Publication

Preprint

    [30] On optimal zero-padding of kernel truncation method. (with Xin Liu, Shaobo Zhang and Yong Zhang).

    [29] An efficient numerical method for computing ground states of spin-2 Bose--Einstein condensates (with Weizhu Bao and Yongjun Yuan).

Published

    [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 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 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)