 (elctronic).

[45]

*Multi-phase Computations of the Semiclassical Limit of the Schrodinger Equation and Related Problems: Whitham vs. Wigner,*

[44]

*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).

[43]

*Robust Numerical Simulation of Porosity Evolution in Chemical Vapor Infiltration III: Three Space Dimension,*

[42]

*Numerical Approximations of Pressureless and Isothermal Gas Dynamics,*

[41]

*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.

[40]

*High-Order I-Stable Central Difference Schemes for Viscous Compressible Flows*, (with W.Z. Bao), J. Comp. Math. 21, 101-112, 2003

**2002**[39]

*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

[38]

*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

[37]

*The Random Projection Method for Stiff Multi-Species Detonation Capturing*, (with W.Z. Bao), J. Comp. Phys. 178, 37-57, 2002.

[36]

*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.

[35]

*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.

**2001**[34]

*The Random Projection Method for Stiff Detonation Waves*, (with W.Z. Bao), SIAM J. Sci. Comp. 23, 1000-1026, 2001.

[33]

*A steady-state capturing method for hyperbolic systems with geometrical source terms*, , Math. Model. Num. Anal. 35, 631-646, 2001.

[32]

*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.

[31]

*Regularization of the Burnett Equations via Relaxation*, (with M. Slemrod), J. Stat. Phys. 103, 1009-1033, 2001.

[30]

*On the Computation of Roll Waves*, (with Y.J. Kim), Math. Model. Num. Anal. 35, 463-480, 2001.

[29]

*Regularization of the Burnett Equations for Fast Granular Flows via Relaxation*, (with M. Slemrod), Physica D 150, 207-218, 2001.

**2000**[28]

*Zero Reaction Limit for Hyperbolic Conservation Laws with Source Terms*, (with H. Fan and Z.-H. Teng), J. Differential Equations 168, 270-294, 2000.

[27]

*The Random Projection Method for Hyperbolic Systems with Stiff Reaction Terms*, (with W.Z. Bao), J. Comp. Phys. 163, 216-248, 2000

[26]

*Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations*, (with L. Pareschi and G. Toscani), SIAM J. Num. Anal. 38, 913-936, 2000 (electronic).

[25]

*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.

[24]

*Hyperbolic Systems with Supercharacteristic Relaxations and Roll Waves*, (with M.A. Katsoulakis), SIAM J. Appl. Math. 61, 273-292, 2000 (electronic).

[23]

*A Diffusive Subcharacteristic Condition for Hyperbolic Systems with Diffusive Relaxation*, (with H.L. Liu), Transport Theory and Statistical Physics 29, 583-593, 2000.

[22]

*Discretization of the Multiscale Semiconductor Boltzmann Equation by Diffusive Relaxation Schemes,*, (with L. Pareschi), J. Comp. Phys. 161, 312-330, 2000.

**1999**[21]

*Relaxation Schemes for Curvature-Dependent Front Propagation*, (with M. Katsoulakis and Z.P. Xin), Comm. Pure Appl. Math. 52, 1587-1615, 1999.

[20]

*Efficient Asymptotic-Preserving (AP) Schemes for Some Multiscale Kinetic Equations*, SIAM J. Sci. Comp. 21, 441-454, 1999 (electronic).

[19]

*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.

[18]

*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.

**1998**[17]

*Diffusive Relaxation Schemes for Discrete-Velocity Kinetic Equations*(with L. Pareschi and G. Toscani), SIAM J. Numerical Analysis, 35, 2405-2439, 1998.

[16]

*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.

[15]

*Diffusion Limit of a Hyperbolic System with Relaxation*(with H.L. Liu), Methods and Applications of Analysis, 5, 317-334, 1998.

[14]

*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.

**1997**[13]

*Relaxation Approximations to Front Propagation*(with M. Katsoulakis), Journal of Differential Equations 138, 380-387 (1997).

[12]

*Uniformly Accurate Schemes for Hyperbolic Systems with Relaxations*(with R.E. Caflisch and G. Russo), SIAM J. Numerical Analysis 34, 246-281 (1997).

[11]

*Physical Symmetry and Lattice Symmetry in Lattice Boltzmann Method*(with N. Cao, S.Y. Chen and D. Martinez), Physical Review E 55, 21 (1997).

**1996**[10]

*The Effects of Numerical Viscosities I: Slowly Moving Shocks*(with J.G. Liu), J. Computational Physics 126 (1996), 373-389.

[9]

*A Convex Entropy for a Hyperbolic System with Relaxation*, J. Differential Equations, 127, 95-107 (1996).

[8]

*Numerical Schemes for Hyperbolic Conservation Laws with Stiff Relaxation Terms*(with C.D. Levermore), J. Computational Physics 126 (1996), 449-467.

**1995**[7]

*Numerical Integrations of Systems of Conservation Laws of Mixed Type,*SIAM J. Applied Mathematics, 55 (1995), 1536-1551.

[6]

*Runge-Kutta Methods for Hyperbolic Conservation Laws with Stiff Relaxation Terms*, J. Computational Physics, 122 (1995), 51-67.

[5]

*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.

**1994**[4]

*Relaxation and Diffusion Enhanced Dispersive Waves*(with J.G. Liu), Proceedings of Royal Society London A, 446 (1994), 555-563.

**1993**[3]

*Fully-Discrete Numerical Transfer in Diffusive Regimes*(with C.D. Levermore), Transport Theory and Statistical Physics 22 (1993), 739-791.

**1991**[2]

*The Discrete-Ordinate Method in Diffusive Regime*(with C.D. Levermore), Transport Theory and Statistical Physics 20 (1991), 413-439.

**1989**[1]

*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).

[10]
*Multi-phase computations of the semiclassical limit of the
Schrodinger equation
*, (with X.T. Li), Geometry and Nonl. PDEs 29, 63-75, 2002.

[9]
*A steady-state capturing method for hyperbolic systems with
geometrical source terms
*, , to appear.

[8]
*The random projection method for stiff multi-species detonation
computation
*, (with W.Z. Bao), pp 139-148, in Hyperbolic Problems: Theory, Numerics,
Applications, Ed. H. Freistuhler and G. Warnecke, Birkhauser-Verlag,
Berlin, 2001.

[7]
* 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.

[6]
* Remarks on the Relaxation Approximations of the Burnett
Equations *, (with M. Slemrod), Methods Appl. Anal.
8, 539-544, 2001.

[5]
* Relaxation and the Chapman-Enskog Expansion
*, (with M. Slemrod), WASCOM 99". 10th Conference on
Waves and Stability in Continuous Media (Vulcano), 265--271, World Sci. Publishing, River Edge, NJ, 2001.

[4]
* The Random projection Method
*, (with W.Z. Bao), pp. 1-11,
Advances in Scientific Computing,
Ed. by Z.C. Shi, M. Mu, W. Xue and J. Zou, Science Press, 2001.

[3]
* 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.

[2]
* Oscillations Induced by Numerical Viscosities
* (with J.G. Liu),
Mathem\'atica Contempor\^nea 10, 169-180 (1996).

[1]
* The Relaxation Schemes * (with Z.P. Xin),
Proceedings of the Fifth International Conference on Hyperbolic
Problems, 361-367 (ed. J. Glimm etc.), World Scientific (1996).