I have conducted research in Bose-Einstein condensation; computational fluid dynamics; computational quantum physics and chemistry; highly oscillatory PDEs; hyperbolic conservation laws; multiscale modeling, simulation and applications; quantized vortices in superfluidity and superconductivity; numerical methods for problems in unbounded domains; solid-state dewetting; finite element method for some nonlinear problems; numerical analysis and scientific computing; computational and applied mathematics in general.

**In refereed journals**# Submitted:

[132]

*Error estimates of a regularized finite difference method for the logarithmic Schrodinger equation*(with R. Carles, C. Su and Q. Tang ), arXiv: 1803.10068.

[131]

*Fundamental gaps of the fractional Schrodinger operator*(with X. Ruan, J. Shen and C. Sheng), arXiv: 1801.06517.

[130]

*Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates*(with Y. Cai, Y. Yuan, M. Rosenkranz and H. Pu), arXiv: 1801.07225.

[129]

*A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation*(with J. Yin), arXiv: 1711.07193.

# Accepted:

[128]

*Fundamental gaps of the Gross-Pitaevskii equation with repulsive interaction*(with X. Ruan),*Asymptotic Analysis*, to appear (arXiv: 1512.07123).

[127]

*Mathematical models and numerical methods for spinor Bose-Einstein condensates*(with Y. Cai),*Commun. Comput. Phys.*, to appear (arXiv: 1709.03840).

[126]

*Quantized vortex dynamics and interaction patterns in superconductivity based on the reduced dynamical law*(with S. Shi, and Z. Xu),*Discrete Contin. Dyn. Syst. Ser. B*, to appear (arXiv: 1701.01030).

# Published:

**2018**[125]

*Mechanical transduction via a single soft polymer*(with R. Hou, N. Wang and Z. Wang),*Phys. Rev. E*, Vol.**97**(2018), article 042504.

[124]

*Uniform error bounds of a finite difference method for the Klein-Gordon-Zakharov system in the subsonic limit regime*(with C. Su),*Math. Comp.*, Vol.**87**(2018), pp. 2133-2158 (arXiv: 1612.09404).

[123]

*Uniform error estimates of a finite difference method for the Klein-Gordon-Schrodinger system in the nonrelativistic and massless limit regimes*(with C. Su),*Kinet. Relat. Mod.*, Vol.**11**(2018), pp. 1037-1062.

[122]

*Uniformly and optimally accurate methods for the Zakharov system in the subsonic limit regime*(with C. Su),*SIAM J. Sci. Comput.*, Vol.**40**(2018), pp. A929-A953.

**2017**[121]

*Stable equilibria of anisotropic particles on substrates: a generalized Winterbottom construction*(with W. Jiang, D. J. Srolovitz and Y. Wang),*SIAM J. Appl. Math.*, Vol.**77**(2017), pp. 2093-2118 (arXiv: 1608.08481).

[120]

*A regularized Newton method for computing ground states of Bose-Einstein condensates*(with X. Wu and Z. Wen),*J. Sci. Comput.*, Vol.**73**(2017), pp. 303-329 (arXiv: 1504.02891).

[119]

*Uniform error bounds of a finite difference method for the Zakharov system in the subsonic limit regime via an asymptotic consistent formulation*(with C. Su),*Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal*, Vol.**15**(2017), pp. 977-1002 (arXiv: 1604.04685).

[118]

*Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime*(with Y. Cai, X. Jia and Q. Tang),*J. Sci. Comput.*, Vol.**71**(2017), pp. 1094-1134 (arXiv: 1504.02881).

[117]

*Triple junction drag effects during topological changes in the evolution of polycrystalline microstructures*(with Q. Zhao, W. Jiang and D. J. Srolovitz),*Acta Mater.*, Vol.**128**(2017), pp. 345-350 (arXiv: 1611.09449).

[116]

*A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the Klein-Gordon-Schrodinger equations in the nonrelativistic limit regime*(with X. Zhao),*Numer. Math.*, Vol.**135**(2017), pp. 833-873 (arXiv: 1505.00083).

[115]

*Dimension reduction for dipolar Bose-Einstein condensates in the strong interaction regime*(with L. Le Treust and F. Mehats),*Kinet. Relat. Mod.*, Vol.**10**(2017), pp. 553-571 (arXiv: 1501.02177).

[114]

*A parametric finite element method for solid-state dewetting problems with anisotropic surface energies*(with W. Jiang, Y. Wang and Q. Zhao),*J. Comput. Phys.*, Vol.**330**(2017), pp. 380-400 (arXiv: 1601.05877).

**2016**[113]

*The kinematic effects of the defects in liquid crystal dynamics*(with R. Chen and H. Zhang),*Commun. Comput. Phys.*, Vol.**20**(2016), pp. 234-249.

[112]

*A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon-Zakharov system in the high-plasma-frequency limit regime*(with X. Zhao),*J. Comput. Phys.*, Vol.**327**(2016), pp. 270-293.

[111]

*Error estimates of numerical methods for the nonlinear Dirac equation in the nonrelativistic limit regime*(with Y. Cai, X. Jia and J. Yin),*Sci. China Math.*, Vol.**59**(2016), pp. 1461-1494 (arXiv: 1511.01192v3).

[110]

*A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime*(with Y. Cai, X. Jia and Q. Tang),*SIAM J. Numer. Anal.*, Vol.**54**(2016), pp. 1785-1812 (arXiv: 1507.04103).

[109]

*Hubbard model for atomic impurities bound by the vortex lattice of a rotating BEC*(with T. H. Johnson, Y. Yuan, S. R. Clark, C. Foot and D. Jaksch),*Phys. Rev. Lett.*, Vol.**116**(2016), article 240402 (arXiv: 1512.09334) and its suplemmentary material.

[108]

*Mean-field regime and Thomas-Fermi approximations of trapped Bose-Einstein condensates with higher order interactions in one and two dimensions*(with Y. Cai and X. Ruan),*J. Phys. B: At. Mol. Opt. Phys.*, Vol.**49**(2016), article 125304 (arXiv: 1511.00141).

[107]

*Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT*(with Q. Tang and Y. Zhang),*Commun. Comput. Phys.*, Vol.**19**(2016), pp. 1141-1166 (arXiv: 1504.02897).

[106]

*Solid-state dewetting and island morphologies in strongly anisotropic materials*(with W. Jiang, Y. Wang, Q. Zhao, D. J. Srolovitz),*Scripta Materialia*, Vol.**115**(2016), pp. 123-127 (arXiv: 1510.03303).

**2015**[105]

*Fractional quantum mechanics in polariton condensates with velocity dependent mass*(with F. Pinsker, Y. Zhang, H. Ohadi, A. Dreismann and J. J. Baumberg),*Phys. Rev. B*, Vol.**92**(2015), article 195310 (arXiv: 1508.03621).

[104]

*Computing the ground state and dynamics of the nonlinear Schroedinger equation with nonlocal interactions via the nonuniform FFT*(with S. Jiang, Q. Tang and Y. Zhang),*J. Comput. Phys.*, Vol.**296**(2015), pp. 72-89 (arXiv: 1410.3584).

[103]

*Dimension reduction for anisotropic Bose-Einstein condensates in the strong interaction regime*(with L. Le Treust and F. Mehats),*Nonlinearity*, Vol.**28**(2015), pp. 755-772.

[102]

*Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates*(with Y. Cai),*SIAM J. Appl. Math.*, Vol.**75**(2015), pp. 492-517.

[101]

*Sharp interface model for solid-state dewetting problems with weakly anisotropic surface energy*(with W. Jiang, D. J. Srolovitz, Y. Wang),*Phys. Rev. B*, Vol.**91**(2015), article 045303.

**2014**[100]

*Mathematical models and numerical methods for Bose-Einstein condensation*,*Proceedings of the International Congress of Mathematicians (Seoul 2014)*, Vol.**IV**(2014), pp. 971-996 (arXiv: 1403.3884 (math.ph)).

[99]

*A uniformly accurate multiscale time integrator pseudospectral method for the Klein-Gordon equation in the nonrelativistic limit regime*(with Y. Cai and X. Zhao),*SIAM J. Numer. Anal.*, Vol.**52**(2014), pp. 2488-2511.

[98]

*Fast and accurate evaluation of nonlocal Coulomb and dipole-dipole interactions via the nonuniform FFT*(with L. Greengard and S. Jiang),*SIAM J. Sci. Comput.*, Vol.**36**(2014), pp. B777-B794.

[97]

*Uniformly accurate multiscale time integrators for highly oscillatory second order differential equations*(with X. Dong and X. Zhao),*J. Math. Study*, Vol.**47**(2014), pp. 111-150.

[96]

*Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator*(with Y. Cai),*SIAM J. Numer. Anal.*, Vol.**52**(2014), pp. 1103-1127.

[95]

*Numerical study of quantized vortex interaction in nonlinear Schroedinger equation on bounded domains*(with Q. Tang),*Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal*, Vol.**12**(2014), pp. 411-439.

[94]

*A variational-difference numerical method for designing progressive-addition lenses*(with W. Jiang, Q. Tang and H. Wang),*Computer-Aided Design*, Vol.**48**(2014), pp. 17-27.

**2013**[93]

*An exponential wave integrator pseudospectral method for the Klein-Gordon-Zakharov system*(with X. Dong and X. Zhao),*SIAM J. Sci. Comput.*, Vol.**35**(2013), pp. A2903-A2927.

[92]

*A simple and efficient numerical method for computing the dynamics of rotating Bose-Einstein condensates via a rotating Lagrangian coordinate*(with D. Marahrens, Q. Tang and Y. Zhang),*SIAM J. Sci. Comput.*, Vol.**35**(2013), pp. A2671-A2695.

[91]

*Dimension reduction of the Schrodinger equation with Coulomb and anisotropic confining potentials*(with H. Jian, N. J. Mauser and Y. Zhang),*SIAM J. Appl. Math.*, Vol.**73**(2013), pp. 2100-2123.

[90]

*Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations*(with X. Antoine and C. Besse),*Comput. Phys. Commun.*, Vol.**184**(2013), pp. 2621-2633 (**An Invited Feature Article**).

[89]

*Efficient methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations*(with I-L. Chern and Y. Zhang),*J. Comput. Phys.*, Vol.**253**(2013), pp. 189-208.

[88] Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates (with Y. Cai and M. Rosenkranz),

*Phys. Rev. A*, Vol.**88**(2013), article 013616.

[87]

*Numerical study of quantized vortex interaction in the Ginzburg-Landau equation on bounded domains*(with Q. Tang), Commun. Comput. Phys., Vol.**14**(2013), pp. 819-850.

[86]

*Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrodinger equation*(with Q. Tang and Z. Xu),*J. Comput. Phys.*, Vol.**235**(2013), pp. 423-445.

[85]

*Mathematical theory and numerical methods for Bose-Einstein condensation*(with Y. Cai),*Kinet. Relat. Mod.*, Vol.**6**(2013), pp. 1-135 (**An Invited Review Paper**).

[84]

*Optimal error estimates of finite difference methods for the Gross-Pitaevskii equation with angular momentum rotation*(with Y. Cai),*Math. Comp.*, Vol.**82**(2013), pp. 99-128.

**2012**[83]

*Subdiffusive spreading of a Bose-Einstein condensate in random potentials*(with B. Min, T. Li, and M. Rosenkranz),*Phys. Rev. A*, Vol.**86**(2012), article 053612.

[82]

*Phase field approach for simulating solid-state dewetting problems*(with W. Jiang, C. V. Thompson and D. J. Srolovitz),*Acta Mater.*, Vol.**60**(2012), pp. 5578-5592.

[81]

*Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement*(with N. Ben Abdallah and Y. Cai),*SIAM J. Math. Anal.*, Vol.**44**(2012), pp. 1713-1741.

[80]

*Breathing oscillations of a trapped impurity in a Bose gas*(with T. J. Johnson, M. Bruderer, Y. Cai, S. R. Clark and D. Jaksch),*EPL -- Europhysics Letters*, Vol.**98**(2012), article 26001.

[79]

*Uniform error estimates of finite difference methods for the nonlinear Schrodinger equation with wave operator*(with Y. Cai),*SIAM J Numer. Anal.*, Vol.**50**(2012), pp. 492-521.

[78]

*Analysis and comparison of numerical methods for Klein-Gordon equation in nonrelativistic limit regime*(with X. Dong),*Numer. Math.*, Vol.**120**(2012), pp. 189-229.

**2011**[77]

*Scattering and bound states in two-dimensional anisotropic potentials*(with M. Rosenkranz),*Phys. Rev. A*, Vol.**84**(2011), article 050701(R).

[76]

*Numerical methods for computing ground state and dynamics of nonlinear relativistic Hartree equation for boson stars*(with X. Dong),*J. Comput. Phys.*, Vol.**230**(2011), pp. 5449-5469.

[75]

*Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction*(with Y. Cai),*East Asia Journal on Applied Mathematics*, Vol.**1**(2011), pp. 49-81.

**2006 --- 2010**[74]

*Dynamical laws of the coupled Gross-Pitaevskii equations for spin-1 Bose-Einstein condensates*(with Y. Zhang),*Methods and Applications of Analysis*, Vol.**17**(2010), pp. 49-80.

[73]

*Singular limits of Klein-Gordon-Schrodinger equations to Schrodinger-Yukawa equations*(with X. Dong and S. Wang),*Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal*, Vol.**8**(2010), pp. 1742-1769.

[72]

*Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions*(with Y. Cai, M. Rosenkranz and Z. Lei),*Phys. Rev. A*, Vol.**82**(2010), article 043623.

[71]

*Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates*(with Y. Cai and H. Wang),*J. Comput. Phys.*, Vol.**229**(2010), pp. 7874-7892.

[70]

*Comparisons between sine-Gordon equation and perturbed nonlinear Schrodinger equations for modeling light bullets beyond critical collapse*(with X. Dong and J. Xin),*Physica D*, Vol.**239**(2010), pp. 1120-1134.

[69]

*A generalized-Laguerre-Fourier-Hermite pseudospectral method for computing the dynamics of rotating Bose-Einstein condensates*(with H. Li and J. Shen),*SIAM J. Sci. Comput.*, Vol.**31**(2009), pp. 3685-3711.

[68]

*Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential*(with B. Xiang, J. Gong, H. Pu and B. Li),*Phys. Rev. A*, Vol.**79**(2009), article 013626.

[67]

*Numerical methods for computing the ground state of spin-1 Bose-Einstein condensates in uniform magnetic field*(with F. Y. Lim),*Phys. Rev. E*, Vol.**78**(2008), article 066704.

[66]

*A generalized-Laguerre-Hermite pseudospectral method for computing symmetric and central vortex states in Bose-Einstein condensates*(with J. Shen),*J. Comput. Phys.*, Vol.**227**(2008), pp. 9778-9793.

[65]

*Quantized vortex stability and interaction in the nonlinear wave equation*(with R. Zeng and Y. Zhang),*Physica D*, Vol.**237**(2008), pp. 2391-2410.

[64]

*Self-trapping of Bose-Einstein condensates expanding in shallow optical lattices*(with M. Rosenkranz, D. Jaksch and F. Y. Lim),*Phys. Rev. A*, Vol.**77**(2008), article 063607.

[63]

*Computing ground states of spin-1 Bose-Einstein condensates by the normalized gradient flow*(with F. Y. Lim),*SIAM J. Sci. Comput.*, Vol.**30**(2008), pp. 1925-1948.

[62]

*Self-trapping of impurities in Bose-Einstein condensates: Strong attractive and repulsive coupling*(with M. Bruderer and D. Jaksch),*EPL -- Europhysics Letters*, Vol.**82**(2008), article 30004 (was chosen to be part of special online collection of most frequently downloaded articles on ultracold gases and related areas published in EPL, see details ).

[61]

*A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems*(with M.-H. Chai),*Commun. Comput. Phys.*, Vol.**4**(2008), pp. 135-160.

[60]

*Convergence rate of dimension reduction in Bose-Einstein condensates*(with Y. Ge, D. Jaksch, P. A. Markowich and R. M. Weishaeupl),*Comput. Phys. Commun.*, Vol.**177**(2007), pp. 832-850.

[59]

*The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schrodinger equations*(with Q. Du and Y. Zhang),*SIAM J. Appl. Math.*, Vol.**67**(2007), pp. 1740-1775.

[58]

*Dynamics of vortices in weakly interacting Bose-Einstein condensates*(with A. Klein, D. Jaksch and Y. Zhang),*Phys. Rev. A*, Vol.**76**(2007), article 043602.

[57]

*A mass and magnetization conservative and energy diminishing numerical method for computing ground state of spin-1 Bose-Einstein condensates*(with H. Wang),*SIAM J. Numer. Anal.*, Vol.**45**(2007), pp. 2177-2200.

[56]

*Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation*(with H. Li and Y. Zhang),*Physica D*, Vol.**234**(2007), pp. 49-69.

[55]

*Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation*(with Q. Du and Y. Zhang),*Eur. J. Appl. Math.*, Vol.**18**(2007), pp. 607-630.

[54]

*Efficient and accurate numerical methods for the Klein-Gordon-Schrodinger equations*(with L. Yang),*J. Comput. Phys.*, Vol.**225**(2007), pp. 1863-1893.

[53]

*Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime*(with F. Y. Lim and Y. Zhang),*Bulletin of the Institute of Mathematics, Academia Sinica*, Vol.**2**(2007), pp. 495-532.

[52]

*Dynamics of the center of mass in rotating Bose-Einstein condensates*(with Y. Zhang),*Appl. Numer. Math.*, Vol.**57**(2007), pp. 697-709.

[51]

*A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities*(with C. Zheng),*Commun. Comput. Phys.*, Vol.**2**(2007), pp. 123-140.

[50]

*Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates*(with I-L. Chern and F. Y. Lim),*J. Comput. Phys.*, Vol.**219**(2006), pp. 836-854.

[49]

*An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates*(with H. Wang),*J. Comput. Phys.*, Vol.**217**(2006), pp. 612-626.

[48]

*Dynamics of rotating Bose-Einstein condensates and their efficient and accurate numerical computation*(with Q. Du and Y. Zhang),*SIAM J. Appl. Math.*, Vol.**66**(2006), pp. 758-786.

**2000 --- 2005**[47]

*Dynamics of the ground state and central vortex states in Bose-Einstein condensation*(with Y. Zhang),*Math. Models Meth. Appl. Sci.*, Vol.**15**(2005), pp. 1863-1896.

[46]

*A fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates*(with J. Shen),*SIAM J. Sci. Comput.*, Vol.**26**(2005), pp. 2010-2028.

[45]

*On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments*(with P. A. Markowich, C. Schmeiser and R. M. Weishaupl ),*Math. Models Meth. Appl. Sci.*, Vol.**15**(2005), pp. 767-782.

[44]

*Continuous configuration time-dependent self-consistent field method for polyatomic quantum dynamical problems*(with D. H. Zhang, M. H. Yang and S.-Y. Lee),*J. Chem. Phys.*, Vol.**122**(2005), pp. 1101-1104.

[43]

*Ground, symmetric and central vortex states in rotating Bose-Einstein condensates*(with H. Wang and P. A. Markowich),*Comm. Math. Sci.*, Vol.**3**(2005), pp. 57-88.

[42]

*Efficient and stable numerical methods for the generalized and vector Zakharov System*, (with F. F. Sun),*SIAM J. Sci. Comput.*, Vol.**26**(2005), pp. 1057-1088.

[41]

*Numerical methods for the nonlinear Schrodinger equation with nonzero far-field conditions*,*Methods and Applications of Analysis*, Vol.**11**(2004), pp. 367-388.

[40]

*An efficient and stable numerical method for the Maxwell-Dirac system*(with X.-G. Li),*J. Comput. Phys.*, Vol.**199**(2004), pp. 663-687.

[39]

*Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow*(with Q. Du),*SIAM J. Sci. Comput.*, Vol.**25**(2004), pp. 1674-1697.

[38]

*Ground states and dynamics of multi-component Bose-Einstein condensates*,*Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal*, Vol.**2**(2004), pp. 210-236.

[37]

*Three dimensional simulation of jet formation in collapsing condensates*(with D. Jaksch and P. A. Markowich),*J. Phys. B: At. Mol. Opt. Phys.*, Vol.**37**(2004), pp. 329-343.

[36]

*Effective one particle quantum dynamics of electrons: a numerical study of the Schrodinger-Poisson-X_\alpha model*(with N. J. Mauser, H. P. Stimming),*Comm. Math. Sci.*, Vol.**1**(2003), pp. 809-828.

[35]

*Approximation and comparison for motion by mean curvature with intersection points*,*Computers & Math. Appl.*, Vol.**46**(2003), pp. 1211-1228.

[34] An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity

*SIAM J. Numer. Anal.*, Vol.**41**(2003), pp. 1406-1426.

[33]

*Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semi-classical regimes*(with S. Jin and P. A. Markowich ),*SIAM J. Sci. Comput.*, Vol.**25**(2003), pp. 27-64.

[32] Numerical methods for the generalized Zakharov system

*J. Comput. Phys.*, Vol.**190**(2003), pp. 201 - 228.

[31]

*Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation*(with D. Jaksch and P. A. Markowich),*J. Comput. Phys.*, Vol.**187**(2003), pp. 318 - 342.

[30]

*Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional*(with W. J. Tang),*J. Comput. Phys.*, Vol.**187**(2003), pp. 230 - 254.

[29]

*Error bounds for the finite element approximation of the exterior Stokes equations in two dimensions*,*IMA J. Numer. Anal.*, Vol.**23**(2003), pp. 125-148.

[28]

*High-order I-stable central difference schemes for viscous compressible flows*(with J. Shi),*J. Comput. Math.*, Vol.**21**(2003), pp. 101-112.

[27]

*Error bounds for the finite element approximation of an incompressible material in an unbounded domain*(with H. Han),*Numer. Math.*, Vol.**93**(2003), pp. 415-444.

[26]

*Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms*(with S. Jin),*Appl. Numer. Math.*, Vol.**43**(2002), pp. 315-333.

[25]

*An economical finite element approximation of a generalized Newtonian flow*,*Comput. Methods Appl. Mech. Engrg.*, Vol.**191**(2002), pp. 3637-3648.

[24]

*The random projection method for stiff multi-species detonation capturing*(with S. Jin),*J. Comput. Phys.*, Vol.**178**(2002), pp. 37-57.

[23]

*On time-splitting spectral approximation for the Schrodinger equation in the semiclassical regime*(with J. Shi and P. A. Markowich),*J. Comput. Phys.*, Vol.**175**(2002), pp. 487-524.

[22]

*The random projection method for stiff detonation capturing*(with S. Jin),*SIAM J. Sci. Comput.*, Vol.**23**(2001), pp. 1000-1026.

[21]

*Error estimates for the finite element approximation of linear elastic equations in an unbounded domain*(with H. Han),*Math. Comput.*, Vol.**70**(2001), pp. 1437-1459.

[20]

*On inf-sup conditions of mixed finite element formulations for acoustic fluids*(with X. Wang and K. J. Bathe),*Math. Mod. Meth. Appl. Sci.*, Vol.**11**(2001), pp. 883-901.

[19]

*Numerical simulations of fracture problems by coupling the FEM and the direct method of lines*(with H. Han and Z. Huang),*Comput. Methods Appl. Mech. Engrg.*, Vol.**190**(2001), pp. 4831-4846.

[18]

*Weakly compressible high-order I-stable central difference schemes for incompressible viscous flows*(with S. Jin),*Comput. Methods Appl. Mech. Engrg.*, Vol.**190**(2001), pp. 5009-5026.

[17]

*The random projection method for hyperbolic systems with stiff reaction terms*(with S. Jin),*J. Comput. Phys.*, Vol.**163**(2000), pp. 216-248.

[16]

*Artificial boundary conditions for incompressible Navier-Stokes equations: A well-posed result*,*Comput. Methods Appl. Mech. Engrg.*, Vol.**188**(2000), pp. 595-611.

[15]

*The artificial boundary conditions for computing the flow around a submerged body*(with. X. Wen ),*Comput. Methods Appl. Mech. Engrg.*, Vol.**188**(2000), pp. 473-482.[14]

*High-order local artificial boundary conditions for problems in unbounded domains*(with H. Han),*Comput. Methods Appl. Mech. Engrg.*, Vol.**188**(2000), pp. 455-471.

[13]

*Error estimates for the finite element approximation of problems in unbounded domains*(with H. Han),*SIAM J. Numer. Anal.*, Vol.**37**(2000), pp. 1101-1119.

**Before 2000**[12]

*The discrete artificial boundary condition on a polygonal artificial boundary for the exterior problem of Poisson equation by using the direct method of lines*(with H. Han),*Comput. Methods Appl. Mech. Engrg.*, Vol.**179**(1999), pp. 345-360.

[11]

*The direct method of lines for the problem of infinite elastic foundation*(with H. Han),*Comput. Methods Appl. Mech. Engrg.*, Vol.**175**(1999), pp. 157-173.

[10]

*A priori and posteriori error bounds for nonconforming linear finite element approximation of a non-Newtonian flow*(with J. W. Barrett),*M^2AN Math. Model. Numer. Anal.*, Vol.**32**(1998), pp. 843-858.

[9]

*The approximations of the exact boundary condition at an artificial boundary for linearized incompressible viscous flow*,*J. Comput. Math.*, Vol.**16**(1998), pp. 239-256.

[8]

*The artificial boundary conditions for incompressible materials on an unbounded domain*(with H. Han),*Numer. Math.*, Vol.**77**(1997), pp. 347-363.

[7]

*Numerical simulation for the problem of infinite elastic foundation*(with H. Han and T. Wang),*Comput. Methods Appl. Mech. Engrg.*, Vol.**147**(1997), pp. 369-385.

[6]

*Artificial boundary conditions for two-dimensional incompressible viscous flows around an obstacle*,*Comput. Methods Appl. Mech. Engrg.*, Vol.**147**(1997), pp. 263-273.

[5]

*Local artificial boundary conditions for the incompressible viscous flow in a slip channel*(with H. Han),*J. Comput. Math.*, Vol.**15**(1997), pp. 335-344.

[4]

*Nonlocal artificial boundary conditions for the incompressible viscous flow in a channel using spectral techniques*(with H. Han),*J. Comput. Phys.*, Vol.**126**(1996), pp. 52-63.

[3]

*An artificial boundary condition for the incompressible viscous flows using the method of lines*(with H. Han),*Int. J. Numer. Methods Fluids*, Vol.**22**(1996), pp. 483-493.

[2]

*An artificial boundary condition for the incompressible viscous flows in a no-slip channel*(with H. Han),*J. Comput. Math.*, Vol.**13**(1995), pp. 51-65.

[1]

*A discrete artificial boundary condition for steady incompressible viscous flows in a no-slip channel using a fast iterative method*(with H. Han and J. Lu),*J. Comput. Phys.*, Vol.**114**(1994), pp. 201-208.

**Refered Conference Proceedings and Chapters Books**[7]

*Analysis and computation for the semiclassical limits of the ground and excited states of the Gross-Pitaevskii equation*(with F. Y. Lim), Proc. Sympos. Appl. Math., Amer. Math. Soc., Vol. 67 (2009), pp. 195-215.

[6]

*Analysis and efficient computation for the dynamics of two-component Bose-Einstein condensates*, Contemporary Mathematics, American Mathematical Society, Vol. 473 (2008), pp. 1-26.

[5]

*The nonlinear Schroedinger equation and applications in Bose-Einstein condensation and plasma physics*, Chapter 3 in Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization (IMS Lecture Notes Series Volume 9), World Scientific (2007), pp. 141-240.

[4]

*Ground states and dynamics of rotating Bose-Einstein condensates*, Chapter 10 in Transport Phenomena and Kinetic Theory: Applications to Gases, Semiconductors, Photos, and Biological Systems. Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2006), pp. 215-255.

[3]

*Quantum kinetic theory: modeling and numerics for Bose-Einstein condensation*(with P. A. Markowich and L. Pareschi), Chapter 10 in Modeling and Computational Methods for Kinetic Equations. Series: Modeling and Simulation in Science, Engineering and Technology, Birkhauser (2004), pp. 287-321.

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*The random projection method for stiff multi-species detonation computation*(with J. Shi), Proceedings of Hyperbolic Problems: Theory, Numerics, Applications, Birkhauser-Verlag (2001), pp. 139-148.

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*The random projection method*(with J. Shi), Advances in Scientific Computing (Proceeding of the Workshop on Scientific Computing 99 in Hong Kong), Science Press (2001), pp.1-11.

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*Modeling and Simulation for Solid-State Dewetting
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*Multiscale Methods & Analysis for Nonlinear Klein-Gordon
Equation in Nonrelativistic Limit Regime* .

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*Modeling, Analysis and Simulation for Degenerate Dipolar Quantum
Gas* .

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* Quantized Vortex Stability and Dynamics in Superfluidity and
Superconductivity* .

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* Computational Methods for the Dynamics of
Nonlinear Schrodinger / Gross-Pitaevskii Equations* .

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* Analysis & Computation for Ground States of Degenerate
Quantum Gas* .

[3]
* Mathematical Models & Numerical Simulation for Bose-Einstein
Condensation* .

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* The Random Project Method for Stiff Detonation
Capturing* .

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*Communications in Computational Physics (CiCP),
Vol 19, No 5, 2016*
(A special issue dedicated to Professor
Eitan Tadmor's 60th Birthday,
Guest edited with Siddhartha Mishra and Tao Tang),
Global Science Press.

[4]
*Innovation -- The Singapore Magazine of Research, Technology and
Education, Vol 13, No 2, 2014*
(Guest edited with Y. M. Chee and K. H. Hang),
World Scientific Publisher.

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* Multiscale Modeling and Analysis for Materials Simulation
* (edited with Q. Du), World Scientific, 2011
(
* Book flyer and order form*).

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* Kinetic and Related Models (KRM), Vol 4, No 4, 2011*
(Guest edited with A. Arnold, J. Dolbeault and P. Pietra),
American Institute of Mathematical Sciences.

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* Dynamics in Models of Coarsening, Coagulation,
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