[CV]

Personal Data

Name: H. (Hong) Zhang (张弘)

Dept.: College of Science, National University of Defense Technology

Address: Fuyuan Road No. 1, Kaifu District, Changsha, P.R. China

Email: zhanghnudt at 163 dot com

Homepage: http://hzhang1991.github.io/

Educational and Academic Data

  • 2020.12 - present: Associate Professor in College of Science, National University of Defense Technology, P.R. China
  • 2018.12 - 2020.12: Lecturer in College of Science, National University of Defense Technology, P.R. China

  • 2018.4 -2018.6: Short term visiting scholar in Department of Mathematics The University of Kansas, USA

    Adviser: Prof. Weizhang Huang

  • 2015.10 - 2018.10: Ph.D in Mathematical Institute, Utrecht University, the Netherlands

    Thesis Title: Computational of non-monotone wave and fingers in two-phase flow. [pdf]

    Adviser: Professor Paul A. Zegeling

  • 2012.9 - 2014.12: M.Sc. in Department of Mathematics and System Science, NUDT, P.R. China

    Thesis Title: Study on two classes of structure-preserving methods for Hamiltonian partial differential equations. [pdf]

    Adviser: Professor Songhe Song

  • 2008.9 - 2012.6: B.Sc. in Department of Mathematics, Zhejiang University, P.R. China

    Thesis Title: Simulation of incompressible flow using lattice Boltzmann method on multi-threaded platform. [pdf]

    Adviser: Professor Xianliang Hu

Research Interests

  1. Geometric numerical integration
  2. Phase field models
  3. Moving mesh methods
  4. Computational fluid dynamics

Publications

  1. Zhang H*, Wang H, Wang Y, Qian X. Global-in-time energy stability for a general class of stabilization single-step schemes applied to the Swift–Hohenberg equation[J]. CSIAM Transactions on Applied Mathematics, 2025, 6(3), 555-592. [DOI: 10.4208/csiam-am.SO-2024-0069]
  2. Fu T, Qian X, Song S H, Zhang H. A novel energy-preserving relaxation extended Runge–Kutta Nyström framework for oscillatory Hamiltonian systems[J]. Mathematics and Computers in Simulation, 2025. [DOI: 10.1016/j.matcom.2025.08.011]
  3. Wang Y, Wang H, Zhang H, et al. A second-order maximum bound principle-preserving exponential Runge–Kutta scheme for the convective Allen–Cahn equation[J]. Computers & Mathematics with Applications, 2025, 193: 297-314. [DOI: 10.1016/j.camwa.2025.06.029]
  4. Teng X, Zhang H. A Third-Order Energy Stable Exponential-Free Runge–Kutta Framework for the Nonlocal Cahn–Hilliard Equation[J]. Journal of Scientific Computing, 2025, 103(74):1-27. [DOI: 10.1007/s10915-025-02889-y]
  5. Yan J, Zhang H, Wei Y, et al. High-order and mass-conservative regularized implicit-explicit relaxation Runge-Kutta methods for the low regularity Schrödinger equations[J]. Applied Numerical Mathematics, 2025, 216: 210-221. [DOI: 10.1016/j.apnum.2025.05.009]
  6. Teng X, Chen X, **Zhang H. Error estimates for a class of energy dissipative IMEX Runge–Kutta schemes applied to the no-slope-selection thin film model[J]. Communications in Nonlinear Science and Numerical Simulation, 2025, 147: 108797. [DOI: 10.1016/j.cnsns.2025.108797]
  7. Sun J, Wang H, Zhang H, Qian X. On the convergence and energy stability analysis for a second-order accurate scheme of Swift–Hohenberg equation[J]. Journal of Scientific Computing, 2025, (103) 80 [DOI: 10.1007/s10915-025-02839-8]
  8. Liu Y, Teng X, Yan X, Zhang H. A second-order, unconditionally invariant-set-preserving scheme for the FitzHugh-Nagumo equation[J]. Computers & Mathematics with Applications, 2025, 189: 161-175. [DOI: 10.1016/j.camwa.2025.04.013]
  9. Yi Y, Fei M, Zhang H, Song S. High-order energy-preserving methods for the coupled Klein–Gordon–Schrödinger equations with fractional Laplacian [J]. Computational and Applied Mathematics, 2025, 44(6): 284. [DOI: 10.1007/s40314-025-03210-1]
  10. Zhang H, Wang HF, Teng XQ. A second-order, global-in-time energy stable implicit-explicit Runge–Kutta scheme for the phase field crystal equation[J]. SIAM Journal on Numerical Analysis, 2024, 62(6): 2667-2697. [DOI: 10.1137/24M1637623]
  11. Zhang H, Zhang G, Liu Z, et al. On the maximum principle and high-order, delay-free integrators for the viscous Cahn–Hilliard equation[J]. Advances in Computational Mathematics, 2024, 50(3): 1-46. [DOI: 10.1007/s10444-024-10143-6]
  12. Zhang H, Liu L, Qian X, et al. Large time-stepping, delay-free, and invariant-set-preserving integrators for the viscous Cahn–Hilliard–Oono equation[J]. Journal of Computational Physics, 2024, 499: 112708. [DOI: 10.1016/j.jcp.2023.112708]
  13. Zhang H, Qian X, Song S. Third-order accurate, large time-stepping and maximum-principle-preserving schemes for the Allen-Cahn equation[J]. Numerical Algorithms, 2024, 95(3): 1213-1250. [DOI: 10.1007/s11075-023-01606-w]
  14. Zhang H, Liu L, Qian X, et al. Quantifying and eliminating the time delay in stabilization exponential time differencing Runge–Kutta schemes for the Allen–Cahn equation[J]. ESAIM: Mathematical Modelling and Numerical Analysis, 2024, 58(1): 191-221. [DOI: [10.1051/m2an/2023101](https://doi.org/10.1051/m2an/2023101)]
  15. Wang H, Wang Y, Zhang H, et al. Energy stability and error estimate of the RKMK2e scheme for the extended Fisher–Kolmogorov equation[J]. Applied Numerical Mathematics, 2025, 212, 60-76. [DOI: 10.1016/j.apnum.2025.01.014]
  16. Wang H, Sun J, Zhang H, Qian X, Song S. A novel up to fourth-order equilibria-preserving and energy-stable exponential Runge–Kutta framework for gradient flows[J]. CSIAM Transactions on Applied Mathematics, 2025, 6(1), 106-147 [DOI: 10.4208/csiam-am.SO-2024-0032]
  17. Liu Z, Wang H, Zhang H, et al. Render unto Numerics: Orthogonal Polynomial Neural Operator for PDEs with Non-periodic Boundary Conditions[J]. SIAM Journal on Scientific Computing, 2024, 46(4): C323-C348 [DOI: 10.48550/arXiv.2206.12698]
  18. Teng X, Gao Z, Zhang H, et al. Maximum-principle-preserving, delay-free parametric relaxation integrating factor Runge–Kutta schemes for the conservative nonlocal Allen-Cahn equation[J]. Discrete and Continuous Dynamical Systems-B, 2025, 30(5):1472-1498 [DOI: 10.3934/dcdsb.2024136]
  19. Wang Y, Xiao X, Zhang H, et al. Efficient diffusion domain modeling and fast numerical methods for diblock copolymer melt in complex domains[J]. Computer Physics Communications, 2024, 305: 109343. [DOI: 10.1016/j.cpc.2024.109343]
  20. Teng X, Zhang H. High-order L2-bound-preserving Fourier pseudo-spectral schemes for the Allen-Cahn equation[J]. Numerical Algorithms, 2024: 1-36. [DOI: 10.1007/s11075-024-01772-5]
  21. Liu L, Zhang H, Song S. Maximum-Principle-Preserving, Steady-State-Preserving and Large Time-Stepping High-Order Schemes for Scalar Hyperbolic Equations with Source Terms[J]. Communications in Computational Physics, 2024, 35(2): 498-523. [DOI: 10.4208/cicp.OA-2023-0143]
  22. Liu L, Zhang H, Qian X, et al. High-order, large time-stepping integrators for scalar hyperbolic conservation laws[J]. Communications in Nonlinear Science and Numerical Simulation, 2024, 131: 107806. [DOI: 10.1016/j.cnsns.2023.107806]
  23. Liu Z, Zhang H, Qian X, et al. Mass and energy conservative high-order diagonally implicit Runge–Kutta schemes for nonlinear Schrödinger equation[J]. Applied Mathematics Letters, 2024: 109055. [DOI: 10.1016/j.aml.2024.109055]
  24. Zhang H, Qian X, Xia J, Song S. Efficient inequality-preserving integrators for differential equations satisfying forward Euler conditions[J]. ESAIM: M2AN, 57 (2023) 1619–1655 [DOI: 10.1051/m2an/2023029]
  25. Zhang H, Yan J, Qian X, Song S. Temporal high-order, unconditionally maximum-principle-preserving integrating factor multi-step methods for Allen-Cahn-type parabolic equations[J].Applied Numerical Mathematics, 2023, 186: 19-40. [DOI: 10.1016/j.apnum.2022.12.020]
  26. Zhang H, Yan J, Qian X, Song S. Unconditionally maximum principle preserving parametric integrating factor two-step Runge-Kutta schemes for parabolic sine-Gordon equations. CSIAM Transactions on Applied Mathematics 4 (1) (2023) 177–22. [DOI: 10.4208/csiam-am.SO-2022-0019]
  27. Sun J, Zhang H, Qian X, et al. A family of structure-preserving exponential time differencing Runge–Kutta schemes for the viscous Cahn–Hilliard equation[J]. Journal of Computational Physics, 2023, 492: 112414. [DOI: 10.1016/j.jcp.2023.112414]
  28. Qian X, Zhang H, Yan J, et al. Novel High-Order Mass-and Energy-Conservative Runge-Kutta Integrators for the Regularized Logarithmic Schrodinger Equation[J]. Numerical Mathematics-Theory Methods and Applications, 2023, 16(4): 993-1012. [DOI: 10.4208/nmtma.OA-2022-0185]
  29. Sun J, Zhang H, Qian X, et al. Up to eighth-order maximum-principle-preserving methods for the Allen–Cahn equation[J]. Numerical Algorithms, 2023, 92(2): 1041-1062. [DOI: 10.1007/s11075-022-01329-4]
  30. Gao Z, Zhang H, Qian X, et al. High-order unconditionally maximum-principle-preserving parametric integrating factor Runge-Kutta schemes for the nonlocal Allen-Cahn equation[J]. Applied Numerical Mathematics, 2023, 194: 97-114. [DOI: [10.1016/j.apnum.2023.08.010](https://doi.org/10.1016/j.apnum.2023.08.010)]
  31. Xu Qian, Hong Zhang, Jingye Yan, Songhe Song. Novel high-order mass-and energy-conservative Runge-Kutta integrators for the regularized logarithmic Schrödinger equation[J]. Numerical Mathematics Theory Methods and Applications, 2023,16(4):993-1012 [DOI: [10.4208/nmtma.OA-2022-0185](https://doi.org/10.4208/nmtma.OA-2022-0185]
  32. Yang J, Yi N, Zhang H. High-order, unconditionally maximum-principle preserving finite element method for the Allen–Cahn equation[J]. Applied Numerical Mathematics, 2023, 188: 42-61. [DOI: 10.1016/j.apnum.2023.03.002]
  33. Yan X, Qian X, Zhang H, et al. Solving nonlinear delay-differential-algebraic equations with singular perturbation via block boundary value methods [J]. Journal of Computational Mathematics, 2023, 41(4). [DOI: 10.4208/jcm.2109-m2021-0020]
  34. Huang Y, Peng G, Zhang G, Zhang H. High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations[J]. Mathematics and Computers in Simulation, 2023, 208: 603-618. [DOI: 10.1016/j.matcom.2023.01.031]
  35. Zhang H, Yan J, Qian X, Song S. Up to fourth-order unconditionally structure-preserving parametric single-step methods for semilinear parabolic equations. Computational Methods in Applied Mathematics and Engineering, 393 (2022) 114817. [DOI: 10.1016/j.cma.2022.114817]
  36. Zhang H, Yan J, Qian X, Chen X, Song S. Explicit third-order unconditionally structure-preserving schemes for conservative Allen-Cahn equations. Journal of Scientific Computing, 2022, 90(8):1-29 [DOI: 10.1007/s10915-021-01691-w]
  37. Yan J, Zhang H, Qian X, et al. A novel regularized model for the logarithmic Klein-Gordon equation[J]. Applied Numerical Mathematics, 2022, 176: 19-37. [DOI: 10.1016/j.apnum.2022.02.007]
  38. Yan XQ, Qian X, Zhang H, Song SH. Numerical approximation to nonlinear delay-differential–algebraic equations with proportional delay using block boundary value methods. Journal of Computational and Applied Mathematics, 2021, 404(1): 0-113867 [DOI: ]10.1016/j.cam.2021.113867]
  39. Jingye Yan, Xu Qian, Hong Zhang, Songhe Song. Two regularized Energy preserving finite difference methods for the logarithmic Klein–Gordon equation. Journal of Computational and Applied Mathematics, 2021, 393:113478 [DOI: 10.1016/j.cam.2021.113478]
  40. Jingye Yan, Hong Zhang, Xu Qian, Songhe Song. Regularized finite difference methods for the logarithmic Klein-Gordon equation[J]. East Asian Journal on Applied Mathematics, 2021, 11(1): 119-142 [DOI: 10.4208/eajam.140820.250820]
  41. Zhang H, Yan J, Qian X, Gu X, Song S. On the maximum principle preserving and energy stability of high-order implicit-explicit Runge-Kutta schemes for the space-fractional Allen-Cahn equation. Numerical Algorithms, 2021, 88:1309-1336 [DOI: 10.1007/s11075-021-01077-x]
  42. Zhang H, Yan J, Qian X, Song S. Numerical analysis and applications of explicit high order maximum principle preserving integrating factor Runge-Kutta schemes for Allen-Cahn equation [J]. Applied Numerical Mathematics, 2021, 161: 372-390. [DOI: 10.1016/j.apnum.2020.11.022]
  43. Hong Zhang, Xu Qian, Jingye Yan, Songhe Song. Highly efficient invariant-conserving explicit Runge-Kutta schemes for nonlinear Hamiltonian diffierential equations[J]. Journal of Computational Physics, 2020, 418(4–5):109598, [DOI: 10.1016/j.jcp.2020.109598]
  44. Hong Zhang, Xu Qian, Songhe Song. Novel high-order energy-preserving diagonally implicit Runge–Kutta schemes for nonlinear Hamiltonian ODEs[J].Applied Mathematics Letters, 2020, 102: 106091. [DOI: 10.1016/j.aml.2019.106091]
  45. Lingyan Tang, Songhe Song, Hong Zhang. High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws[J]. Applied Mathematics and Mechanics, 2020, 41(1): 173-192. [ DOI: 10.1007/s10483-020-2554-8]
  46. Jingye Yan, Hong Zhang, Ziyuan Liu, Songhe Song. Two novel linear-implicit momentum-conserving schemes for the fractional Korteweg-de Vries equation[J]. Applied Mathematics and Computation, 2020, 367: 124745. [DOI: 10.1007/s10483-020-2554-8]
  47. Ziyuan Liu, Hong Zhang, Jingye Yan, Songhe Song. A fast mass-conserving explicit splitting method for the stochastic space-fractional nonlinear Schrödinger equation with multiplicative noise[J]. Applied Mathematics Letters, 2019, 98: 419-426. [DOI: 10.1016/j.aml.2019.06.033 {:target=”_blank”}]
  48. Mingzhan Song, Xu Qian, Hong Zhang, Jingmin Xia, Songhe Song. Two kinds of new energy-preserving schemes for the coupled nonlinear Schrodinger equations, Communications in Computational Physics, 2019, 25(4): 1127-1143 [DOI: 10.4208/cicp.OA-2017-0212]
  49. Yunrui Guo, Lingyan Tang, Hong Zhang and Songhe Song. A Maximum-Principle-Preserving Third Order Finite Volume SWENO Scheme on Unstructured Triangular Meshes[J]. Adv. Appl. Math. Mech., 10 (2018), pp. 114-137. [DOI: 10.4208/aamm.OA-2016-0196]
  50. Y.R. Guo, W.J. Yang, H. Zhang, J. Wang and S.H. Song. A splitting method for the Degasperis-Procesi equation using an optimized WENO scheme and the Fourier pseudospectral method [J], Advances in Applied Mathematics and Mechanics, 2019, 11: 53-71 [DOI: 10.4208/aamm.OA-2018-0054]
  51. Y.R. Guo, H. Zhang, W.J. Yang, J. Wang and S.H. Song. A high order operator splitting method for the Degasperis-Procesi equation [J], Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 884-905. [DOI: 10.4208/nmtma.OA-2018-0048 ]
  52. Zhang H, Zegeling P A. Simulation of thin film flows with a moving mesh mixed finite element method, Applied Mathematics and Computation, 2018, 338: 274-289. [DOI: 10.1016/j.amc.2018.06.017]
  53. Zhang H, Zegeling P A. A numerical study of two-phase flow models with dynamic capillary pressure and hysteresis[J]. Transport in Porous Media, 2017, 116(2): 825–846. [DOI: 10.1007/s11242-016-0802-z] [BibTex]
  54. Zhang H, Zegeling P A. Numerical investigations of two-phase flow with dynamic capillary pressure in porous media via a moving mesh method[J]. Journal of Computational Physics, 2017, 345: 510-527. [DOI: 10.1016/j.jcp.2017.05.041] [BibTex]
  55. Zhang H, Zegeling P A. A moving mesh finite difference method for non-monotone solutions of non-equilibrium equations in porous media[J]. Communications in Computational Physics, 2017, 22(4): 935-964. [DOI: 10.4208/cicp.OA-2016-0220 ] [BibTex]
  56. Song M, Qian X, Zhang H and Song SH. Hamiltonian Boundary Value Method for the Nonlinear Schrödinger Equation and the Korteweg-de Vries Equation[J]. Advances in Applied Mathematics and Mechanics, 2017, 9(4): 868-886. [DOI: 10.4208/aamm.2015.m1356] [BibTex]
  57. H. Zhang, S. H. Song, X. D. Chen, et al. Average vector field methods for the coupled Schrodinger-KdV equations[J]. Chinese Physics B, 2014, 23(7): 070208. [DOI: 10.1088/1674-1056/23/7/070208] [BibTex]
  58. H. Zhang, S. H. Song, W. E. Zhou, et al. Multi-symplectic method for the coupled Schrodinger-KdV equations[J]. Chinese Physics B, 2014, 23(8): 080204. [DOI: 10.1088/1674-1056/23/8/080204] [BibTex]

Conferences, summer schools and workshops

  1. 2019 Young Scholar Symposium on Numerical Calculation of Stochastic Differential Equations, Central South University, Changsha, China (section talk)
  2. The 12th annual conference of Chinese Computational Mathematics Society, 2019.7, Haerbin, China (section talk)
  3. The 16th conference of Numerical methods for partial differential equation, 2019.8, Qufu, China (section talk)
  4. ICOSAHOM 2018, 2018.7.9-2018.7.13, London, UK (mini-symposium talk)
  5. BIRS Adaptive Numerical Methods for Partial Differential Equations with Applications, 2018.5.27-2018.6.1 Banff, Canada (conference talk)
  6. Midwest Numerical Analysis Day, 2018.4.14, Lawrence, USA (poster presentation)
  7. ENUMATH 2017, 2017.9.25-2017.9.29, Voss, Norway
  8. Woudschoten Conferences WSC, 2017.10.4-2017.10.6, Zeist, the Netherlands (poster presentation)
  9. The 11th annual conference of Chinese Computational Mathematics Society, 2017, Xi’an, China
  10. Spring meeting WSC, 2017.5.19, Antwerp, Belgium
  11. The 53 Nederlands Mathematisch congress, 2017.4.11, Utrecht, the Netherlands (poster presentation)
  12. Forefront of PDEs: Modelling, Analysis and Numerics, 2016.12.12-2016.12.14, Vienna, Austria
  13. 1st SRP NUPUS meeting, 2016.10.5-2016.10.7, Stuttgart, Germany

  14. 1st NUPUS summer school “Discretization of the groundwater transport equations”

    Mentor: Rainer Helmig (Stuttgart)

  15. DUNE::FEM summer school, 2016.9.26-2016.9.30, Stuttgart, Germany

    Mentors: Robert Klofkorn (IRIS, Bergen), Claus Heine (IANS, Stuttgart)

  16. XVI International Conference on Hyperbolic Problems: Theory, Numerics, Applications, HYP2016, 2016.8.1-2016.8.5, Aachen, Germany
  17. NDNS workshop, 2016.7.4-2016.7.5, Twente, the Netherlands
  18. Moving mesh methods workshop, 2016.6.13-2016.6.16, Bath, UK
  19. Spring meeting WSC, 2016.5.13, Utrecht, the Netherlands
  20. Summer school on numerical methods for coupled fluid-solid dynamics, 2014.8, Beijing, China
  21. The 1st postgraduate forum on numerical methods for partial differential equations, 2014.8, Beijing, China
  22. The 12th annual conference of Chinese Computational Mathematics Society, 2013.10, Changsha, China
  23. International conference on compressed sensing: theory and applications, 2013.7, Changsha, China
  24. Postgraduate summer school on Applied Mathematics, 2013.7, Changsha, China
  25. Summer school on Applied Mathematics, 2011.7, Zhengzhou, China

Skills

  • Spoken languages: Chinese, English
  • Computer languages: LaTex, C/C++, Matlab, Fortran, Shell Script

Research Grants

  1. National Natural Science Foundation of China, General Program, PI, No. 12271523, 2023.1-2026.12
  2. National Natural Science Foundation of China, Youth Program, PI, No. 11901577, 2020.1-2022.12
  3. Natural Scicence Foundation of Hunan, Youth Program, PI, No. S2020JJQNJJ1615, 2020.1-2022.12
  4. Research Fund from National University of Defense Technology, PI, 2020.1-2022.12
  5. Dutch NDNS+ Ph.D Travel Grant, 2018
  6. China Scholarship Council Grant, No. 201503170430, 2015-2018

Awards

  1. First prize of Young Excellent Papers of the 16th annual conference of Numerical methods for partial differential equation China, 2019.8
  2. Second prize of Young Excellent Papers of the 3ed annual conference of Computational Mathematics and Applied Software Society of Hunan, 2019.4
  3. Excellent M.Sc Dissertation of NUDT, 2014
  4. TOP 100 B.Sc Dissertation of Zhejiang University, 2012
  5. Outstanding Graduate Student of Zhejiang University, 2012
  6. Scholarship for Outstanding Merits, Zhejiang University, 2009, 2010, 2011
  7. Scholarship for Outstanding Students, Zhejiang University, 2009, 2010, 2011
  8. Prize of the National Talents Training Base, Zhejiang University, 2010