Weizhu Bao

I have conducted research in Bose-Einstein condensation; multiscale methods and analysis for highly oscillatory PDEs; solid-state dewetting and geometric flows; 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:

[180] Computing ground states of spin-2 Bose-Einstein condensate by the normalized gradient flow (with Q. Tang and Y. Yuan).

[179] Dynamics of small solid particles on substrates of arbitrary topography (with Q. Zhao, W. Jiang, Y. Wang, D. J. Srolovitz and T. Qian), arXiv: 2409.03468.

[178] Computing ground states of Bose-Einstein condensation by normalized deep neural network (with Z. Chang and X. Zhao).

[177] An energy-stable parametric finite element method for the planar Willmore flow (with Y. Li), arXiv: 2401.13274.

### Accepted:

[176] A unified structure-preserving parametric finite element method for anisotropic surface diffusion (with Y. Li), *Math. Comp.*, to appear (arXiv: 2401.00207).

[175] Convergence rates in the nonrelativistic limit of the cubic Klein-Gordon equation (with Y. Lu and Z. Zhang), *SIAM J. Math. Anal.*, to appear (arXiv: 2304.06920).

[174] A robust hybridizable discontinuous Galerkin scheme with harmonic averaging technique for steady state of real-world semiconductor devices (with Q. Shi, Y. Cai, C. Zhuang, B. Lin, D. Wu and R. Zeng), * J. Comput. Phys., to appear (arXiv: 2408.09692). *

[141]

### Published:

**2024**

[173] An explicit and symmetric exponential wave integrator for the nonlinear Schroedinger equation with low regularity potential and nonlinearity (with C. Wang), *SIAM J. Numer. Anal.*, Vol **62 ** (2024), pp. 1901-1928 (arXiv: 2310.20181).

[172] An extended Fourier pseudospectral method for the Gross-Pitaevskii equation with low regularity potential (with B. Lin, Y. Ma and C. Wang), *East Asian J. Appl. Math.*, Vol **14 ** (2024), pp. 530-550 (arXiv: 2310.20177).

[171] A structure-preserving parametric finite element method for geometric flows with anisotropic surface energy (with Y. Li), *Numer. Math.*, Vol **156 ** (2024), pp. 609-639 (arXiv: 2211.00297).

[170] Improved uniform error bounds on time-splitting methods for the long-time dynamics of the weakly nonlinear Dirac equation (with Y. Cai and Y. Feng), *IMA J. Numer. Anal.*, Vol **44 ** (2024), pp. 654-679 (arXiv: 2203.05886).

[169] Optimal error bounds on time-splitting methods for the nonlinear Schroedinger equation with low regularity potential and nonlinearity (with Y. Ma and C. Wang), *Math. Models Methods Appl. Sci.*, Vol **34 ** (2024), pp. 803-844 (arXiv: 2308.15089).

[168] Error estimates of the time-splitting methods for the nonlinear Schroedinger equation with semi-smooth nonlinearity (with C. Wang), *Math. Comp.*, Vol **93 ** (2024), pp. 1599-1631 (arXiv: 2301.02992).

[167] Optimal error bounds on the exponential wave integrator for the nonlinear Schroedinger equation with low regularity potential and nonlinearity (with C. Wang), *SIAM J. Numer. Anal.*, Vol. **62** (2024), pp. 93-118 (arXiv: 2302.09262).

**2023**

[166] An energy-stable parametric finite element method for simulating solid-state dewetting problems in three dimensions (with Q. Zhao), *J. Comput. Math.*, Vol. **41** (2023), pp. 771–796 (arXiv: 2012.11404).

[165] Phase-field simulations for dripping-to-jetting transitions: effects of low interfacial tension and bulk diffusion (with F. Huang and T. Qian), *Physics of Fluids*, Vol. **35** (2023), article 074105.

[164] A symmetrized parametric finite element method for anisotropic surface diffusion in 3D (with Y. Li), *SIAM J. Sci. Comput.*, Vol. **45** (2023), pp. A1438–A1461 (arXiv: 2206.01883).

[163] Quantized vortex dynamics of the nonlinear Schroedinger equation on torus with non-vanishing momentum (with H. Jian and Y. Zhu), *Physica D*, Vol. **453** (2023), article 133812 (arXiv: 2304.02987).

[162] Regularized numerical methods for the nonlinear Schroedinger equation with singular nonlinearity (with Y. Feng and Y. Ma), *East Asian J. Appl. Math.*, Vol. **13** (2023), pp. 646–670 (arXiv: 2210.16361).

[161] A symmetrized parametric finite element method for anisotropic surface diffusion of closed curves (with W. Jiang and Y. Li), *SIAM J. Numer. Anal.*, Vol. **61** (2023), pp. 617–641 (arXiv: 2112.00508).

[160] Improved uniform error bounds of the time-splitting methods for the long-time (nonlinear) Schroedinger equation (with Y. Cai and Y. Feng), *Math. Comp.*, Vol. **92** (2023), pp. 1109–1139 (arXiv: 2109.08940).

[159] A structure-preserving finite element approximation of surface diffusion for curve networks and surface clusters (with H. Garcke, R. Nurnberg, Q. Zhao), *Numer. Methods Partial Differential Eq.*, Vol. **39** (2023), pp. 759–794 (arXiv: 2202.06775).

**2022**

[158] Improved uniform error bounds on time-splitting methods for the long-time dynamics of the Dirac equation with small potentials (with Y. Feng and J. Yin), *Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal*, Vol. **20** (2022), pp. 1040-1062 (arXiv: 2112.03616).

[157] Diffuse-interface approach to competition between viscous flow and diffusion in pinch-off dynamics (with F. Huang and T. Qian), *Phys. Rev. Fluids*, Vol. **7** (2022), article 094004 (arXiv: 2207.10300).

[156] Improved uniform error bounds on time-splitting methods for long-time dynamics of the nonlinear Klein-Gordon equation with weak nonlinearity (with Y. Cai and Y. Feng), *SIAM J. Numer. Anal.*, Vol. **60** (2022), pp. 1962-1984 (arXiv: 2109.14902).

[155] Volume-preserving parametric finite element methods for axisymmetric geometric evolution equations (with H. Garcke, R. Nurnberg, Q. Zhao), *J. Comput. Phys.*, Vol. **460** (2022), article 111180 (arXiv: 2111.13565).

[154] 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.*, Vol. **91** (2022), pp. 811-842 (arXiv: 2001.10868).

[153] Error estimates of local energy regularization for the logarithmic Schroedinger equation (with R. Carles, C. Su and Q. Tang), *Math. Models Methods Appl. Sci.*, Vol. **32** (2022), pp. 101-136 (arXiv: 2006.05114).

**2021**

[152] A structure-preserving parametric finite element method for surface diffusion (with Q. Zhao), *SIAM J. Numer. Anal.*, Vol. **59** (2021), pp. 2775-2799 (arXiv: 2104.01432).

[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] *Regularized numerical methods for the logarithmic Schroedinger 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.*

[131]

[121]

[113]

[105]

[74]

[47]

[12][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 Schroedinger 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

[13] *Energy-Stable Parametric Finite Element Methods (PFEM) for Geometric PDEs and Applications*.

[12] *From Weyl Conjecture to Fundamental Gap Conjecture and Beyond*.

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

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

[8] *Multiscale Methods & Analysis for Nonlinear Klein-Gordon Equation in Nonrelativistic 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

[8] *Modeling and Simulation for Collective Dynamics *(edited with Peter A. Markowich, Benoit Perthame and Eitan Tadmor), World Scientific, 2023 ( *Book flyer and order form*).

[7] *Models and Methods for Quantum Condensation and Fluids *(edited with Yongyong Cai, Ionut Danaila and Peter A. Markowich), World Scientific, 2023 ( *Book flyer and order form*).

[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.