☰
Manting XIE

Publications

In Preparation

  1. An efficient and spectrally-accurate solver for computing the Bogoliubov-de Gennes excitations of rotating Bose-Einstein condensates
    Li, Yu; Xie, Manting; Zhang, Shaobo; Zhang, Yong.
  2. Augmented subspace adaptive finite element method for computing band gaps of photonic crystals
    Yue, Meiling; Xie, Hehu; Xie, Manting*.

Published (reverse order)

  1. A structure-preserving Fourier spectral method for computing the Bogoliubov-de Gennes excitations of spin-1 Bose-Einstein Condensates
    Li, Yu; Li, Zhixuan; Xie, Manting*; Zhang, Yong
    Multiscale Model. Simul., accepted, 2026.
  2. Computing the Bogoliubov-de Gennes excitations of two-component Bose-Einstein condensates
    Xie, Manting; Zhang, Yong
    J. Comput. Phys., 556 (2026), Paper No. 114813, 18 pp.
  3. A novel augmented subspace adaptive finite element method for the eigenvalue problem with discontinuous coefficients
    Xie, Manting; Yue, Meiling
    SIAM J. Numer. Anal., accepted, 2026.
  4. An efficient adaptive mesh redistribution method for nonlinear eigenvalue problems in Bose-Einstein condensates
    Xie, Hehu; Xie, Manting*; Yin, Xiaobo; Zhao, Gang
    J. Sci. Comput., 94 (2023), no. 2, Paper No. 37, 20 pp.
  5. Local and parallel multigrid method for semilinear Neumann problem with nonlinear boundary condition
    Xu, Fei; Wang, Bingyi; Xie, Manting*
    Numer. Algorithms, doi: https://doi.org/10.1007/s11075-023-01643-5.
  6. A posteriori and superconvergence error analysis for finite element approximation of the Steklov eigenvalue problem
    Xiong, Chunguang; Xie, Manting*; Luo, Fusheng; Su, Hongling
    Comput. Math. Appl., 144 (2023), 90-99.
  7. Multigrid method for nonlinear eigenvalue problems based on Newton iteration
    Xu, Fei; Xie, Manting; Yue, Meiling
    J. Sci. Comput., 94 (2023), no. 2, Paper No. 42, 21 pp.
  8. A spectrally accurate numerical method for computing the Bogoliubov-de Gennes excitations of dipolar Bose-Einstein condensates
    Tang, Qinglin; Xie, Manting; Zhang, Yong; Zhang, Yuqing
    SIAM J. Sci. Comput., 44 (2022), no. 1, B100-B121.
  9. An efficient adaptive multigrid method for the elasticity eigenvalue problem
    Xu, Fei; Huang, Qiumei; Xie, Manting*
    BIT, 62 (2022), no. 4, 2005-2033.
  10. A new family of mixed method for the biharmonic eigenvalue problem based on the first order equations of Hellan-Herrmann-Johnson type
    Li, Yu; Xie, Manting; Xiong, Chunguang
    J. Sci. Comput., 93 (2022), no. 3, Paper No. 66, 23 pp.
  11. Convergence and optimality of adaptive multigrid method for multiple eigenvalue problems
    Xu, Fei; Xie, Manting; Huang, Qiumei; Yue, Meiling; Ma, Hongkun
    J. Comput. Appl. Math., 415 (2022), Paper No. 114450, 20 pp.
  12. A multilevel Newton's method for the Steklov eigenvalue problem
    Yue, Meiling; Xu, Fei; Xie, Manting*
    Adv. Comput. Math., 48 (2022), no. 3, Paper No. 33, 29 pp.
  13. Efficient and accurate computation of the Bogoliubov-de Gennes excitations for the quasi-2D dipolar Bose-Einstein condensates
    Zhang, Yuqing; Liu, Xin; Xie, Manting*
    East Asian J. Appl. Math., 11 (2021), no. 4, 686-707.
  14. A multigrid method for the ground state solution of Bose-Einstein condensates based on Newton iteration
    Xu, Fei; Xie, Hehu; Xie, Manting; Yue, Meiling
    BIT, 61 (2021), no. 2, 645-663.
  15. A type of full multigrid method for non-selfadjoint Steklov eigenvalue problems in inverse scattering
    Xie, Manting; Xu, Fei; Yue, Meiling
    ESAIM Math. Model. Numer. Anal., 55 (2021), no. 5, 1779-1802.
  16. Adaptive time-stepping algorithms for molecular beam epitaxy: based on energy or roughness
    Luo, Fusheng; Xie, Hehu; Xie, Manting; Xu, Fei
    Appl. Math. Lett., 99 (2020), 105991, 8 pp.
  17. An efficient multigrid method for semilinear elliptic problems (in Chinese)
    Xie, Hehu; Xie, Manting; Zhang, Ning
    J. Numer. Methods Comput. Appl., 146 (2019), 55-72.
  18. Computable error estimates for ground state solution of Bose-Einstein condensates
    Xie, Hehu; Xie, Manting*
    J. Sci. Comput., 81 (2019), no. 2, 1072-1087.
  19. Explicit lower bounds for Stokes eigenvalue problems by using nonconforming finite elements
    Xie, Manting; Xie, Hehu; Liu, Xuefeng
    Jpn. J. Ind. Appl. Math., 35 (2018), no. 1, 335-354.
  20. Computable error estimates for a nonsymmetric eigenvalue problem
    Xie, Hehu; Xie, Manting; Yin, Xiaobo; Yue, Meiling
    East Asian J. Appl. Math., 7 (2017), no. 3, 583-602.
  21. A full multigrid method for nonlinear eigenvalue problems
    Jia, Shanghui; Xie, Hehu; Xie, Manting; Xu, Fei
    Sci. China Math., 59 (2016), no. 10, 2037-2048.
  22. A multigrid method for ground state solution of Bose-Einstein condensates
    Xie, Hehu; Xie, Manting
    Commun. Comput. Phys., 19 (2016), no. 3, 648-662.