Weizhu Bao
I have conducted research in BoseEinstein condensation; multiscale methods and analysis for highly oscippatory PDEs; solidstate 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.
Multiscale Methods & Analysis for Oscillatory PDEs
 For longtime dynamics
 Uniform error bounds of a timesplitting spectral method for the longtime dynamics of the nonlinear KleinGordon euqation with weak nonlinearity (with Y. Feng and C. Su), arXiv: 2001.10868.
 Long time error analysis of finite difference time domain methods for the nonlinear KleinGordon equation with weak nonlinearity (with Y. Feng and W. Yi), Commun. Comput. Phys., Vol. 26 (2019), pp. 13071334 (arXiv: 1903.01133).
 For KleinGordon and Dirac equations (nonrelativistic limit)
 Uniform error bounds of timesplitting methods for the nonlinear Dirac equation in the nonrelativistic limit regime (with Y. Cai and J. Yin), arXiv: 1906.11101.
 Superresolution of timesplitting methods for the Dirac equation in the nonrelativistic regime (with Y. Cai and J. Yin), Math. Comp., Vol. 89, (2020), 21412173 (arXiv: 1811.02174).
 Comparison of numerical methods for the nonlinear KleinGordon equation in the nonrelativistic limit regime (with X. Zhao), J. Comput. Phys, Vol. 398 (2019), article 108886 (arXiv: 1903.09915).
 A fourthorder compact timesplitting Fourier pseudospectral method for the Dirac equation (with J. Yin), Res. Math. Sci., Vol. 6 (2019), article 11 (arXiv: 1711.07193).
 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. 10941134 (arXiv: 1504.02881).
 A uniformly accurate (UA) multiscale time integrator Fourier pseoduspectral method for the KleinGordonSchrodinger equations in the nonrelativistic limit regime (with X. Zhao), Numer. Math., Vol. 135 (2017), pp. 833873 (arXiv: 1505.00083).
 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. 17851812 (arXiv: 1507.04103).
 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. 14611494 (arXiv: 1511.01192v3).
 A uniformly accurate multiscale time integrator pseudospectral method for the KleinGordon equation in the nonrelativistic limit regime (with Y. Cai and X. Zhao), SIAM J. Numer. Anal., Vol. 52 (2014), pp. 24882511.
 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. 111150.
 Analysis and comparison of numerical methods for KleinGordon equation in nonrelativistic limit regime (with X. Dong), Numer. Math., Vol. 120 (2012), pp. 189229.
 An efficient and stable numerical method for the MaxwellDirac system (with X.G. Li), J. Comput. Phys., Vol. 199 (2004), pp. 663687.
 For nonlinear Schrodinger equation (semiclassical limit)
 Error estimates of energy regularization for the logarithmic Schrodinger equation (with R. Carles, C. Su and Q. Tang), arXiv: 2006.05114.
 Reguarized numerical methods for the logarithmic Schrodinger equation (with R. Carles, C. Su and Q. Tang), Numer. Math., Vol. 143 (2019), pp. 461487.
 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. 657680 (arXiv: 1803.10068).
 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. 11031127.
 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. 21002123.
 Computational methods for the dynamics of the nonlinear Schrodinger/GrossPitaevskii equations (with X. Antoine and C. Besse), Comput. Phys. Commun., Vol. 184 (2013), pp. 26212633 (An Invited Feature Article).
 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. 423445.
 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. 492521.
 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. 54495469.
 Comparisons between sineGordon 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. 11201134.
 Continuous configuration timedependent selfconsistent 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. 11011104.
 Numerical methods for the nonlinear Schrodinger equation with nonzero farfield conditions, Methods and Applications of Analysis, Vol. 11 (2004), pp. 367388.
 Effective one particle quantum dynamics of electrons: a numerical study of the SchrodingerPoissonX_\alpha model (with N. J. Mauser, H. P. Stimming), Comm. Math. Sci., Vol. 1 (2003), pp. 809828.
 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. 14061426.
 Numerical solution of the GrossPitaevskii equation for BoseEinstein condensation (with D. Jaksch and P. A. Markowich), J. Comput. Phys., Vol. 187 (2003), pp. 318 – 342.
 On timesplitting spectral approximation for the Schrodinger equation in the semiclassical regime (with J. Shi and P. A. Markowich), J. Comput. Phys., Vol. 175 (2002), pp. 487524.
 For Zakharov system (subsonic limit)
 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. A929A953.
 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. 9771002 (arXiv: 1604.04685).
 Efficient and stable numerical methods for the generalized and vector Zakharov System , (with F. F. Sun), SIAM J. Sci. Comput., Vol. 26 (2005), pp. 10571088.
 Numerical methods for the generalized Zakharov system (with F. F. Sun and G. W. Wei), J. Comput. Phys., Vol. 190 (2003), pp. 201 – 228.
 For coupled dispersive PDEs
 Uniform error bounds of a finite difference method for the KleinGordonZakharov system in the subsonic limit regime (with C. Su), Math. Comp., Vol. 87 (2018), pp. 21332158 (arXiv: 1612.09404).
 Uniform error estimates of a finite difference method for the KleinGordonSchrodinger system in the nonrelativistic and massless limit regimes (with C. Su), Kinet. Relat. Mod., Vol. 11 (2018), pp. 10371062.
 A uniformly accurate multiscale time integrator pseudospectral method for the KleinGordonZakharov system in the highplasmafrequency limit regime (with X. Zhao), J. Comput. Phys., Vol. 327 (2016), pp. 270293.
 An exponential wave integrator pseudospectral method for the KleinGordonZakharov system (with X. Dong and X. Zhao), SIAM J. Sci. Comput., Vol. 35 (2013), pp. A2903A2927.
 Singular limits of KleinGordonSchrodinger equations to SchrodingerYukawa equations (with X. Dong and S. Wang), Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 8 (2010), pp. 17421769.
 Efficient and accurate numerical methods for the KleinGordonSchrodinger equations (with L. Yang), J. Comput. Phys., Vol. 225 (2007), pp. 18631893.
 A timesplitting spectral method for threewave interactions in media with competing quadratic and cubic nonlinearities (with C. Zheng), Commun. Comput. Phys., Vol. 2 (2007), pp. 123140.
Modeling & Simulation for SolidState Deweeting
 Onsager variational approach
 Powerlaw scaling for solidstate dewetting of thin films: an Onsager variational approach (with W. Jiang, X. Xu and D. J. Srolovitz), arXiv: 2001.09331.
 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. 154160 (arXiv: 1806.08272).
 Parametric finite element method (PFEM)
 An energystable parametric finite element method for simulating solidstate dewetting problems in three dimensions (with Q. Zhao), arXiv: 2012.11404.
 An energystable parametric finite element method for anisotropic surface diffusion (with Y. Li), arXiv: 2012.05610.
 An energystable parametric finite element method for simulating solidstate dewetting (with W. Jiang and Q. Zhao), arXiv: 2003.01677.
 A parametric finite element method for solidstate dewetting problems in three dimensions (with W. Jiang and Q. Zhao), SIAM J. Sci. Comput., Vol. 42, (2020), B327B352 (arXiv: 1908.08311).
 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. 345350 (arXiv: 1611.09449).
 A parametric finite element method for solidstate dewetting problems with anisotropic surface energies (with W. Jiang, Y. Wang and Q. Zhao), J. Comput. Phys., Vol. 330 (2017), pp. 380400 (arXiv: 1601.05877).
 Sharp interface model
 Sharpinterface model for simulating solidstate dewetting in three dimensions (with W. Jiang and Q. Zhao), SIAM J. Appl. Math., to appear (arXiv: 1902.05272).
 Solidstate dewetting on curved subtrates (with W. Jiang, Y. Wang and D. Srolovitz), Phys. Rev. Mater., Vol. 2 (2018), article 113401 (arXiv: 1806.00744).
 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. 20932118 (arXiv: 1608.08481).
 Solidstate dewetting and island morphologies in strongly anisotropic materials (with W. Jiang, Y. Wang, Q. Zhao, D. J. Srolovitz), Scripta Materialia, Vol. 115 (2016), pp. 123127 (arXiv: 1510.03303).
 Sharp interface model for solidstate dewetting problems with weakly anisotropic surface energy (with W. Jiang, D. J. Srolovitz, Y. Wang), Phys. Rev. B, Vol. 91 (2015), article 045303.
 Phase field model
 Phase field approach for simulating solidstate dewetting problems (with W. Jiang, C. V. Thompson and D. J. Srolovitz), Acta Mater., Vol. 60 (2012), pp. 55785592.
BoseEinstein Condensation (BEC)
 Review Papers
 Mathematical models and numerical methods for spinor BoseEinstein condensates (with Y. Cai), Commun. Comput. Phys., Vol. 24 (2018), pp. 899965 (arXiv: 1709.03840).
 Mathematical models and numerical methods for BoseEinstein condensation, Proceedings of the International Congress of Mathematicians (Seoul 2014), Vol. IV (2014), pp. 971996 (arXiv: 1403.3884 (math.ph)).
 Mathematical theory and numerical methods for BoseEinstein condensation (with Y. Cai), Kinet. Relat. Mod., Vol. 6 (2013), pp. 1135 (An Invited Review Paper).
 Fundamental gaps and related topics
 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), arXiv: 1910.12186.
 Fundamental gaps of the fractional Schrodinger operator (with X. Ruan, J. Shen and C. Sheng), Commun. Math. Sci., Vol. 17 (2019), pp. 447471 (arXiv: 1801.06517).
 Fundamental gaps of the GrossPitaevskii equation with repulsive interaction (with X. Ruan), Asymptotic Analysis, Vol. 110 (2018), pp. 5382 (arXiv: 1512.07123).
 For singlecomponent BEC
 Computing ground states of BoseEinstein Condensates with higher order interaction via a regularized density function formulation (with X. Ruan), SIAM J. Sci. Comput., Vol. 41 (2019), pp. B1284B1309 (arXiv: 1908.09096).
 Ground states of BoseEinstein condensates with higher order interaction (with Y. Cai and X. Ruan), Physica D, Vol. 386387 (2019), pp. 3848 (arXiv: 1701.01245).
 A regularized Newton method for computing ground states of BoseEinstein condensates (with X. Wu and Z. Wen), J. Sci. Comput., Vol. 73 (2017), pp. 303329 (arXiv: 1504.02891).
 Meanfield regime and ThomasFermi approximations of trapped BoseEinstein 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).
 Dimension reduction for anisotropic BoseEinstein condensates in the strong interaction regime (with L. Le Treust and F. Mehats), Nonlinearity, Vol. 28 (2015), pp. 755772.
 Subdiffusive spreading of a BoseEinstein condensate in random potentials (with B. Min, T. Li, and M. Rosenkranz), Phys. Rev. A, Vol. 86 (2012), article 053612.
 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.
 Selftrapping of BoseEinstein condensates expanding in shallow optical lattices (with M. Rosenkranz, D. Jaksch and F. Y. Lim), Phys. Rev. A, Vol. 77 (2008), article 063607.
 Selftrapping of impurities in BoseEinstein 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 ).
 A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems (with M.H. Chai), Commun. Comput. Phys., Vol. 4 (2008), pp. 135160.
 Convergence rate of dimension reduction in BoseEinstein condensates (with Y. Ge, D. Jaksch, P. A. Markowich and R. M. Weishaeupl), Comput. Phys. Commun., Vol. 177 (2007), pp. 832850.
 Energy and chemical potential asymptotics for the ground state of BoseEinstein condensates in the semiclassical regime (with F. Y. Lim and Y. Zhang), Bulletin of the Institute of Mathematics, Academia Sinica, Vol. 2 (2007), pp. 495532.
 Efficient and spectrally accurate numerical methods for computing ground and first excited states in BoseEinstein condensates (with IL. Chern and F. Y. Lim), J. Comput. Phys., Vol. 219 (2006), pp. 836854.
 Dynamics of the ground state and central vortex states in BoseEinstein condensation (with Y. Zhang), Math. Models Meth. Appl. Sci., Vol. 15 (2005), pp. 18631896.
 A fourthorder timesplitting LaguerreHermite pseudospectral method for BoseEinstein condensates (with J. Shen), SIAM J. Sci. Comput., Vol. 26 (2005), pp. 20102028.
 On the GrossPitaevskii 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. 767782.
 Computing the ground state solution of BoseEinstein condensates by a normalized gradient flow (with Q. Du), SIAM J. Sci. Comput., Vol. 25 (2004), pp. 16741697.
 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. 329343.
 Numerical solution of the GrossPitaevskii equation for BoseEinstein condensation (with D. Jaksch and P. A. Markowich), J. Comput. Phys., Vol. 187 (2003), pp. 318 – 342.
 Ground state solution of BoseEinstein condensate by directly minimizing the energy functional (with W. J. Tang), J. Comput. Phys., Vol. 187 (2003), pp. 230 – 254.
 For rotating BEC

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.
 A simple and efficient numerical method for computing the dynamics of rotating BoseEinstein condensates via a rotating Lagrangian coordinate (with D. Marahrens, Q. Tang and Y. Zhang), SIAM J. Sci. Comput., Vol. 35 (2013), pp. A2671A2695.
 Optimal error estimates of finite difference methods for the GrossPitaevskii equation with angular momentum rotation (with Y. Cai), Math. Comp., Vol. 82 (2013), pp. 99128.
 A generalizedLaguerreFourierHermite pseudospectral method for computing the dynamics of rotating BoseEinstein condensates (with H. Li and J. Shen), SIAM J. Sci. Comput., Vol. 31 (2009), pp. 36853711.
 A generalizedLaguerreHermite pseudospectral method for computing symmetric and central vortex states in BoseEinstein condensates (with J. Shen), J. Comput. Phys., Vol. 227(2008), pp. 97789793.
 Dynamics of the center of mass in rotating BoseEinstein condensates (with Y. Zhang), Appl. Numer. Math., Vol. 57 (2007), pp. 697709.
 An efficient and spectrally accurate numerical method for computing dynamics of rotating BoseEinstein condensates (with H. Wang), J. Comput. Phys., Vol. 217 (2006), pp. 612626.
 Dynamics of rotating BoseEinstein condensates and their efficient and accurate numerical computation (with Q. Du and Y. Zhang), SIAM J. Appl. Math., Vol. 66 (2006), pp. 758786.
 Ground, symmetric and central vortex states in rotating BoseEinstein condensates (with H. Wang and P. A. Markowich), Comm. Math. Sci., Vol. 3 (2005), pp. 5788.
 For dipolar BEC
 Vortex patterns and the critical rotational frequency in rotating dipolar BoseEinstein condensates (with Y. Cai, Y. Yuan, M. Rosenkranz and H. Pu), Phys. Rev. A, Vol. 98 (2018), article 023610 (arXiv: 1801.07225).
 Dimension reduction for dipolar BoseEinstein condensates in the strong interaction regime (with L. Le Treust and F. Mehats), Kinet. Relat. Mod., Vol. 10 (2017), pp. 553571 (arXiv: 1501.02177).
 Accurate and efficient numerical methods for computing ground states and dynamics of dipolar BoseEinstein condensates via the nonuniform FFT (with Q. Tang and Y. Zhang), Commun. Comput. Phys., Vol.19 (2016), pp. 11411166 (arXiv: 1504.02897).
 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. 7289 (arXiv: 1410.3584).
 Fast and accurate evaluation of nonlocal Coulomb and dipoledipole interactions via the nonuniform FFT (with L. Greengard and S. Jiang), SIAM J. Sci. Comput., Vol. 36 (2014), pp. B777B794.
 Effective dipoledipole interactions in multilayered dipolar BoseEinstein condensates (with Y. Cai and M. Rosenkranz), Phys. Rev. A, Vol. 88 (2013), article 013616.
 GrossPitaevskiiPoisson equations for dipolar BoseEinstein condensate with anisotropic confinement (with N. Ben Abdallah and Y. Cai), SIAM J. Math. Anal., Vol. 44 (2012), pp. 17131741.
 Scattering and bound states in twodimensional anisotropic potentials (with M. Rosenkranz), Phys. Rev. A, Vol. 84 (2011), article 050701(R).
 Meanfield regime of trapped dipolar BoseEinstein condensates in one and two dimensions (with Y. Cai, M. Rosenkranz and Z. Lei), Phys. Rev. A, Vol. 82 (2010), article 043623.
 Efficient numerical methods for computing ground states and dynamics of dipolar BoseEinstein condensates (with Y. Cai and H. Wang), J. Comput. Phys., Vol. 229 (2010), pp. 78747892.
 Symmetry breaking and selftrapping of a dipolar BoseEinstein condensate in a doublewell potential (with B. Xiang, J. Gong, H. Pu and B. Li), Phys. Rev. A, Vol. 79 (2009), article 013626.
 For spinor and multicomponent BEC
 Collective synchronization of the multicomponent GrossāPitaevskiiLohe system (with S.Y. Ha, D. Kim and Q. Tang), Physica D, Vol. 400 (2019), pp. 132158.
 Ground states and dynamics of spinorbitcoupled BoseEinstein condensates (with Y. Cai), SIAM J. Appl. Math., Vol. 75 (2015), pp. 492517.
 Efficient methods for computing ground states of spin1 BoseEinstein condensates based on their characterizations (with IL. Chern and Y. Zhang), J. Comput. Phys., Vol. 253 (2013), pp. 189208.
 Ground states of twocomponent BoseEinstein condensates with an internal atomic Josephson junction (with Y. Cai), East Asia Journal on Applied Mathematics, Vol. 1 (2011), pp. 4981.
 Dynamical laws of the coupled GrossPitaevskii equations for spin1 BoseEinstein condensates (with Y. Zhang), Methods and Applications of Analysis, Vol. 17 (2010), pp. 4980.
 Numerical methods for computing the ground state of spin1 BoseEinstein condensates in uniform magnetic field (with F. Y. Lim), Phys. Rev. E, Vol. 78 (2008), article 066704.
 Computing ground states of spin1 BoseEinstein condensates by the normalized gradient flow (with F. Y. Lim), SIAM J. Sci. Comput., Vol. 30 (2008), pp. 19251948.
 A mass and magnetization conservative and energy diminishing numerical method for computing ground state of spin1 BoseEinstein condensates (with H. Wang), SIAM J. Numer. Anal., Vol. 45 (2007), pp. 21772200.
 Dynamics of rotating twocomponent BoseEinstein condensates and its efficient computation (with H. Li and Y. Zhang), Physica D, Vol. 234 (2007), pp. 4969.
 Ground states and dynamics of multicomponent BoseEinstein condensates, Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 2 (2004), pp. 210236.
 For polariton condensate
 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).
Quantized Vortex in Superfluidity & Superconductivity
 Reduced dynamical laws
 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. 22652297 (arXiv: 1701.01030).
 Vortex dynamics on bounded domain
 The kinematic effects of the defects in liquid crystal dynamics (with R. Chen and H. Zhang), Commun. Comput. Phys., Vol. 20 (2016), pp. 234249.
 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. 411439.
 Numerical study of quantized vortex interaction in the GinzburgLandau equation on bounded domains (with Q. Tang), Commun. Comput. Phys., Vol. 14 (2013), pp. 819850.
 Vortex dynamics in whole space
 The dynamics and interaction of quantized vortices in GinzburgLandauSchrodinger equations (with Q. Du and Y. Zhang), SIAM J. Appl. Math., Vol. 67 (2007), pp. 17401775.
 The dynamics and interaction of quantized vortices in GinzburgLandauSchrodinger equations (with Q. Du and Y. Zhang), SIAM J. Appl. Math., Vol. 67 (2007), pp. 17401775.
 Dynamics of vortices in weakly interacting BoseEinstein condensates (with A. Klein, D. Jaksch and Y. Zhang), Phys. Rev. A, Vol. 76 (2007), article 043602.
 Numerical simulation of vortex dynamics in GinzburgLandauSchrodinger equation (with Q. Du and Y. Zhang), Eur. J. Appl. Math., Vol. 18 (2007), pp. 607630.
Artificial Boundary Conditions & Error Estimates
 For incompressible flow
 Artificial boundary conditions for incompressible NavierStokes equations: A wellposed result, Comput. Methods Appl. Mech. Engrg., Vol.188 (2000), pp. 595611.
 The artificial boundary conditions for computing the flow around a submerged body (with. X. Wen ), Comput. Methods Appl. Mech. Engrg., Vol. 188 (2000), pp. 473482.
 The approximations of the exact boundary condition at an artificial boundary for linearized incompressible viscous flow, J. Comput. Math., Vol. 16 (1998), pp. 239256.
 Artificial boundary conditions for twodimensional incompressible viscous flows around an obstacle, Comput. Methods Appl. Mech. Engrg., Vol. 147 (1997), pp. 263273.
 Local artificial boundary conditions for the incompressible viscous flow in a slip channel (with H. Han), J. Comput. Math., Vol. 15 (1997), pp. 335344.
 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. 5263.
 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. 483493.
 An artificial boundary condition for the incompressible viscous flows in a noslip channel (with H. Han), J. Comput. Math., Vol. 13 (1995), pp. 5165.
 A discrete artificial boundary condition for steady incompressible viscous flows in a noslip channel using a fast iterative method (with H. Han and J. Lu), J. Comput. Phys., Vol. 114 (1994), pp. 201208.
 For linear elasticity and incompressile materials
 Error bounds for the finite element approximation of the exterior Stokes equations in two dimensions, IMA J. Numer. Anal., Vol. 23 (2003), pp. 125148.
 Error bounds for the finite element approximation of an incompressible material in an unbounded domain (with H. Han), Numer. Math., Vol. 93 (2003), pp. 415444.
 Error estimates for the finite element approximation of linear elastic equations in an unbounded domain (with H. Han),Math. Comput., Vol. 70 (2001), pp. 14371459.
 The direct method of lines for the problem of infinite elastic foundation (with H. Han), Comput. Methods Appl. Mech. Engrg., Vol. 175 (1999), pp. 157173.
 The artificial boundary conditions for incompressible materials on an unbounded domain (with H. Han), Numer. Math., Vol. 77 (1997), pp. 347363.
 Numerical simulation for the problem of infinite elastic foundation (with H. Han and T. Wang), Comput. Methods Appl. Mech. Engrg., Vol. 147 (1997), pp. 369385.
 For elliptic problems
 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. 48314846.
 Highorder local artificial boundary conditions for problems in unbounded domains (with H. Han), Comput. Methods Appl. Mech. Engrg., Vol. 188 (2000), pp. 455471.
 Error estimates for the finite element approximation of problems in unbounded domains (with H. Han), SIAM J. Numer. Anal., Vol. 37 (2000), pp. 11011119.
 The direct method of lines for the problem of infinite elastic foundation (with H. Han), Comput. Methods Appl. Mech. Engrg., Vol. 175 (1999), pp. 157173.
Computational Fluid Dynamics
 Modeling and simulation for streamer discharge
 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).
 An efficient and accurate MPIbased 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).
 Random projection method for stiff detonation
 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. 315333.
 The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23 (2001), pp. 10001026.
 The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23 (2001), pp. 10001026.
 The random projection method for hyperbolic systems with stiff reaction terms (with S. Jin),J. Comput. Phys., Vol. 163 (2000), pp. 216248.
 For nonNewtonian flow
 An economical finite element approximation of a generalized Newtonian flow, Comput. Methods Appl. Mech. Engrg., Vol. 191 (2002), pp. 36373648.
 A priori and posteriori error bounds for nonconforming linear finite element approximation of a nonNewtonian flow (with J. W. Barrett), M^2AN Math. Model. Numer. Anal., Vol. 32 (1998), pp. 843858.
 For viscous compressible flows
 Highorder Istable central difference schemes for viscous compressible flows (with J. Shi), J. Comput. Math., Vol. 21 (2003), pp. 101112.
 On infsup 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. 883901.
 Weakly compressible highorder Istable central difference schemes for incompressible viscous flows (with S. Jin), Comput. Methods Appl. Mech. Engrg., Vol. 190 (2001), pp. 50095026.
Miscelansous
 Polymerbased accurate positioning: an exact wormlikechain study (with R. Hou, N. Wang and Z. Wang), ACS OMEGA, Vol. 3 (2018), pp. 1431814326.
 Mechanical transduction via a single soft polymer (with R. Hou, N. Wang and Z. Wang), Phys. Rev. E, Vol. 97 (2018), article 042504.
 A variationaldifference numerical method for designing progressiveaddition lenses (with W. Jiang, Q. Tang and H. Wang), ComputerAided Design, Vol. 48 (2014), pp. 1727.
 Approximation and comparison for motion by mean curvature with intersection points, Computers & Math. Appl. , Vol. 46 (2003), pp. 12111228.