Weizhu Bao

 

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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.

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Multiscale Methods & Analysis for Oscillatory PDEs

• For long-time dynamics
  • Uniform error bounds of a time-splitting spectral method for the long-time dynamics of the nonlinear Klein-Gordon 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 Klein-Gordon equation with weak nonlinearity (with Y. Feng and W. Yi), Commun. Comput. Phys., Vol. 26 (2019), pp. 1307-1334 (arXiv: 1903.01133).
• For Klein-Gordon and Dirac equations (nonrelativistic limit)
  • Uniform error bounds of time-splitting methods for the nonlinear Dirac equation in the nonrelativistic limit regime (with Y. Cai and J. Yin), arXiv: 1906.11101.
  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • An efficient and stable numerical method for the Maxwell-Dirac system (with X.-G. Li), J. Comput. Phys., Vol. 199 (2004), pp. 663-687.
• 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. 461-487.
  • 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).
  • 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.
  • 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.
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Numerical methods for the nonlinear Schrodinger equation with nonzero far-field conditions, Methods and Applications of Analysis, Vol. 11 (2004), pp. 367-388.
  • 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.
  • 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.
  • 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.
  • 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.
• 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. A929-A953.
  • 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).
  • 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.
  • 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 Klein-Gordon-Zakharov system in the subsonic limit regime (with C. Su), Math. Comp., Vol. 87 (2018), pp. 2133-2158 (arXiv: 1612.09404).
  • 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.
  • 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.
  • 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.
  • 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.
  • Efficient and accurate numerical methods for the Klein-Gordon-Schrodinger equations (with L. Yang), J. Comput. Phys., Vol. 225 (2007), pp. 1863-1893.
  • 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.

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Modeling & Simulation for Solid-State Deweeting

• Onsager variational approach
  • 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.
  • 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).
• Parametric finite element method (PFEM)
  • An energy-stable parametric finite element method for simulating solid-state dewetting problems in three dimensions (with Q. Zhao), arXiv: 2012.11404.
  • An energy-stable parametric finite element method for anisotropic surface diffusion (with Y. Li), arXiv: 2012.05610.
  • An energy-stable parametric finite element method for simulating solid-state dewetting (with W. Jiang and Q. Zhao), arXiv: 2003.01677.
  • 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).
  • 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).
  • 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).
• Sharp interface model
  • Sharp-interface model for simulating solid-state dewetting in three dimensions (with W. Jiang and Q. Zhao), SIAM J. Appl. Math., to appear (arXiv: 1902.05272).
  • 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).
  • 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).
  • 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).
  • 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.
• Phase field model
  • 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.

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Bose-Einstein Condensation (BEC)

• Review Papers
  • 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).
  • 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)).
  • 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).
• 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. 447-471 (arXiv: 1801.06517).
  • Fundamental gaps of the Gross-Pitaevskii equation with repulsive interaction (with X. Ruan), Asymptotic Analysis, Vol. 110 (2018), pp. 53-82 (arXiv: 1512.07123).
• For single-component BEC
  • 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).
  • 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).
  • 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).
  • 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).
  • 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.
  • 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.
  • 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.
  • 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.
  • 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 ).
  • A uniformly convergent numerical method for singularly perturbed nonlinear eigenvalue problems (with M.-H. Chai), Commun. Comput. Phys., Vol. 4 (2008), pp. 135-160.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
• 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 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.
  • 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.
  • 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.
  • 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.
  • Dynamics of the center of mass in rotating Bose-Einstein condensates (with Y. Zhang), Appl. Numer. Math., Vol. 57 (2007), pp. 697-709.
  • 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.
  • 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.
  • 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.
• For dipolar BEC
  • 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).
  • 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).
  • 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).
  • 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).
  • 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.
  • Effective dipole-dipole interactions in multilayered dipolar Bose-Einstein condensates (with Y. Cai and M. Rosenkranz), Phys. Rev. A, Vol. 88 (2013), article 013616.
  • 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.
  • Scattering and bound states in two-dimensional anisotropic potentials (with M. Rosenkranz), Phys. Rev. A, Vol. 84 (2011), article 050701(R).
  • 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.
  • 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.
  • 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.
• For spinor and multi-component BEC
  • 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.
  • Ground states and dynamics of spin-orbit-coupled Bose-Einstein condensates (with Y. Cai), SIAM J. Appl. Math., Vol. 75 (2015), pp. 492-517.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
  • Ground states and dynamics of multi-component Bose-Einstein condensates, Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 2 (2004), pp. 210-236.
• 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).

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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. 2265-2297 (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. 234-249.
  • 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.
  • 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.
• Vortex dynamics in whole space
  • 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.
  • 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.
  • 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.
  • 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.

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Artificial Boundary Conditions & Error Estimates

• For incompressible flow
  • Artificial boundary conditions for incompressible Navier-Stokes equations: A well-posed result, Comput. Methods Appl. Mech. Engrg., Vol.188 (2000), pp. 595-611.
  • 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.
  • 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.
  • Artificial boundary conditions for two-dimensional incompressible viscous flows around an obstacle, Comput. Methods Appl. Mech. Engrg., Vol. 147 (1997), pp. 263-273.
  • 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.
  • 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.
  • 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.
  • 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.
  • 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.
• 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. 125-148.
  • 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.
  • 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.
  • 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.
  • The artificial boundary conditions for incompressible materials on an unbounded domain (with H. Han), Numer. Math., Vol. 77 (1997), pp. 347-363.
  • 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.
• 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. 4831-4846.
  • 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.
  • 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.
  • 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.

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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 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).
• 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. 315-333.
  • The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23 (2001), pp. 1000-1026.
  • The random projection method for stiff detonation capturing (with S. Jin), SIAM J. Sci. Comput., Vol. 23 (2001), pp. 1000-1026.
  • The random projection method for hyperbolic systems with stiff reaction terms (with S. Jin),J. Comput. Phys., Vol. 163 (2000), pp. 216-248.
• For non-Newtonian flow
  • An economical finite element approximation of a generalized Newtonian flow, Comput. Methods Appl. Mech. Engrg., Vol. 191 (2002), pp. 3637-3648.
  • 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.
• For viscous compressible flows
  • High-order I-stable central difference schemes for viscous compressible flows (with J. Shi), J. Comput. Math., Vol. 21 (2003), pp. 101-112.
  • 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.
  • 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.

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