1. On the ground states of rotating dipolar two component Bose-Einstein condensates (with Wenlei Li and Qinglin Tang), in preparation.
  2. High-order uniformly accurate approximations based on composition methods for kinetic equations in the kinetic limit (with Philippe Chartier, Florian Méhats and Mohammed Lemou), in preparation.
  3. An efficient anisotropic method for computing the ground state and dynamics of the rotating dipolar BEC (with Hanquan Wang and Qinglin Tang), in preparation.


  1. A spectrally accurate numerical method for computing the Bogoliubov-de Gennes excitations of dipolar Bose-Einstein condensates(with Qinglin Tang, Manting Xie and Yuqing Zhang), submitted.


  1. A unified structure preserving scheme for a multi-species model with a gradient flow structure and nonlocal interactions via singular kernels (with Yu Zhao and Zhennan Zhou), SIAM Journal on Scientific Computing, 2021, accepted.
  2. Fast one-dimensional convolution with general kernels using sum-of-exponentials approximation (with Shidong Jiang and Chijie Zhuang), Commun. Comput. Phys., 2020, accepted.
  3. Derivation and analysis of computational methods for fractional Laplacian equations with absorbing layers (with Emmanuel Lorin and Xavier Antoine), Numerical Algorithms, 2020,
  4. Compositions of pseudo-symmetric integrators with complex coefficients for the numerical integration of differential equations (with Fernando Casas, Philippe Chartier and Alejandro Escorihuela-Tomàs), J. Comput. Appl. Math., 381, 2021,article 113006
  5. On the rotating Klein-Gordon equation for vorticity dynamics: non-relativistic limit and numerical methods (with Xiaofei Zhao and Norbert J. Mauser), Multiscale Modeling and Simulation (MMS), 18(2) 2020, 999–1024.
  6. Electric Field Evaluation around Slender Conductors by Collocation Boundary Element Method (with Chijie Zhuang and Rong Zeng), CSEE Journal Of Power And Energy Systems, 4 (5) 2019, 483-488.
  7. The anisotropic truncated kernel method for convolution with free-space Green's functions (with Shidong Jiang and Leslie Greengard), SIAM Journal on Scientific Computing, 40(6) 2018, A3733--A3754.
  8. A Preconditioned Conjugated Gradient method for computing ground states of rotating dipolar Bose-Einstein condensates via Kernel Truncation method for Dipole-Dipole Interaction evaluation (with Xavier Antoine and Qinglin Tang), Commun. Comput. Phys., 24(4) 2018, pp. 966-988.
  9. A Fast Tree Algorithm for Electrical Field Calculation in Electrical Discharge Simulations (with Chijie Zhuang, Xin Zhou, Rong Zeng and Lei Liu), IEEE Transactions on Magnetics, 54(3) (2018), article 7201034.
  10. A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (with Norbert J. Mauser and Qinglin Tang), Computer Physics Communications,219 (2017), pp. 223-235.
  11. Convergence of multi-revolution composition time-splitting methods for highly oscillatory differential equations of Schrödinger type (with Philippe Chartier, Florian Méhats and Mechthild Thalhammer), M2AN, 51 (2017), pp.1859--1882.
  12. A novel nonlocal potential solver based on nonuniform FFT for efficient simulation of the Davey-Stewartson equations (with Hans Peter Stimming and Norbert J. Mauser), M2AN, 51 (2017), pp. 1527--1538.
  13. An improved semi-Lagrangian time splitting spectral method for the Schrödinger equation with vector potentials using NUFFT (with Zheng Ma and Zhennan Zhou), Applied Numerical Mathematics, 111 (2017), pp.144-159.
  14. Accurate and efficient computation of nonlocal potentials based on Gaussian-sum approximation (with Lukas Exl and Norbert J Mauser), J. Comput. Phys., 327 (2016), pp.629-642.
  15. On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions (with Xavier Antoine and Qinglin Tang), J. Comput. Phys., 325 (2016), pp.74-97.
  16. A fast implementation of fourth-order compact finite difference scheme for Poisson equation with Dirichlet boundary conditions (with Hanquan Wang, X. Ma, J. Qiu and Y. Liang), Computers and Mathematics with Applications, 71(9) (2016), pp.1843-1860.
  17. Improved error estimates for splitting methods applied to highly-oscillatory nonlinear Schrödinger equations ( with Philippe Chartier, Florian Méhats and Mechthild Thalhammer), Math. Comp., 85(302) (2016), pp.2863-3.
  18. Solving highly-oscillatory NLS with SAM: numerical efficiency and long-time behavior ( with Philippe Chartier, Norbert J. Mauser and Florian Méhats), Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 9(5) (2016), pp.1327-1349.
  19. Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT (with Weizhu Bao and Qinglin Tang), Commun. Comput. Phys., 19(5) (2016), pp.1141-1166.
  20. Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT (with Weizhu Bao, Shidong Jiang and Qinglin Tang), J. Comput. Phys., 296 (2015), pp. 72-89.
  21. Fractional quantum mechanics in polariton condensates with velocity dependent mass ( with Florian Pinsker, Weizhu Bao et al), Physical Review B, 92, (2015), 195310.
  22. Exact artificial boundary condition for the Poisson equation in the simulation of the 2D Schrödinger-Poisson system (with Norbert J. Mauser), Commun. Comput. Phys.,16 (3) (2014), pp. 764-780.
  23. Optimal error estimates of compact finite difference discretizations for the Schrödinger-Poisson system, Commun. Comput. Phys.,13 (2013), pp. 1357-1388.
  24. Calculation of surface electric field on UHV transmission lines under lightning stroke ( with Zhanqing Yu, Qian Li, Rong Zeng, Jinliang He, Zhizhao Li, Chijie Zhuang and Yongli Liao), Electric Power Systems Research, 94 (2013), pp. 79-85.
  25. Dimension reduction of the Schrödinger equation with Coulomb and anisotropic confining potentials (with Weizhu Bao, Norbert J. Mauser and Huaiyu Jian), SIAM J. Appl. Math., 73 (6) (2013), pp. 2100-2123.
  26. On the computation of ground state and dynamics of Schrödinger-Poisson-Slater system (with Xuanchun Dong), J. Comput. Phys., 230 (2011), pp. 2660-2676.


  1. A Boundary Element Method with Reduced-basis for Computing Electrical Field around Long Slim Conductors (with Chijie Zhuang, Yong Zhang, Rong Zeng and Jinliang He), Proc. of the IEEE Compumag Conference, Montreal, Canada, 2015.
  2. Research on Characteristics of Surface Electric Field on Transmission Lines under Lightning Stroke , 7th Asia-Pacific International Conference on Lightning, November 1-4, 2011, Chengdu, China.
  3. Research on Characteristics of Conductor Surface Electric Field Considering Downward Lightning Leader (with Li Zhizhao, Wang Zhiyong, Zeng Rong, Zhang Yong, Yu Zhanqing), 2010 Asia-Pacific International Symposium on Electromagnetic Compatibility, April 12-16, 2010, Beijing, China.

Ph.D. Thesis

  • Title: Numerical Methods and Analysis for the Schrödinger-Poisson Equations and Their Applications
  • Advisor: Huaiyu JIAN (Tsinghua Univeristy) and Weizhu BAO (National University of Singapore)