Information

Publications

Conference

Lectures

Positions

中文版

Prepare

    [60] Soliton dynamics in a class of NLSE. (with Chaobing Zhang).

    [59] On a unified structure-preserving numerical approach for simulating dynamics of spinnor BECs. (with Zixuan Li and Yong Zhang).

    [58] Ground states of BEC with high-order term: mass-preserving and energy-diminishing approach. (with Zixu Feng and Kaizhi Tang).

    [57] On NGF for computing ground states of least-action BEC: energy dissipation and its convergence. (with Zixu Feng and Lunxu Liu).

Preprint

    [56] A new preconditioned L2-Riemannian conjugate gradient method for computing the ground states of Bose-Einstein condensates with rotation. (with Zixu Feng and Wei Qu).

    [55] An accelerated projected gradient flow method for computing the ground states of rotating Bose-Einstein condensates with higher order interaction (with Kaizhi Tang and Shaobo Zhang), 2025.

    [54] An accelerated preconditioned Riemannian Conjugate Gradient (ApRCG) method for computing the ground states of rotating Bose-Einstein condensates (with Zixu Feng and Jian Mi), 2025.

    [53] On accelerated gradient flow methods for computing the ground states of rotating Bose-Einstein condensates: why acceleration and local convergence rate. (with Zixu Feng), 2025.

    [52] An accurate and efficient numerical method to compute the ground states of the rotating spin-1 dipolar Bose-Einstein condensates (with Zhixuan Li, Jing Wang and Yong Zhang), 2025.

    [51] Improved structure preserving schemes for NLSE (with Qingzhou Shu and Jie Shen), 2025.

    [50] A linearly implicit and energy conservative method for the logarithmic Klein-Gordon equation (with Qingzhou Shu and Chunmei Su), 2025.

    [49] An efficient numerical method for the dynamics of abitrary-angle rotating BEC via orthonormal coordinate transformation (with Qingzhou Shu, Yongjun Yuan and Yong Zhang), 2025.

    [48] An efficient and accurate numerical method for computing the ground states of three-dimensional rotating dipolar Bose-Einstein condensates under strongly anisotropic trap (with Hanquan Wang, Shaobo Zhang and Yong Zhang).

Submitted

    [47] On the discrete normalized gradient flow for computing ground states of rotating multi-component BEC: energy dissipation and global convergence (with Zixu Feng and Lunxu Liu), submitted to M3AS, arXiv:2510.19392, 2025.

    [46] A relaxed energy-optimized exponential scalar auxiliary variable method for solving the Ginzburg-Landau equation and its applications in vortex dynamic simulation (with Lin Guo and Teng Zhang), submitted to ESIAM J. Appl. Math., 2025.

    [45] Fast convolution solvers using moment-matching (with Xin Liu and Yong Zhang), submitted to SINUM, 2025.

    [44] On ground states of Spin-1 dipolar Bose-Einstein condensates: dimension reduction and numerical computation (with Zhixuan Li, Hanquan Wang and Yong Zhang), submitted to JCP, 2025.

    [43] Second-order asymptotic analysis and computations for periodic composite Mindlin plate and Timoshenko beam (with Mengyu Zhang, Zhihui Li, Junzhi Cui and Qiang Ma), submitted to JSC, 2025.

    [42] On preconditioned Riemannian gradient methods for minimizing the Gross-Pitaevskii energy functional: algorithms, global convergence and optimal local convergence rate (with Zixu Feng), submitted to Math. Comput., arXiv:2510.13516, 2025.

Published/Accepted

    [41] 基于改进源迭代法与间断有限元的中子输运方程数值研究 (with Jinliang Li and Qian Zhang), Journal on Numerical Methods and Computer Applications (数值计算与计算机应用), accepted, 2025.

    [40] 基于无梯度优化的燃料棒包壳热-力耦合求解加速方法 (with Mengyu Zhang and Weizhen Liu), Mathematica Numerica Sinica (计算数学), accepted, 2025.

    [39] Mass-preserving and energy-diminishing semi-implicit schemes for computing ground states of rotating Bose-Einstein condensates (with Zixu Feng and Qingzhou Shu), Journal of Scientific Computing, accepted, 2025.

    [38] Computing ground states of spin-1 BEC by Riemannian optimization (with Wen Huang and Zilin Yang), SIAM Journal on Scientific Computing, accepted, 2025.

    [37] On a class of high-order structure-preserving methods for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations (with Xin Li and Xuanxuan Zhou), Computer Physics Communications, 319, article 109946, 2026.

    [36] On the discrete normalized gradient flow for computing ground states of rotating Bose-Einstein condensates: energy dissipation and global convergence (with Zixu Feng and Chushan Wang), IMA Journal of Numerical Analysis, accepted, https://doi.org/10.1093/imanum/draf100, 2025.

    [35] On the ground states of rotating two-component dipolar Bose-Einstein condensates (with Wenlei Li, Jing Wang, Yong Zhang and Ruijie Zou), Journal of Computational Physics, Vol. 540, article 114275, 2025.

    [34] High-order compact splitting spectral methods for the rotating spin-1 Bose-Einstein condensates in a magnetic field (with Xin Liu, Xiangyu Meng and Yong Zhang), Mathematical Models and Methods in Applied Sciences, Vol. 35, No. 09, pp. 2013-2045, 2025.

    [33] A normalized gradient flow method for computing ground states of spin-2 Bose-Einstein condensates (with Weizhu Bao and Yongjun Yuan), SIAM Journal on Scientific Computing, Vol. 47, pp. B710-B734, 2025.

    [32] Second-order three-scale asymptotic analysis and algorithms for Steklov eigenvalue problems in composite domain with hierarchical cavities (with Shuyu Ye, Qiang Ma, Junzhi Cui and Zhihui Li), Journal of Scientific Computing, Vol. 98, article 61, 2024.

    [31] A preconditioned Riemannian conjugate gradient method for computing the ground states of arbitrary-angle rotating Bose-Einstein condensates (with Qingzhou Shu, Shaobo Zhang and Yong Zhang), Journal of Computational Physics, Vol. 512, article 113130, 2024.

    [30] On optimal zero-padding of kernel truncation method (with Xin Liu, Shaobo Zhang and Yong Zhang), SIAM Journal on Scientific Computing, Vol. 46, pp. A23-A49, 2024.

    [29] A mass- and energy-preserving numerical scheme for solving coupled Gross-Pitaevskii equations in high dimensions (with Jianfeng Liu and Tingchun Wang), Numerical Methods Partial Differential Equations, Vol. 39, pp. 4248-4269, 2023.

    [28] A quantitative study on the approximation error and speed-up of the multi-scale MCMC (Monte Carlo Markov chain) method for molecular dynamics (with Jie Liu, Jisheng Kou, Dingguo Xu, Tao Zhang and Shuyu Sun), Journal of Computational Physics, Vol. 469, article 111491, 2022.

    [27] A spectrally accurate numerical method for computing the Bogoliubov-de Gennes excitations of dipolar Bose-Einstein condensates (with Manting Xie, Yong Zhang and Yuqing Zhang), SIAM Journal on Scientific Computing, Vol. 44, pp. B100-B121, 2022.

    [26] Error estimates of local energy regularization for the logarithmic Schrödinger equation (with Weizhu Bao, Remi Carles and Chunmei Su), Mathematical Models and Methods in Applied Sciences, Vol 32, pp. 101-136, 2022.

    [25] BEC2HPC: a HPC spectral solver for nonlinear Schrödinger and rotating Gross-Pitaevskii equations. Stationary states computation (with Xavier Antoine and Jeremie Gaidamour), Computer Physics Communications, Vol. 265, article 108007, 2021.

    [24] Scalar Auxiliary Variable/Lagrange multiplier based pseudospectral schemes for the dynamics of nonlinear Schrödinger/Gross-Pitaevskii equations (with Xavier Antoine and Jie Shen), Journal of Computational Physics, Vol. 437, article 110328, 2021.

    [23] Spin soliton with a negative-positive mass transition (with Lichen Zhao, Wenlong Wang, Zhan-Ying Yang, Wen-li Yang and Jie Liu), Physical Review A, Vol. 101, article 043621, 2020.

    [22] Perfectly matched layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates (with Xavier Antoine and Christophe Geuzaine), Communications in Nonlinear Science and Numerical Simulation, Vol. 90, article 105406, 2020.

    [21] Collective synchronization of the multi-component Gross-Pitaevskii-Lohe system (Weizhu Bao, Seung-Yeal Ha and Dohyun Kim), Physica D: Nonlinear Phenomena, Vol 400, pp. 132--158, 2019.

    [20] Numerical methods for the logarithmic Schrödinger equation (with Weizhu Bao, Remi Carles and Chunmei Su), Numerische Mathematik, Vol 143, pp. 461--487, 2019.

    [19] Error estimates of a regularized finite difference method for the logarithmic Schrödinger equation (with Weizhu Bao, Remi Carles and Chunmei Su), SIAM Journal on Numerical Analysis, Vol. 57, No. 2, pp. 657--680, 2019.

    [18] The numerical study of the ground states of spin-1 Bose-Einstein condensates with spin-orbit-coupling (with Yongjun Yuan, Zhiguo Xu and Hanquan Wang), East Asian Journal on Applied Mathematics, Vol. 8, No. 3, pp. 598-610, 2018.

    [17] On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations (with Xavier Antonie and Jiwei Zhang), International Journal of Computer Mathematics, Taylor & Francis, Vol. 95, Issue 6-7, pp. 1423--1443, 2018.

    [16] 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 Yong Zhang), Communications in Computational Physics, Vol. 24, No 4, pp. 966-988, 2018.

    [15] A robust and efficient numerical method to compute the dynamics of the rotating two-component dipolar Bose-Einstein condensates (with Norbert J. Mauser and Yong Zhang), Computer Physics Communications, Vol. 219, pp. 223--235, 2017.

    [14] A friendly review of absorbing boundary conditions and perfectly matched layers for classical and relativistic quantum waves equations (with Xavier Antoine and Emmanuel Lorin), Molecular Physics, Vol. 115, Issue 15-16, pp. 1861--1879, 2017.

    [13] Numerical methods and comparison for the Dirac equation in the nonrelativistic limit regime (with Weizhu Bao, Yongyong Cai and Xiaowei Jia), Journal of Scientific Computing, Vol. 71, pp. 1094--1134, 2017.

    [12] Efficient spectral computation of the stationary states of rotating Bose-Einstein condensates by preconditioned nonlinear conjugate gradient methods (with Xavier Antoine and Antoine Levitt), Journal of Computational Physics, Vol. 343, pp. 92--109, 2017.

    [11] 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 Yong Zhang), Journal of Computational Physics, Vol. 325, pp.74-97, 2016.

    [10] A uniformly accurate multiscale time integrator pseudospectral method for the Dirac equation in the nonrelativistic limit regime (with Weizhu Bao, Yongyong Cai and Xiaowei Jia), SIAM Journal on Numerical Analysis, Vol. 54, pp. 1785--1812, 2016.

    [9] Accurate and efficient numerical methods for computing ground states and dynamics of dipolar Bose-Einstein condensates via the nonuniform FFT (with Weizhu Bao and Yong Zhang), Communications in Computational Physics, Vol. 19, No. 5, pp.1141-1166, 2016.

    [8] Computing the ground state and dynamics of the nonlinear Schrödinger equation with nonlocal interactions via the nonuniform FFT (with Weizhu Bao, Shidong Jiang and Yong Zhang), Journal of Computational Physics, Vol. 296, pp. 72-89, 2015.

    [7] Numerical study of quantized vortex interaction in the nonlinear Schrödinger equation on bounded domains (with Weizhu Bao), Multiscale Modeling and Simulation: a SIAM Interdisciplinary Journal, Vol. 12, pp. 411--439, 2014.

    [6] A variational--difference numerical method for designing progressive--addition lenses (with Weizhu Bao, Wei Jiang and Hanquan Wang), Computer--Aided Design, Vol. 48, pp. 17--27, 2014.

    [5] An efficient spectral method for computing the dynamics of rotating two--component Bose-Einstein condensates via coordinate transformation (with Ming Ju and Yanzhi Zhang), Journal of Computational Physics, Vol. 258, pp. 538--554, 2014.

    [4] Numerical study of quantized vortex interaction in complex Ginzburg--Landau equation on bounded domains (with Wei Jiang), Applied Mathematics and Computation, Vol. 222, pp. 210--230, 2013.

    [3] A simple and efficient numerical method for computing the dynamics of rotating Bose--Einstein condensates via rotating Lagrangian coordinates (with Weizhu Bao, Daniel Marahrens and Yanzhi Zhang), SIAM Journal on Scientific Computing, Vol. 35, pp. A2671--A2695, 2013.

    [2] Numerical study of quantized vortex interaction in the Ginzburg--Landau equation on bounded domains (with Weizhu Bao), Communications in Computational Physics, Vol. 14, pp. 819--850, 2013.

    [1] Numerical methods and comparisons for computing dark and bright solitons in nonlinear Schrödinger equation (with Weizhu Bao and Zhiguo Xu), Journal of Computational Physics, Vol. 235, pp. 423--445, 2013.


Ph.D. Thesis

  • Title: Numerical Studies on Quantized Vortex Dynamics in Superfluidity and Superconductivity
  • Advisor: Weizhu BAO (National University of Singapore)