Submitted:

[96] Computational methods for the dynamics of the nonlinear Schrodinger/Gross-Pitaevskii equations (with Xavier Antoine and Christophe Besse), arXiv: math.NA 1305.1093.

[95] Dimension reduction of the Schrodinger equation with Coulomb and anisotropic confining potentials (with Huaiyu Jian, Norbert J. Mauser and Yong Zhang), preprint.

[94] A simple and efficient numerical method for computing the dynamics of rotating Bose-Einstein condensates via a rotating Lagrangian coordinate (with Daniel Marahrens, Qinglin Tang and Yanzhi Zhang), arXiv: cond-mat 1305.1378.

[93] Numerical study of quantized vortex interaction in nonlinear Schrodinger equation on bounded domain (with Qinglin Tang), preprint.

[92] Uniformly correct multiscale time integrators for highly oscillatory second order differential equations (with Xuanchun Dong and Xiaofei Zhao), arXiv: math.NA 1212.4939.

[91] Efficient methods for computing ground states of spin-1 Bose-Einstein condensates based on their characterizations (with I-Liang Chern and Yanzhi Zhang), preprint.

[90] Uniform and optimal error estimates of an exponential wave integrator sine pseudospectral method for the nonlinear Schrodinger equation with wave operator (with Yongyong Cai), preprint.

[89] An exponential wave integrator pseudospectral method for the Klein-Gordon-Zakharov system (with Xuanchun Dong and Xiaofei Zhao), preprint.

Accepted:

[88] Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates (with Yongyong Cai and Matthias Rosenkranz), Phys. Rev. A, to appear.

Published:

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

[86] Numerical methods and comparison for computing dark and bright solitons in the nonlinear Schrodinger equation (with Qinglin Tang and Zhiguo Xu), J. Comput. Phys., Vol. 235, pp. 423-445, 2013.

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

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

[83] Subdiffusive spreading of a Bose-Einstein condensate in random potentials (with Tiejun Li, Bin Min and Matthias Rosenkranz), Phys. Rev. A, Vol. 86, 2012, article 053612.

[82] Phase field approach for simulating solid-state dewetting problems (with Wei Jiang, Carl V. Thompson and David J. Srolovitz), Acta Mater., Vol. 60, pp. 5578-5592, 2012.

[81] Gross-Pitaevskii-Poisson equations for dipolar Bose-Einstein condensate with anisotropic confinement (with Naoufel Ben Abdallah and Yongyong Cai), SIAM J. Math. Anal., Vol. 44, pp. 1713-1741, 2012.

[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 Yongyong Cai), SIAM J Numer. Anal., Vol. 50, pp. 492-521, 2012.

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

[77] Scattering and bound states in two-dimensional anisotropic potentials (with Matthias 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 Xuanchun Dong), J. Comput. Phys., Vol. 230, pp. 5449-5469, 2011.

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

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

[73] Mean-field regime of trapped dipolar Bose-Einstein condensates in one and two dimensions (with Yongyong Cai, Matthias Rosenkranz and Zhen Lei), Phys. Rev. A, Vol. 82, 2010, article 043623.

[72] Ground states of two-component Bose-Einstein condensates with an internal atomic Josephson junction (with Yongyong Cai), East Asia Journal on Applied Mathematics, Vol. 1, pp. 49-81, 2010.

[71] Efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates (with Yongyong Cai and Hanquan Wang), J. Comput. Phys., Vol. 229, pp. 7874-7892, 2010.

[70] Comparisons between sine-Gordon equation and perturbed nonlinear Schrodinger equations for modeling light bullets beyond critical collapse (with Xuanchun Dong and Jack Xin), Physica D: Nonlinear Phenomena, Vol. 239, pp. 1120-1134, 2010.

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

[68] Symmetry breaking and self-trapping of a dipolar Bose-Einstein condensate in a double-well potential (with Bo Xiang, Jiangbin Gong, Han Pu and Baowen 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 Fong Yin 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 Jie Shen), J. Comput. Phys., Vol. 227, pp. 9778-9793, 2008.

[65] Quantized vortex stability and interaction in the nonlinear wave equation (with Rong Zeng and Yanzhi Zhang), Physica D, Vol. 237, pp. 2391-2410, 2008.

[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 Fong Yin Lim), SIAM J. Sci. Comput., Vol. 30, No. 4, pp. 1925-1948, 2008.

[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 Ming-Huang Chai), Commun. Comput. Phys., Vol. 4, No. 1, pp. 135-160, 2008.

[60] Convergence rate of dimension reduction in Bose-Einstein condensates (with Yunyi Ge, Dieter Jaksch, Peter A. Markowich and Rada M. Weishaeupl), Comput. Phys. Commun., Vol. 177, No. 11, pp. 832-850, 2007.

[59] The dynamics and interaction of quantized vortices in Ginzburg-Landau-Schrodinger equations (with Qiang Du and Yanzhi Zhang), SIAM J. Appl. Math., Vol. 67, No. 6, pp. 1740-1775, 2007.

[58] Dynamics of vortices in weakly interacting Bose-Einstein condensates (with Alexander Klein, Dieter Jaksch and Yanzhi 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 Hanquan Wang), SIAM J. Numer. Anal., Vol. 45, No. 5, pp. 2177-2200, 2007.

[56] Dynamics of rotating two-component Bose-Einstein condensates and its efficient computation (with Hailiang Li and Yanzhi Zhang), Physica D, Vol. 234 , pp. 49-69, 2007.

[55] Numerical simulation of vortex dynamics in Ginzburg-Landau-Schrodinger equation (with Qiang Du and Yanzhi Zhang), Eur. J. Appl. Math., Vol. 18, pp. 607-630, 2007.

[54] Efficient and accurate numerical methods for the Klein-Gordon-Schrodinger equations (with Li Yang), J. Comput. Phys., Vol. 225, No. 2, pp. 1863-1893, 2007.

[53] Energy and chemical potential asymptotics for the ground state of Bose-Einstein condensates in the semiclassical regime (with Fong Yin Lim and Yanzhi Zhang), Bulletin of the Institute of Mathematics, Academia Sinica, Vol. 2, No. 2, pp. 495-532, 2007.

[52] Dynamics of the center of mass in rotating Bose-Einstein condensates (with Yanzhi Zhang), Appl. Numer. Math., Vol. 57, No. 5-7, pp. 697-709, 2007.

[51] A time-splitting spectral method for three-wave interactions in media with competing quadratic and cubic nonlinearities (with Chunxiong Zheng), Commun. Comput. Phys., Vol. 2, No. 1, pp. 123-140, 2007.

[50] Efficient and spectrally accurate numerical methods for computing ground and first excited states in Bose-Einstein condensates (with I-Liang Chern and Fong Yin Lim), J. Comput. Phys., Vol. 219, No. 2, pp. 836-854, 2006.

[49] An efficient and spectrally accurate numerical method for computing dynamics of rotating Bose-Einstein condensates (with Hanquan Wang), J. Comput. Phys., Vol. 217, No. 2, pp. 612-626, 2006.

[48] Dynamics of rotating Bose-Einstein condensates and their efficient and accurate numerical computation (with Qiang Du and Yanzhi Zhang), SIAM J. Appl. Math., Vol. 66 , No. 3, pp. 758-786, 2006.

[47] Dynamics of the ground state and central vortex states in Bose-Einstein condensation (with Y.Z. Zhang), Math. Models Meth. Appl. Sci., Vol. 15 , No. 12, pp. 1863-1896, 2005.

[46] A fourth-order time-splitting Laguerre-Hermite pseudo-spectral method for Bose-Einstein condensates (with J. Shen), SIAM J. Sci. Comput., Vol. 26 , No. 6, pp. 2010-2028, 2005.

[45] On the Gross-Pitaevskii equation with strongly anisotropic confinement: formal asymptotics and numerical experiments (with Peter A. Markowich, Christian Schmeiser and Rada M. Weishaupl ), Math. Models Meth. Appl. Sci., Vol. 15, No. 5, pp. 767-782, 2005.

[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, No. 9, pp. 1101-1104, 2005.

[43] Ground, symmetric and central vortex states in rotating Bose-Einstein condensates (with H.Q. Wang and P.A. Markowich), Comm. Math. Sci., Vol. 3, No. 1, pp. 57-88, 2005.

[42] Efficient and stable numerical methods for the generalized and vector Zakharov System , (with F.F. Sun), SIAM J. Sci. Comput., Vol. 26, No. 3, pp. 1057-1088, 2005.

[41] Numerical methods for the nonlinear Schrodinger equation with nonzero far-field conditions, Methods and Applications of Analysis, Vol. 11, No. 3, pp. 367-388, 2004.

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

[39] Computing the ground state solution of Bose-Einstein condensates by a normalized gradient flow (with Q. Du), SIAM J. Sci. Comput., Vol. 25, No. 5. pp. 1674-1697, 2004.

[38] Ground states and dynamics of multi-component Bose-Einstein condensates , Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 2, No. 2. pp. 210-236, 2004.

[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, No. 2, pp. 329-343, 2004.

[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, No. 4. pp. 809-828, 2003.

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

[34] An explicit unconditionally stable numerical method for solving damped nonlinear Schrodinger equations with a focusing nonlinearity (with D. Jaksch), SIAM J. Numer. Anal., Vol. 41, No. 4. pp. 1406-1426, 2003.

[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, No. 1. pp. 27-64, 2003.

[32] Numerical methods for the generalized Zakharov system (with F.F. Sun and G.W. Wei), J. Comput. Phys., Vol. 190, No. 1, pp. 201 - 228, 2003.

[31] Numerical solution of the Gross-Pitaevskii equation for Bose-Einstein condensation (with D. Jaksch and P.A. Markowich), J. Comput. Phys., Vol. 187, No. 1, pp. 318 - 342, 2003.

[30] Ground state solution of Bose-Einstein condensate by directly minimizing the energy functional (with W.J. Tang), J. Comput. Phys., Vol. 187, No. 1, pp. 230 - 254, 2003.

[29] Error bounds for the finite element approximation of the exterior Stokes equations in two dimensions , IMA J. Numer. Anal., Vol. 23, No. 1, pp. 125-148, 2003.

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

[27] Error bounds for the finite element approximation of an incompressible material in an unbounded domain (with H. Han), Numer. Math., Vol. 93, No. 3, pp. 415-444, 2003.

[26] Error estimates on the random projection methods for hyperbolic conservation laws with stiff reaction terms (with S. Jin), Appl. Numer. Math., Vol. 43, No. 4, pp. 315-333, 2002.

[25] An economical finite element approximation of a generalized Newtonian flow , Comput. Methods Appl. Mech. Engrg., Vol. 191 , No. 33, pp. 3637-3648, 2002.

[24] The random projection method for stiff multi-species detonation capturing (with S. Jin), J. Comput. Phys., Vol. 178, No. 1, pp. 37-57, 2002.

[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, pp. 487-524, 2002.

[22] The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23, No. 3, pp. 1000-1026, 2001.

[21] Error estimates for the finite element approximation of linear elastic equations in an unbounded domain (with H. Han), Math. Comput., Vol. 70, No. 236, pp. 1437-1459, 2001.

[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 , No. 5, pp. 883-901, 2001.

[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, pp. 4831-4846, 2001.

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

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

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

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

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

[13] Error estimates for the finite element approximation of problems in unbounded domains (with H. Han), SIAM J. Numer. Anal., Vol. 37, No. 4, pp. 1101-1119, 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, pp. 345-360, 1999.

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

[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, pp. 843-858, 1998.

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

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

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

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

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

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

[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, pp. 483-493, 1996.

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

[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, pp. 201-208, 1994.

[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.

[2] 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.

[1] 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.