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Welcome to Qi Li's Pages

Research

  • Numerical analysis and scientific computing
  • Structure preserving algorithm for nonlinear dispersion equation
  • Phase field model (diffusion interface model) and efficient numerical algorithm for two-phase flow problems
  • Finite element method, Spectral method, Structure-preserving algorithm

Employment

  • Dec. 2022 --- Present, Associate Professor, School of Science, Chang'an University.
  • Aug. 2020 --- Dec. 2022, Lecture, School of Science, Chang'an University.

Education

  • Ph.D. Computational Mathematics, Xi'an Jiaotong University, Sept. 2016 --- Jul. 2020.
    • Advisor: Prof. Liquan Mei
    • Dissertation title: Efficient Numerical Algorithms for the Phase-field Crystal Model and its Multi-component Problem.
  • Ph.D. joint student, Computational Mathematics, University of South Carolina, Columbia, SC, USA. Sep. 2018 --- May. 2020.
  • M. S. Computational Mathematics, Lanzhou University, Sept. 2013 --- Jul. 2016.
  • B. S. Mathematics and Applied Mathematics, Lanzhou University, Aug. 2009 --- Jul. 2013.

Publications

GoogleScholar  ResearchGate

  1. Qi Li, Supei Zheng, Liquan Mei. Three decoupled, second-order accurate, and energy stable schemes for the conserved Allen-Cahn type block copolymer (BCP) model. Numerical Algorithms, 92, 1233–1259, 2023. Link
  2. Qi Li, Ning Cui, Supei Zheng, Liquan Mei. A new Allen-Cahn type two-model phase-field crystal model for fcc ordering and its numerical approximation. Applied Mathematics Letters, 132:108211, 2022. Link
  3. Ning Cui, Pei Wang, Qi Li. A second-order BDF scheme for the Swift-Hohenberg gradient flows with quadratic-cubic nonlinearity and vacancy potential. Computational and Applied Mathematics, 41(2):58, 2022. Link
  4. Shuaichao Pei, Yanren Hou, Qi Li. A linearly second-order, unconditionally energy stable scheme and its error estimates for the modified phase field crystal equation. Computers & Mathematics with Applications, 103:104–126, 2021. Link
  5. Qi Li, Liquan Mei. Numerical approximation of the two-component PFC models for binary colloidal crystals: efficient, decoupled, and second-order unconditionally energy stable schemes. Journal of Scientific Computing, 88(3):60, 2021. Link
  6. Qi Li, Xiaofeng Yang, Liquan Mei. Efficient numerical scheme for the anisotropic modified phase-field crystal model with a strong nonlinear vacancy potential. Communications in Mathematical Sciences, 19 (2), 355-381, 2021. Link
  7. Qi Li, Liquan Mei, Yibao Li. Efficient second-order unconditionally stable numerical schemes for the modified phase field crystal model with long-range interaction. Journal of Computational and Applied Mathematics, 389, 113335, 2021. Link
  8. Qi Li, Liquan Mei. Efficient, decoupled, and second-order unconditionally energy stable numerical schemes for the coupled Cahn–Hilliard system in copolymer/homopolymer mixtures. Computer Physics Communications, 260, 107290, 2021. Link
  9. Qi Li, Xi Li, Xiaofeng Yang, Liquan Mei. Highly efficient and linear numerical schemes with unconditional energy stability for the anisotropic phase-field crystal model. Journal of Computational and Applied Mathematics, 383, 113122, 2021. Link
  10. Ying Wang, Qi Li, Liquan Mei. A linear, symmetric and energy-conservative scheme for the space-fractional Klein–Gordon–Schrödinger equations. Applied Mathematics Letters, 95, 104-113, 2019. Link
  11. Ying Wang, Liquan Mei, Qi Li, Linlin Bu. Split-step spectral Galerkin method for the two-dimensional nonlinear space-fractional Schrödinger equation. Applied Numerical Mathematics 136, 257-278, 2019. Link
  12. Qi Li, Liquan Mei, Xiaofeng Yang, Yibao Li. Efficient numerical schemes with unconditional energy stabilities for the modified phase field crystal equation. Advances in Computational Mathematics 45 (3), 1551-1580, 2019. Link
  13. Qi Li, Liquan Mei, Bo You. A second-order, uniquely solvable, energy stable BDF numerical scheme for the phase field crystal model. Applied Numerical Mathematics 134, 46-65, 2018. Link
  14. Qi Li, Liquan Mei. Local momentum-preserving algorithms for the GRLW equation. Applied Mathematics and Computation 330, 77-92, 2018. Link

Teaching

  • Spring 2023:

    • Finite Element Method
    • Numerical Method

  • Fall 2022:

    • Numerical Analysis
    • Linear Algebra

  • Spring 2022:

    • Finite Element Method
    • Numerical Analysis

  • Fall 2021:

    • Numerical Analysis

  • Spring 2021:

    • Finite Element Method
    • Numerical Method