I have conducted research in hyperbolic conservation laws,
kinetic theory, HamiltonJacobi equations and front propagations,
computational fluid dynamics, high frequency waves, semiclassical
methods for quantum dynamics, and uncertainty quantification.
(incomplete) Citation information from Web of Science
Google Scholar Citation
data
Hyperbolic conservation laws

Relaxation and Diffusion Enhanced Dispersive Waves
(with J.G. Liu), Proceedings of Royal Society London A,
446 (1994), 555563.

The Relaxation Schemes for Systems of Conservation Laws in
Arbitrary Space Dimensions (with Z.P. Xin),
Communication on Pure and Applied Mathematics, 48 (1995), 235276.

RungeKutta Methods for Hyperbolic Conservation Laws with
Stiff Relaxation Terms ,
J. Computational Physics, 122 (1995), 5167.

Numerical Integrations of Systems of Conservation Laws
of Mixed Type,
SIAM J. Applied Mathematics, 55 (1995), 15361551.

Numerical Schemes for Hyperbolic Conservation Laws with
Stiff Relaxation Terms (with C.D. Levermore),
J. Computational Physics 126 (1996), 449467.

A Convex Entropy for a Hyperbolic System with Relaxation
,
J. Differential Equations, 127, 95107 (1996).

The Effects of Numerical Viscosities I: Slowly Moving Shocks
(with J.G. Liu),
J. Computational Physics 126 (1996), 373389.

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. 6490,
1997.

Diffusion Limit of a Hyperbolic System with Relaxation
(with H.L. Liu), Methods and Applications of Analysis,
5, 317334, 1998.

A Diffusive Subcharacteristic Condition for Hyperbolic
Systems with Diffusive Relaxation, (with H.L. Liu), Transport
Theory and Statistical Physics 29, 583593, 2000.

Hyperbolic Systems with Supercharacteristic Relaxations and
Roll Waves
, (with M.A. Katsoulakis), SIAM J. Appl. Math. 61,
273292, 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, 270294, 2000.

The Random Projection Method for Hyperbolic Systems with Stiff
Reaction Terms
, (with W.Z. Bao), J. Comp. Phys. 163, 216248, 2000.

On the Computation of Roll Waves
, (with Y.J. Kim), Math. Model Num. Anal.
35, 463480, 2001.

A steadystate capturing method for hyperbolic systems with
geometrical source terms
, , Math. Model. Num. Anal. 35, 631646, 2001.

Error Estimates on the Random Projection Methods for Hyperbolic
Systems with Stiff Reaction Terms
, (with W.Z. Bao), Appl. Num. Math. 43, 315333, 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,
267291, 2003.

Front Motion in MultiDimensional 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), 701721, 2003.

Numerical Approximations of Pressureless and Isothermal Gas
Dynamics,
(with F. Bouchut and X.T. Li), SIAM J. Num. Anal. 41, 135158, 2003.

An efficient method for computing hyperbolic systems with geometrical source terms
having concentrations,
(with X. Wen),
J. Comp. Math. 22, 230249, 2004.

Two interface type numerical methods for computing hyperbolic systems with geometrical source terms having
concentrations
(with X. Wen),
SIAM J. Sci. Comp. 26, 20792101, 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, 122, 2008.

Shi Jin and Peng Qi,
$l^{1}$error estimates on the immersed interface upwind scheme for linear
convection equations with piecewise constant coefficients: a simple
proof
,
Science China Mathematics 56, 27732782, 2013 (a special issue in
honor of the 80th birthday of Prof. Zhongci Shi).

On Kinetic Flux Vector Splitting Schemes for Quantum Euler
Equations , (with Jingwei Hu),
Kinetic and Related Models 4, 517530, 2011.

A Domain Decomposition Method for Semilinear
Hyperbolic Systems with Twoscale Relaxations (with JianGuo Liu and Li Wang),
Math. Comp. 82, 749779, 2013.
 F. Coquel, S. Jin, J.G. Liu and Li Wang,
Wellposedness and singular limit of a semilinear hyperbolic relaxation system
with a twoscale discontinuous relaxation rate, Arch. Rat. mech. Anal. 214, 10511084, 2014.
 Frederic Coquel, Shi Jin, JianGuo Liu
and Li Wang,
Entropic subcell shock capturing schemes via JinXin
relaxation and Glimm front sampling for scalar hyperbolic conservation laws
, Math. Comp., Math. Comp. 87, 10831126, 2018

Xin Liu,, Xi Chen,, Shi Jin, Alexander Kurganov,
and Hui Yu,
MovingWater Equilibria Preserving Partial Relaxation
Scheme for the SaintVenant System,
preprint.
Kinetic Theory

The DiscreteOrdinate Method in Diffusive Regime
(with C.D. Levermore), Transport Theory and Statistical Physics
20 (1991), 413439.

FullyDiscrete Numerical Transfer in Diffusive Regimes
(with C.D. Levermore), Transport Theory and Statistical Physics
22 (1993), 739791.

Uniformly Accurate Schemes for Hyperbolic Systems with
Relaxations (with R.E. Caflisch and G. Russo),
SIAM J. Numerical Analysis 34, 246281 (1997).

Diffusive Relaxation Schemes for DiscreteVelocity
Kinetic Equations
(with L. Pareschi and G. Toscani),
SIAM J. Numerical Analysis,
35, 24052439, 1998.

The Convergence of Numerical Transfer Schemes in Diffusive
Regimes I: The DiscreteOrdinate Method
(with F. Golse and C.D. Levermore),
SIAM J. Numerical Analysis, 36, 13331369, 1999.

Efficient AsymptoticPreserving (AP) Schemes for Some Multiscale
Kinetic Equations
, SIAM J. Sci. Comp. 21, 441454, 1999 (electronic).

Discretization of the Multiscale Semiconductor Boltzmann
Equation by Diffusive Relaxation Schemes,
, (with L. Pareschi), J. Comp. Phys. 161, 312330, 2000.

Uniformly Accurate Diffusive Relaxation Schemes for Multiscale
Transport Equations , (with L. Pareschi and G. Toscani),
SIAM J. Num. Anal. 38, 913936, 2000 (electronic).

Regularization of the Burnett Equations via Relaxation
, (with M. Slemrod), J. Stat. Phys. 103, 10091033,
2001.

Regularization of the Burnett Equations for Fast Granular
Flows via Relaxation , (with M. Slemrod),
Physica D 150, 207218, 2001.

AsymptoticPreserving (AP) Schemes for Multiscale Kinetic
Equations: a Unified Approach
, (with L. Pareschi), pp 573582, in Hyperbolic Problems: Theory, Numerics,
Applications, Ed. H. Freistuhler and G. Warnecke, BirkhauserVerlag,
Berlin, 2001.

A Relaxation Scheme for Solving the Boltzmann Equation Based on
the ChapmanEnskog Expansion
(with L. Pareschi and M. Slemrod) , Acta Mathematicas Applicatae
Sinica (English Series) 18, 3762, 2002.

A Domain Decomposition Analysis for a TwoScale Linear
Transport Problem,
(with F. Golse and C.D. Levermore), Math. Model Num. Anal., 37,
869892, 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 twoscale linear
transport equation
(with X. Yang, F. Golse, Z.Y. Huang),
Networks and Heterogeneous Media 1(1), 143166, 2006.

A Smooth Transition Model Between Kinetic and Hydrodynamic
Equations
(with P. Degond and L. Mieussens),
J. Comp. Phys. 209, 665694, 2005.

on a uniformly second order numerical method for the
onedimensional discreteordinate transport equation and its
diffusion limit with interface
(with Min Tang and Houde Han),
Networks and Heterogeneous Media 4, 3565, 2009.

A micromacro decomposition based asymptoticpreserving
scheme for the multispecies Boltzmann equation
, (with Yingzhe Shi),
SIAM J. Sci. Comp. 31, 45804606, 2010.

A class of
asymptotic preserving schemes for kinetic equations and related problems with stiff sources
, (with Francis Filbet),
J. Comp. Phys. 229, 76257648, 2010.

An asymptotic preserving scheme for the ESBGK model of
the Boltzmann equation
, (with F. Filbet),
J. Sci. Comp., 46, 204224, 2011.

A numerical scheme for the quantum Boltzmann equation with stiff collision terms
, (with Francis Filbet and Jingwei Hu),
Math. Model Num. Anal 46, 443463, 2012.

A class of asymmptoticpreserving schemes for the
FokkerPlanckLandau equation , (with Bokai Yan),
J. Comp. Phys. 230, 64206437, 2011.

Simulation of fluidparticles flows: heavy particles, flowing regime and
asymptoticpreserving schemes, (with T. Goudon and Bokai Yan),
Comm. Math. Sci. 10, 355385, 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 3, 177216, 2012.

A numerical scheme for the quantum FokkerPlanckLandau equation
efficient in the fluid regime
(with Jingwei Hu and
Bokai Yan),
Comm. Comp. Phys., 12, 15411561, 2012.

AsymptoticPreserving schemes for kineticfluid modeling of disperse twophase flows
, (with T. Goudon, J.G. Liu and B. Yan),
J. Comp. Phys., 246, 145164, 2013.

An asymptotic preserving scheme for the
VlasovPoissonFokkerPlanck system in the high field regime,
(with Li Wang),
Acta Mathematica Scientia 31, 22192232, 2011 (special issue in honor of Peter Lax's 85th birthday).
 S. Jin and Qin Li,
A BGKpenalization asymptoticpreserving scheme for the
multispecies Boltzmann equation,
Numerical Methods for Partial Differential Equations 29, 10561080, 2013.

A successive penaltybased asymptoticpreserving scheme for
kinetic equations , (with Bokai Yan),
SIAM J. Sci. Comput. 35, A150A172, 2013.

AsymptoticPreserving schemes for kineticfluid modeling of
disperse twophase flows with variable fluid density, (with T. Goudon,
JianGuo Liu and Bokai Yan),
International Journal for Numerical Methods in Fluids 75, 81102, 2014.
 Shi Jin and Li Wang,
Asymptoticpreserving numerical schemes for the semiconductor
Boltzmann equation efficient in the high field regime,
SIAM J. Sci. Comp., 35, B799B819, 2013.
 W. Ren, H. Liu and S. Jin,
An AsymptoticPreserving Monte Carlo Method for the Boltzmann Equation, ,
J. Comp. Phys. 276, 380404, 2014.
 Jingwei Hu, Shi Jin, and Li Wang,
An asymptoticpreserving scheme for the semiconductor Boltzmann
equation with twoscale collisions: a splitting approach, ,
Kinetic and Related Models 8, 707723, 2015.
 Kerstin Kupper, Martin Frank and Shi Jin,
An asymptoticpreserving 2D staggered grid method for
multiscale transport equations, , SIAM J. Num. Anal., 54, 440461, 2016.
 Bin Zhang, Hong Liu and Shi Jin,
An Asymptotic Preserving Monte Carlo Method for the
Multispecies Boltzmann Equation ,
J. Comp. Phys. 305, 575588, 2016.
 Shi Jin and MinhBinh Tran,
Quantum hydrodynamic approximations to the finite
temperature trapped Bose gases,
Physica D 380/381, 4557, 2018.
 I. Gamba, Shi Jin and Liu Liu,
Micromacro decomposition based asymptoticpreserving numerical
schemes and numerical moments conservation for collisional nonlinear
kinetic equations,
J. Comp. Phys. 382, 264290, 2019.
 Di Fang, Seungyeal Ha and Shi Jin,
Emergent behaviors of the CuckerSmale emsemble under attractiverepulsive couplings and Rayleigh frictions,
Math Model Methods Appl. Sci., to appear.
 I. Gamba, Shi Jin and Liu Liu,
Asymptoticpreserving schemes for twospecies binary collisional
kinetic system with disparate masses I: time discretization and
asymptotic analysis,
preprint.

Shi Jin, Lei Li and JianGuo Liu,
Random Batch Methods (RBM) for interacting particle systems
,
preprint.
HamiltonJacobi equations and front propagations

Relaxation Approximations to Front Propagation
(with M. Katsoulakis), Journal of Differential Equations 138,
380387 (1997).

Numerical Passage from Systems of Conservation Laws to
HamiltonJacobi Equation, and a Relaxation Scheme
(with Z.P. Xin), SIAM J. Numerical Analysis 35, 23852404, 1998.

A Model for Front Evolution with a NonLocal Growth Rate
, (with X.L. Wang and T.L. Starr),
J. Material Research 14, No.10, 38293832, 1999.

Relaxation Schemes for CurvatureDependent Front Propagation
, (with M. Katsoulakis and Z.P. Xin), Comm. Pure Appl.
Math. 52, 15871615, 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, 467482, 2000.

Robust Numerical Simulation of Porosity Evolution in
Chemical Vapor Infiltration II: Two Dimensional Anisotropic Fronts
(with X.L. Wang), J. Comp. Phys. 179, 557577, 2002.

Robust Numerical Simulation of Porosity Evolution in
Chemical Vapor Infiltration III: Three space Dimension,
(with X.L. Wang), J. Comp. Phys. 186, 582595, 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), 305309 (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 OpenChannel Networks (with M.M. Aral and Y. Zhang),
J. Hydraulic Engineering 124, 11251133, 1998.

HighOrder IStable Central Difference Schemes for Viscous
Compressible Flows
, (with W.Z. Bao), J. Comp. Math. 21, 101112, 2003.

Weakly Compressible HighOrder IStable Central Difference
Schemes for Incompressible Viscous Flows
, (with W.Z. Bao), Comput. Methods Appl. Mech. Eng.,
190, 50095026, 2001.

The Random Projection Method for Stiff Detonation Waves
, (with W.Z. Bao), SIAM J. Sci. Comp. 23, 10001026,
2001.

The Random Projection Method for Stiff MultiSpecies Detonation
Capturing
, (with W.Z. Bao), J. Comp. Phys. 178, 3757, 2002.

Machnumber uniform asymptoticpreserving gauge schemes for
compressible flows
(with Pierre Degond and JianGuo Liu),
Bulletin of the Institute of Mathematics, Academia Sinica, New Series,
2, No. 4, 851892, 2007.

An allspeed asymptoticpreserving method for the isentropic Euler and NavierStokes equation , (with Jeffrey Haack and JianGuo Liu),
Commun. Comp. Phys. 12 (2012), pp. 955980.
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 TimeSplitting Spectral Approximations for the Schrodinger
Equation in the Semiclassical Regime,
(with W.Z. Bao and P. Markowich), J. Comp. Phys.,
175, 487524, 2002.
Numerical Study of TimeSplitting Spectral Discretizations
of Nonlinear Schrodinger Equations in the SemiClassical Regimes
(with W.Z. Bao and P. Markowich), SIAM J. Sci. Comp.25,
2764, 2003 (elctronic).
Multiphase Computations of the Semiclassical Limit of the
Schrodinger Equation and Related Problems: Whitham vs. Wigner,
(with X.T. Li), Physica D 182, 4685, 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, 16891723, 2003.
An Eulerian method for computing multivalued solutions of
the EulerPoisson 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 quasilinear
hyperbolic PDEs and HamiltonJacobi equations,
(with S. Osher),
Comm. Math. Sci. 1(3), 575591, 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, 222241, 2005.
Numerical simulation of a generalized Zakharov system
(with P.A. Markowich and C.X. Zheng),
J. Comp. Phys. 201, 376395, 2004.
A timesplitting spectral method for the generlized Zakharov
system in multidimensions
(with C.X. Zheng),
J. Sci. Comp. 26, 127149, 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 timesplitting spectral scheme for the MaxwellDirac
system
(with Z.Y. Huang, Peter A. Markowich, Christof Sparber and C.X. Zheng),
J. Comp. Phys., 208, 761789, 2005.
Hamiltonianpreserving schemes for the Liouville equation
with discontinuous potentials
(with X. Wen),
Comm. Math. Sci. 3, 285315, 2005.
Computing multivalued physical observables for high frequency limit of
symmetric hyperbolic systems
(with H. Liu, S. Osher and R. Tsai),
J. Comp. Phys. 210, 497518, 2005.
Hamiltonianpreserving schemes for the Liouville equation
of geometrical optics with discontinuous local wave speeds,
(with X. Wen),
J. Comp. Phys. 214, 672697, 2006.
Hamiltonianpreserving schemes for the Liouville equation
of geometrical optics with partial transmissions and reflections
(with X. Wen),
SIAM J. Num. Anal. 44, 18011828, 2006.
The l^1stability of a Hamiltonianpreserving scheme for the
Liouville equation with discontinuous potentials
(with X. Wen),
J. Comp. Math. 27 (2009), pp. 4567.
Computation of Transmissions and Reflections in Geometrical
Optics via the Reduced Liouville Equation
(with X. Wen), Wave Motion 43(8), 667688, 2006.
A Hamiltonianpreserving scheme for high frequency elastic waves
in heterogeneous media
(with Xiaomei Liao),
J. Hyperbolic Diff. Eqn. 3, No. 4, 741777, 2006.
A Bloch decomposition based timesplitting pseudospectral
method for quantum dynamics
with periodic potentials
(with Z.Y. Huang, P.A. Markowich and C. Sparber),
SIAM J. Sci. Comp. 29, 515538, 2007.
A Semiclassical Transport Model for Thin Quantum Barriers
(with k. Novak),
Multiscale Modeling and Simulation, 5(4), 10631086, 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, 19922017, 2008.
Computational high frequency waves through curved interfaces via
the Loiuville equation and Geometric Theory of Diffraction,
(with Dongsheng Yin),
J. Comp. Phys. 227, 61066139, 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. 23, 144169, 2008.
A Semiclassical Transport Model for TwoDimensional
Thin Quantum Barriers
(with K. Novak), J. Comp. Phys. 226, 16231644, 2007.
The VlasovPoisson equations as the semiclassical Limit of the
SchrodingerPoisson Equations: a numerical study
(with Xiaomei Liao and Xu Yang), J. Hyperbolic Diff. Eqn.
5(3), 569587, 2008.
Numerical simulation of the nonlinear Schrodinger equation with
multidimensional periodic potentials
(with Z.Y. Huang, P.A. Markowich and C. Sparber), SIAM Multiscale
Modeling and Simulation 7, 539564, 2008.
On the timesplitting spectral method for the complex
GinzburgLandau equation
in the large time and space scale limit
(with P. Degond and Min Tang), SIAM J. Sci. Comp. 30, 24662487,
2008.
The l^1error estimates for a Hamiltonianpreserving scheme
for the Liouville equation with piecewise constant potentials
(with Xin Wen), SIAM J. Num. Anal. 46, 26882714, 2008.
Recent computational methods for high frequency waves in
heterogeneous media,
, preprint.
A domain decomposition method for a twoscale transport
equation with energy flux conserved at the interface,
(with X. Yang and G.W. Yuan)
, Kinetic and Related Models, 1, 6584, 2008.
A Hybrid PhaseFlow Method for Hamiltonian Systems with Discontinuous
Hamiltonians
, (with H. Wu and Z.Y. Huang), SIAM J. Sci. Comput. 31, 13031321,
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, 1528, 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, 11061128, 2008.
Gaussian beam methods for the Schrodinger equation in the semiclassical
regime: Lagrangian and Eulerian formulations
, (with H. Wu and X. Yang), Comm. Math. Sci. 6, 9951020, 2008.
A coherent semiclassical transport model for purestate
quantum scattering
, (with K. Novak)
Comm. Math. Sci. 8, 253275, 2010.
Bloch DecompositionBased Gaussian Beam Method for the Schr\"odinger equation
with Periodic Potentials
, (with Hao Wu, Xu Yang and Zhongyi Huang)
J. Comp. Phys. 229, 48694883, 2010.
A numerical study of the Gaussian beam methods for
onedimensional Schr\"odingerPoisson equations
, (with Hao Wu and Xu Yang),
J. Comp. Math. 28, 261272, 2010.
SemiEulerian and High Order Gaussian Beam Methods
for the Schrodinger Equation in the Semiclassical Regime
, (with Hao Wu and Xu Yang),
Comm. Comp. Phys., 9, 668687, 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, 258281, 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, 74407455, 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, 295316, 2011.
On the quasirandom choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds , (with Jingwei Hu),
J. Comp. Math. 31, 573591, 2013.
Mathematical and computational methods for semiclassical Schrodinger equations
, (with P.A. Markowich and C. Sparber),
Acta Numerica 20, 211289, 2011.
A particle method for the semiclassical limit of the
Schrodinger equation and the VlasovPoisson equations, (with
Dongming Wei,
SIAM J. Num. Anal. 50, 32593279, 2012.
A Hybrid Schr\"odinger/Gaussian Beam Solver for Quantum Barriers and
Surface Hopping, (with Peng Qi),
Kinetic and Related Models 4, 10971120, 2011.
Gaussian beam methods for the Dirac equation in the semiclassical regime,
, (with Hao Wu, Zhongyi Huang, and Dongsheng Yin),
Comm. Math. Sci., 10, 13011315, 2012.
Gaussian beam methods for the Schrodinger equation with discontinuous
potentials, (with Dongming Wei and Dongsheng Yin),
J. Comp. Appl. Math., to appear 265, 199219, 2014 (a special issue in honor of Prof.
Benyu Guo's 70th birthday).
Dongsheng Yin, Min Tang and Shi Jin,
The Gaussian beam method for the Wigner equation with discontinuous
potentials,
Inverse Problems and Imaging 7, 10511074, 2013 (a special issue in honor of the 60th birthday
of Tony Chan).
Lihui Chai, Shi Jin, and Qin Li,
Semiclassical Models for the Schrodinger Equation with Periodic Potentials and Band Crossings, Kinetic and Related Models 6, 505532, 2013.
L. Jefferis and Shi Jin,
Computing high frequency solutions of symmetric
hyperbolic systems with polarized waves, Comm. Math. Sci. 13,
10011024, 2015.
(special issue in honor of George Papanicolaou's 70th birthday)
L. Jefferis and S. Jin,
A Gaussian Beam Method for High Frequency Solution of
Symmetric Hyperbolic Systems with Polarized Waves,
SIAM Multiscale
Model. Simulation 13, 733765, 2015
S. Jin and Z. Zhou,
A semiLagrangian time splitting method for the
Schrodinger equation with vector potentials, Communications in Information and Systems,
13, 247289, 2013. (a special issue in honor of Marshall Slemrod's 70th birthday)
Lihui Chai, Shi Jin, Qin Li and Omar Morandi,
A multiband semiclassical model for surface hopping quantum dynamics, , SIAM Multiscale Modeling and Simulation, 13, 205230,
2015.
Shi Jin, C. Sparber and Zhennan Zhou,
On the classical limit of a timedependent selfconsistent field system: analysis and
computation, Kinetic and Related Models 10, 263298, 2017. (A special
issue in honor of the 60th birthday of Peter Markowich).
Ali Faraj and Shi Jin,
The LandauZener transition and the surface hopping
method for the 2D Dirac equation for graphene
, Comm. Comp. Phys., 21, 313357, 2017.
Nicolas Crouseilles, Shi Jin and Mohammed Lemou,
Nonlinear geometric optics method based multiscale numerical
schemes for a class of highlyoscillatory transport equations,
Math. Model Methods Applied Sci., 27, 20312070, 2017.
Lihui Chai, Shi Jin and P.A. Markowich,
A hybrid method for computing the Schrodinger equations
with periodic potential with bandcrossings in the
momentum space,
Comm. Comp. Phys. 24, 9891020, 2018. (a special issue in honor of the 80th birthday of
Prof. Houde Han).
Di Fang, Shi Jin and Christof Sparber,
An efficient timesplitting method for the Ehrenfest dynamics,
(SIAM) Multiscale Modeling and Simulation 16, 900921, 2018.
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,
preprint.
N. Crouseilles, S. Jin, M. Lemou and F. Mehats,
A micromacro method for a kinetic graphene model in onespace dimension,
preprint.
F. Golse, Shi Jin and T. Paul,
On the Convergence of Time Splitting Methods for Quantum
Dynamics in the Semiclassical Regime,
preprint.
Uncertainty Quantification for Kinetic and Hyperbolic Equations
Shi Jin, Dongbin Xiu and Xueyu Zhu,
Asymptoticpreserving methods for
hyperbolic and transport equations with random inputs and
diffusive scalings, , J. Comp. Phys. 289, 3552, 2015.
Jingwei Hu, Shi Jin, and Dongbin Xiu,
A stochastic Galerkin method for HamiltonJacobi equations with uncertainty, , SIAM J. Sci. Comp. 37, A2246A2269, 2015.
Shi Jin, Dongbin Xiu and Xueyu Zhu,
A wellbalanced stochastic Galerkin method for scalar
hyperbolic balance laws with random inputs
, J. Sci. Comp., 67, 11981218, 2016.
Jingwei Hu and Shi Jin,
A stochastic Galerkin method for the Boltzmann equation
with uncertainty
, J. Comp. Phys, 315, 575588, 2016.
Alina Chertock, Shi Jin and Alexander
Kurganov,
An operator splitting based stochastic Galerkin method for the onedimensional
compressible Euler equations with uncertainty,
Preprint.
Alina Chertock, Shi Jin and Alexander
Kurganov,
A wellbalanced operator splitting based stochastic Galerkin method for the onedimensional
SaintVenant system with uncertainty,
Preprint.
Shi Jin and Liu Liu,
An AsymptoticPreserving Stochastic Galerkin Method for
the Semiconductor Boltzmann Equation with Random Inputs
and Diffusive Scalings
SIAM Multiscale Modeling and Simulation 15, 157183, 2017.
Erratum
Shi Jin and Hanqing Lu,
An AsymptoticPreserving Stochastic Galerkin Method for the Radiative Heat Transfer Equations with Random Inputs and Diffusive Scalings,
J. Comp. Phys., 334, 182206, 2017.
Shi Jin, JianGuo 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 micromacro 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/s4068701701051.
Yuhua Zhu and Shi Jin,
The VlasovPoissonFokkerPlanck system with uncertainty and a
onedimensional asymptoticpreserving method ,
SIAM Multiscale Model. Simul.,15, 15021529, 2017.
Ruiwen Shu, Jingwei Hu and Shi Jin,
A Stochastic Galerkin Method for the Boltzmann Equation with multidimensional random inputs using sparse wavelet bases,
Num. Math.: Theory, Methods and Applications (NMTMA) 10, 465488, 2017.
(A special issue in honor of the 80th birthday of Prof. Zhenhuan Teng)
Shi Jin and Ruiwen Shu,
A stochastic AsymptoticPreserving scheme for a kineticfluid
model for disperse twophase flows with uncertainty,
J. Comp. Phys., 335, 905924, 2017.
Shi Jin and Zheng Ma,
The discrete stochastic Galerkin method for hyperbolic equations with
nonsmooth and random coefficeints,
J. Sci. Comp. 74, 97121, 2018.
Shi Jin, Hanqing Lu and Lorenzo Pareschi,
Efficient stochastic Asymptoticpreserving IMEX methods for transport
equations with diffusive scalings and random inputs,
SIAM J. Sci. Comput., 40, A671A696, 2018.
Jingwei Hu, Shi Jin and Ruiwen Shu,
A stochastic Galerkin method for the FokkerPlanckLandau equation with random uncertainties,
Proc. 16th Int'l Conf. on Hyperbolic Problems, (eds. C. Klingenberg and M. Westdickenberg), Vol. 2, 119, Springer, 2018.
Shi Jin and Yuhua Zhu,
Hypocoercivity and Uniform Regularity for the
VlasovPoissonFokkerPlanck System with Uncertainty and
Multiple Scales,
SIAM J. Math. Anal. 50, 17901816, 2018.
Jingwei Hu and Shi Jin,
Uncertainty Quantification for Kinetic Equations,
Uncertainty Quantification for Kinetic and Hyperbolic Equations, SEMASIMAI Springer Series, ed. S. Jin and L. Pareschi, Springer, 2017.
Shi Jin, Hanqing Lu and Lorenzo Pareschi,
A High Order Stochastic Asymptotic Preserving Scheme for
Chemotaxis Kinetic Models with Random Inputs,
Multiscale Model. Simult., 16, 18841915, 2018.
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,
(SIAM) Multiscale Modeling and Simulation 16, 10851114, 2018.
Shi Jin,
Mathematical Analysis and Numerical Methods for Multiscale Kinetic Equations with Uncertainties,
Proceedings of The International Congress of Mathematicians,
Rio de Janeiro, Vol. 3, 35953624, 2018.
SeungYeal Ha and Shi Jin,
Local sensitivity analysis for the CuckerSmale model with random inputs,
Kinetic and Related Models 11, 859889, 2018. (special tenyear anniversary issue
of KRM).
SeungYeal Ha, Shi Jin, and Jinwook Jung,
A local sensitivity analysis for the kinetic CuckerSmale equation with random inputs,
J. Diff. Eqn. 265, 36183649, 2018.
Ruiwen Shu and Shi Jin,
Uniform regularity in the random space and spectral
accuracy of the stochastic Galerkin method for a
kineticfluid twophase flow model with random initial
inputs in the light particle regime,
Math. Model Num. Anal. 52, 16511678, 2018.
Ruiwen Shu and Shi Jin,
A study of Landau damping with random initial inputs,
J. Diff. Eqn. 266, 19221945, 2019.
SeungYeal Ha, Shi Jin, and Jinwook Jung,
Local sensitivity analysis for the Kuramoto model with random
inputs in a large coupling regime,
preprint.
Yingda Li and Shi Jin,
Local sensitivity analysis and spectral convergence of the stochastic
Galerkin method for discretevelocity Boltzmann equations with
multiscales and random inputs,
Kinetic and Related Models, to appear.
SeungYeal Ha, Shi Jin, and Jinwook Jung,
A local sensitivity analysis for the kinetic CuckerSmale model with random inputs,
preprint.
SeungYeal Ha, Shi Jin, and Jinwook Jung,
A local sensitivity analysis for the kinetic Kuramoto model with random inputs,
Networks and Heterogeneous Media 14, 317340, 2019.
Zhiyan Ding and Shi Jin,
Random regularity of a nonlinear Landau Damping solution for the
VlasovPoisson equations with random inputs,
preprint.
Zhiyan Ding, SeungYeal Ha and Shi Jin,
A local sensitivity analysis in Landau Damping for the kinetic
Kuramoto equation with random inputs,
preprint.
Shi Jin and Ruiwen Shu,
A study of hyperbolicity of kinetic stochastic Galerkin system
for the isentropic Euler equations with uncertainty,
Chinese Annals of Mathematics, Ser B, (a special issue in honor of
Prof. Andrew Majda's 70th birthday), to appear.
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,
Kinetic and Related Models 12, 909922, 2019.
SeungYeal Ha, Shi Jin, Jinwook Jung and Woojoo Shim,
A local sensitivity analysis for the hydrodynamic CuckerSmale model
with random inputs,
preprint.
Jingwei Hu, Shi Jin, and Ruiwen Shu,
On stochastic Galerkin approximation of the nonlinear Boltzmann equation with uncertainty in the fluid regime,
preprint.
Shi Jin, Liu Liu, Giovanni Russo and Zhennan Zhou,
Gaussian wave packet transform based numerical scheme for
the semiclassical Schrodinger equation with random inputs,
preprint.
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,
preprint.