Publication

 

Weizhu Bao

 


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


 

In Refereed Journals

Submitted:

[157] Improved uniform error bounds for the time-splitting methods for the long-time dynamics of the Schroedinger/nonlinear Schroedinger equation (with Y. Cai and Y. Feng), arXiv: 2109.08940.

[156] An energy-stable parametric finite element method for simulating solid-state dewetting problems in three dimensions (with Q. Zhao), arXiv: 2012.11404.

[155] Power-law scaling for solid-state dewetting of thin films: an Onsager variational approach (with W. Jiang, X. Xu and D. J. Srolovitz), arXiv: 2001.09331.

Accepted:

[154] Error estimates of local energy regularization for the logarithmic Schrodinger equation (with R. Carles, C. Su and Q. Tang), Math. Models Methods Appl. Sci., to appear (arXiv: 2006.05114).

[153] Uniform error bounds of a time-splitting spectral method for the long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity  (with Y. Feng and C. Su), Math. Comp., to appear (arXiv: 2001.10868).

[152] A structure-preserving parametric finite element method for surface diffusion (with Q. Zhao), SIAM J. Numer. Anal., to appear (arXiv: 2104.01432).

Published:

2021

[151] An energy-stable parametric finite element method for anisotropic surface diffusion (with Y. Li), J. Comput. Phys., Vol. 446 (2021), article 110658 (arXiv: 2012.05610).

[150] Controlling fingering instabilities in Hele-Shaw flows in the presence of wetting film effects (with Pedro H. A. Anjos, M. Zhao, J. Lowengrub and S. Li), Phys. Rev. E, Vol. 103 (2021), article 063105 (arXiv: 2103.05206).

[149] An energy-stable parametric finite element method for simulating solid-state dewetting (with W. Jiang and Q. Zhao), IMA J. Numer. Anal., Vol. 41 (2021), pp. 2026-2055 (arXiv: 2003.01677).

[148] Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic regime without magnetic potential (with Y. Cai and J. Yin), SIAM J. Numer. Anal., Vol. 59 (2021), pp. 1040-1066 (arXiv: 1906.11101).

2020

[147] Accurate and efficient calculation of photoionization in streamer discharges using the fast multipole method (with B. Lin, C. Zhuang Z. Cai and R. Zeng), Plasma Sources Sci. Technol., Vol. 29 (2020), article 125010 (arXiv: 2006.03515).

[146] A Jacobi spectral method for computing eigenvalue gaps and their distribution statistics of the fractional Schrodinger operator (with L. Chen, X. Jiang and Y. Ma), J. Comput. Phys., Vol. 421 (2020), article 109733 (arXiv: 1910.12186).

[145] Sharp-interface model for simulating solid-state dewetting in three dimensions (with W. Jiang and Q. Zhao), SIAM J. Appl. Math., Vol. 80 (2020), 1654-1677 (arXiv: 1902.05272).

[144] Super-resolution of time-splitting methods for the Dirac equation in the nonrelativistic regime (with Y. Cai and J. Yin), Math. Comp., Vol. 89 (2020), 2141-2173 (arXiv: 1811.02174).

[143] A parametric finite element method for solid-state dewetting problems in three dimensions  (with W. Jiang and Q. Zhao), SIAM J. Sci. Comput., Vol. 42 (2020), B327-B352 (arXiv: 1908.08311).

[142] An efficient and accurate MPI-based parallel simulator for streamer discharges in three dimensions (with B. Lin, C. Zhuang, Z. Cai and R. Zeng), J. Comput. Phys., Vol. 401 (2020), article 109026   (arXiv: 1812.08606).

2019

141]  Computing ground states of Bose-Einstein Condensates with higher order interaction via a regularized density function formulation  (with X. Ruan), SIAM J. Sci. Comput., Vol. 41 (2019), pp. B1284-B1309  (arXiv: 1908.09096).

[140] Comparison of numerical methods for the nonlinear Klein-Gordon equation in the nonrelativistic limit regime (with X. Zhao), J. Comput. Phys, Vol. 398 (2019), article 108886  (arXiv: 1903.09915).

[139] Reguarized numerical methods for the logarithmic Schrodinger equation (with R. Carles, C. Su and Q. Tang), Numer. Math., Vol. 143 (2019), pp. 461-487.

[138] Long time error analysis of finite difference time domain methods for the nonlinear Klein-Gordon equation with weak nonlinearity (with Y. Feng and W. Yi), Commun. Comput. Phys., Vol. 26 (2019), pp. 1307-1334 (arXiv: 1903.01133).

[137] Collective synchronization of the multi-component Gross–Pitaevskii-Lohe system  (with S.-Y. Ha, D. Kim and Q. Tang), Physica D, Vol. 400 (2019), pp. 132-158.

[136] Fundamental gaps of the fractional Schrodinger operator (with X. Ruan, J. Shen and C. Sheng), Commun. Math. Sci., Vol. 17 (2019), pp. 447-471 (arXiv: 1801.06517).

[135] Error estimates of a regularized finite difference method for the logarithmic Schrodinger equation (with R. Carles, C. Su and Q. Tang ), SIAM J. Numer. Anal., Vol. 57 (2019), pp. 657-680 (arXiv: 1803.10068).

[134] A fourth-order compact time-splitting Fourier pseudospectral method for the Dirac equation  (with J. Yin), Res. Math. Sci., Vol. 6 (2019), article 11 (arXiv: 1711.07193).

[133] Ground states of Bose-Einstein condensates with higher order interaction (with Y. Cai and X. Ruan), Physica D, Vol. 386-387 (2019), pp. 38-48 (arXiv: 1701.01245).

[132] Application of the Onsager’s variational principle to the dynamics of a solid toroidal island on a substrate (with W. Jiang, Q. Zhao, T. Qian and D. Srolovitz), Acta Mater., Vol. 163 (2019), pp. 154-160 (arXiv: 1806.08272).

2018

[131] Solid-state dewetting on curved subtrates (with W. Jiang, Y. Wang and D. Srolovitz), Phys. Rev. Mater., Vol. 2 (2018), article 113401 (arXiv: 1806.00744).

[130] Fundamental gaps of the Gross-Pitaevskii equation with repulsive interaction (with X. Ruan), Asymptotic Analysis, Vol. 110 (2018), pp. 53-82 (arXiv: 1512.07123).

[129] Polymer-based accurate positioning: an exact worm-like-chain study (with R. Hou, N. Wang and Z. Wang),  ACS OMEGA, Vol. 3 (2018), pp. 14318-14326.

[128] Vortex patterns and the critical rotational frequency in rotating dipolar Bose-Einstein condensates (with Y. Cai, Y. Yuan, M. Rosenkranz and H. Pu), Phys. Rev. A, Vol. 98 (2018), article 023610 (arXiv: 1801.07225).

[127] 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).

[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, Vol. 23(2018), pp. 2265-2297 (arXiv: 1701.01030).

[125] Mathematical models and numerical methods for spinor Bose-Einstein condensates (with Y. Cai), Commun. Comput. Phys., Vol. 24 (2018), pp. 899-965 (arXiv: 1709.03840).

[124] 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.

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

[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).

2011 — 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.

[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.

[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.

[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.

[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 Methods 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 (with D. Jaksch), SIAM J. Numer. Anal., Vol. 41 (2003), pp. 1406-1426.

[33] Numerical study of time-splitting spectral discretizations of nonlinear Schrodinger equations in the semiclassical 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 (with F. F. Sun and G. W. Wei), 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. Models Methods 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.

 

In Refered Conference Proceedings and Books Chapters

[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.

 

Past and Recent Talks and/or Presentations

[11] A tutorial on Numerical methods for the Dynamics of the Nonlinear Schrodinger / Gross-Pitaevskii Equations .

[10] A tutorial on Multiscale methods and Analysis for the Dirac Equation in the Nonrelativistic Limit Regime .

[9] Modeling and Simulation for Solid-State Dewetting Problems .

[8] Multiscale Methods & Analysis for Nonlinear Klein-Gordon Equation in Nonrelativistic Limit Regime .

[7] Modeling, Analysis and Simulation for Degenerate Dipolar Quantum Gas .

[6] Quantized Vortex Stability and Dynamics in Superfluidity and Superconductivity .

[5] Computational Methods for the Dynamics of Nonlinear Schrodinger / Gross-Pitaevskii Equations .

[4] Analysis & Computation for Ground States of Degenerate Quantum Gas .

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

[2] The Random Project Method for Stiff Detonation Capturing.

[1] Numerical Methods for Problems in Unbounded Domains.

 

Books Edited or Published

[6] Communications in Computational Physics (CiCP), Vol 24, No 4, 2018 (A special issue dedicated to Professor Houde Han’s 80th Birthday, Guest edited with Jingfang Huang, ZHongyi Huang and Chunxiong Zheng), Global Science Press.

[5] 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.

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

[2] 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.

[1] Dynamics in Models of Coarsening, Coagulation, Condensation and Quantization (edited with J.-G. Liu), World Scientific, 2007.