[119]
The Gaussian beam method for the Wigner equation with discontinuous
potentials, (with Dongsheng Yin and Min Tang),
preprint.
[118]
Gaussian beam methods for the Schrodinger equation with discontinuous
potentials, (with Dongming Wei and Dongsheng Yin),
preprint.
[117]
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.
[116]
A successive penalty-based asymptotic-preserving scheme for
kinetic equations , (with Bokai Yan),
preprint.
[115]
A BGK-penalization asymptotic-preserving scheme for the
multispecies Boltzmann equation, (with Qin Li),
preprint.
[114]
Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows
, (with T. Goudon, J.G. Liu and B. Yan),
preprint.
[113]
A novel numerical method for the semiclassical limit of the
Schrodinger equation and the Vlasov-Poisson equations, (with
Dongming Wei),
preprint.
[112]
On the random choice method for the Liouville equation of geometrical optics with discontinuous local wave speeds , (with Jingwei Hu),
preprint.
[111]
$l^{1}$-error estimates on the immersed interface upwind scheme for linear
convection equations with piecewise constant coefficients: a simple
proof
, (with P. Qi),
preprint.
[110]
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.
[109]
A numerical scheme for the quantum Fokker-Planck-Landau equation
efficient in the fluid regime
(with Jingwei Hu and
Bokai Yan),
Commn. Comp. Phys., to appear.
[108]
A Domain Decomposition Method for Semilinear
Hyperbolic Systems with Two-scale Relaxations (with Jian-Guo Liu and Li Wang),
Math. Comp., to appear.
[107]
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 Universita di Parma, to appear.
[106]
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.
[105]
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.
[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.
[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, (with Peng Qi),
Kinetic and Related Models 4, 1097-1120, 2011.
[101]
A class of asymmptotic-preserving schemes for the
Fokker-Planck-Landau equation , (with Bokai Yan),
J. Comp. Phys. 230, 6420-6437, 2011.
[100]
Mathematical and computational methods for semiclassical Schrodinger equations
, (with P.A. Markowich and C. Sparber),
Acta Numerica 20, 211-289, 2011.
[99]
On Kinetic Flux Vector Splitting Schemes for Quantum Euler
Equations , (with Jingwei Hu),
Kinetic and Related Models 4, 517-530, 2011.
[98]
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.
[97]
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.
[96]
An asymptotic preserving scheme for the ES-BGK model of
the Boltzmann equation
, (with F. Filbet),
J. Sci. Comp. 46, 204-224, 2011.
[95]
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.
[94]
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.
[93]
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.
[92]
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.
[91]
A micro-macro decomposition based asymptotic-preserving
scheme for the multispecies Boltzmann equation
, (with Yingzhe Shi),
SIAM J. Sci. Comp. 31, 4580-4606, 2010.
[90]
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.
[89]
A coherent semiclassical transport model for pure-state
quantum scattering
, (with K. Novak),
Comm. Math. Sci. 8, 253-275, 2010.
[88]
Recent computational methods for high frequency waves in
heterogeneous media,
, Industrial and Applied Mathematics in China, 49--64, Ser.
Contemp. Appl. Math. CAM, 10, Higher Ed. Press, Beijing, 2009
[87]
Numerical methods for hyperbolic systems with singular
coefficients: well-balanced scheme, Hamiltonian preservation, and beyond,
,
Proc. of the 12th International Conference on Hyperbolic Problems:
Theory, Numerics, Applications, Univeristy of Maryland, College Park.
Proceedings of Symposia in Applied Mathematics Vol 67-1, 93-104, 2009,
American Mathematical Society.
[86]
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.
[85]
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.
[84]
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.
[83]
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.
[82]
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.
[81]
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.
[80]
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.
[79]
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.
[78]
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.
[77]
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.
[76]
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.
[75]
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.
[74]
Computation of interface reflection and regular or diffuse
transmission of the planar symmetric radiative transfer equation with
isotropic scattering and its diffusion limit
(with Xiaomei Liao and Xu Yang),
SIAM J. Sci. Comp. 30, 1992-2017, 2008.
[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
(with Xin Wen), J. Comp. Math. 26, 1-22, 2008.
[71]
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.
[70]
A Semiclassical Transport Model for Two-Dimensional
Thin Quantum Barriers
(with K. Novak), J. Comp. Phys. 226, 1623-1644, 2007.
[69]
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.
[68]
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.
[67]
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.
[66]
A Semiclassical Transport Model for Thin Quantum Barriers
(with K. Novak),
Multiscale Modeling and Simulation, 5(4), 1063-1086, 2006.
[65]
Computation of Transmissions and Reflections in Geometrical
Optics via the Reduced Liouville Equation
(with X. Wen), Wave Motion, 43(8), 667-688, 2006.
[64]
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.
[63]
A time-splitting spectral method for the generlized Zakharov
system in multi-dimensions
(with C.X. Zheng),
J. Sci. Comp. 26, 127-149, 2006.
[62]
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.
[61]
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.
[60]
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).
[59]
Hamiltonian-preserving schemes for the Liouville equation
with discontinuous potentials
(with X. Wen),
Comm. Math. Sci. 3, 285-315, 2005.
[58]
A Smooth Transition Model Between Kinetic and Hydrodynamic
Equations
(with P. Degond and L. Mieussens),
J. Comp. Phys. 209, 665-694, 2005.
[57]
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.
[56]
A smooth transition model between kinetic and diffusion equations,
(with P. Degond),
SIAM J. Num. Anal. 42, 2671 - 2687, 2005 (electronic)
[55]
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.
[54]
Eulerian calculations of electron overtaking and multi-valued
solutions in a traveling
wave tube,
(with J.G. Wohlbier and S. Sengele),
Physics of Plasmas 12, 023106, 2005.
[53]
Numerical simulation of a generalized Zakharov system
(with P.A. Markowich and C.X. Zheng),
J. Comp. Phys. 201, 376-395, 2004.
[52]
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.
[51]
An efficient method for computing hyperbolic systems with geometrical source terms
having concentrations,
(with X. Wen),
J. Comp. Math. 22, 230-249, 2004.
[50]
On Two Moment Systems for Computing Multiphase Semiclassical
Limits of the Schrodinger Equation,
(with L. Gosse and X.T. Li), Math. Model Methods Appl. Sci.
13, No. 12, 1689-1723, 2003.
[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,
(with F. Golse and C.D. Levermore), Math. Model Num. Anal. 37,
869-892, 2003.
[47]
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.
[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,
(with X.T. Li), Physica D 182, 46-85, 2003.
[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,
(with X.L. Wang), J. Comp. Phys. 186, 582-595, 2003.
[42]
Numerical Approximations of Pressureless and Isothermal Gas
Dynamics,
(with F. Bouchut and X.T. Li), SIAM J. Num. Anal. 41, 135-158, 2003.
[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
[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.
[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.
[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.
[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.
[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.
[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).
[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.
[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.
[4]
Relaxation and Diffusion Enhanced Dispersive Waves
(with J.G. Liu), Proceedings of Royal Society London A,
446 (1994), 555-563.
[3]
Fully-Discrete Numerical Transfer in Diffusive Regimes
(with C.D. Levermore), Transport Theory and Statistical Physics
22 (1993), 739-791.
[2]
The Discrete-Ordinate Method in Diffusive Regime
(with C.D. Levermore), Transport Theory and Statistical Physics
20 (1991), 413-439.
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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).