刘争光

职  称：教授

办公室：长清湖校区文渊楼A254

邮  箱：liuzhg@sdnu.edu.cn

个人简介 

刘争光，教授，博士生导师，山东省泰山学者青年专家，省优青，山东师范大学东岳学者。2013-2018年山东大学计算数学专业博士。2017-2018年赴美国普渡大学访问。近年来致力于复杂梯度流模型的无条件能量稳定算法研究，获得一批应用基础性研究成果。在国际权威期刊“SIAM J Sci Comput”、“Math Comp”、 “J Comput Phys”、“Comput Methods Appl Mech Engrg”、“J Sci Comput”等发表SCI收录论文40余篇；主持国家自然科学基金，中国博士后科学基金、山东省自然科学优秀青年项目、面上项目、青年项目等。

研究方向及兴趣

复杂相场模型数值模拟；非线性模型高效算法；油藏数值模拟

开设课程

本科生：高等数学1、高等数学2、计算方法、数值代数

研究生：发展方程有限元

招生方向

在读硕士研究生3名。每年招收1-2名硕士研究生，欢迎报考。

科研项目

1. 山东省自然科学优秀青年基金：复杂梯度流模型的高效算法研究（2024.01-2026.12），在研，主持；

2. 国家自然科学基金：非局部相场模型的快速高阶能量稳定方法及算法优化研究（2021.01-2023.12），结题，主持；

3. 山东省自然科学面上项目：复杂相场模型的高效保结构线性优化算法研究与分析（2025.01-2027.12），在研，主持；

4. 中国博士后科学基金第67批面上项目：复杂相场模型的高阶自适应优化算法研究（2020.07-2022.04），结题，主持；

5. 山东省自然科学青年基金：相场模型的能量稳定高阶自适应数值方法研究（2021.01-2023.12），结题，主持。

6. 湖南省重点实验室开放课题：非局部相场模型的快速算法研究（2019.12-2022.01），已结题，主持。

奖励与荣誉

2024.08 泰山学者青年专家

2024.11 山东师范大学东岳学者

学术兼职

1. 美国《数学评论》评论员

2. 期刊《Science Journal of Applied Mathematics and Statistics》编委（2019-2022）

3. 期刊《中国理论数学前沿》编委（2021-2025）

代表性成果

在SIAM J Sci Comput、Math Comp、JCP，CMAME等计算数学顶级期刊发表论文40余篇。

1. Liu Z*, Li X. The exponential scalar auxiliary variable (E-SAV) approach for phase field models and its explicit computing. SIAM Journal on Scientific Computing, 2020, 42(3): B630-B655.

2. Liu Z, Li X. A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system. Journal of Computational Physics, 2021, 447: 110703.

3. Li X, Shen J, Liu Z. New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis. Mathematics of Computation, 2022, 91(333): 141-167.

4. Liu Z, Zhang Y, Li X. A Novel Energy-Optimized Technique of SAV-Based (EOP-SAV) Approaches for Dissipative Systems. Journal of Scientific Computing, 2024, 101(2): 38.

5. Liu Z, Zheng N, Li X. An Enhanced and Highly Efficient Semi‐Implicit Combined Lagrange Multiplier Approach Preserving Original Energy Law for Dissipative Systems. International Journal for Numerical Methods in Engineering, 2025, 126(1): e7619.

6. Liu Z, Li X. A novel Lagrange Multiplier approach with relaxation for gradient flows. CSIAM Transactions on Applied Mathematics, 2024, 5(1): 110-141.

7. Liu Z, Li X. A parallel CGS block-centered finite difference method for a nonlinear time-fractional parabolic equation. Computer Methods in Applied Mechanics and Engineering, 2016, 308: 330-348.

8. Liu Z, Chen C. On efficient semi-implicit auxiliary variable methods for the six-order Swift–Hohenberg model. Journal of Computational and Applied Mathematics, 2023, 419: 114730.

9. Liu Z, Li X. Efficient modified techniques of invariant energy quadratization approach for gradient flows. Applied Mathematics Letters, 2019, 98: 206-214.

10. Liu Z, Li X. A fast finite difference method for a continuous static linear bond-based peridynamics model of mechanics. Journal of Scientific Computing, 2018, 74(2): 728-742.

11. Liu Z, He Q. A novel relaxed scalar auxiliary variable approach for gradient flows. Applied Mathematics Letters, 2023, 141: 108613.

12. Chen Y, Liu Z*, Meng X. Partially and fully implicit multi-step SAV approaches with original dissipation law for gradient flows. Communications in Nonlinear Science and Numerical Simulation, 2024: 108379.

13. Meng X, Cheng A, Liu Z. The high-order exponential semi-implicit scalar auxiliary variable approach for the general nonlocal Cahn-Hilliard equation. Communications in Nonlinear Science and Numerical Simulation, 2024, 137: 108169.

14. Liu Z, Li X. Efficient modified stabilized invariant energy quadratization approaches for phase-field crystal equation. Numerical Algorithms, 2020, 85(1): 107-132.

15. Liu Z, Li X. Two fast and efficient linear semi-implicit approaches with unconditional energy stability for nonlocal phase field crystal equation. Applied Numerical Mathematics, 2020, 150: 491-506.

16. Liu Z, Li X. Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows. Numerical Algorithms, 2022, 89(1): 65-86.

17. Liu Z, Li X. The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn–Hilliard equation. Numerical Methods for Partial Differential Equations, 2021, 37(1): 244-261.

18. Liu Z, Li X, Huang J. Accurate and efficient algorithms with unconditional energy stability for the time fractional Cahn–Hilliard and Allen–Cahn equations. Numerical Methods for Partial Differential Equations, 2021, 37(3): 2613-2633.

19. Liu Z, Chen S. Novel linear decoupled and unconditionally energy stable numerical methods for the modified phase field crystal model. Applied Numerical Mathematics, 2021, 163: 1-14.

20. Liu Z. Novel energy stable schemes for Swift-Hohenberg model with quadratic-cubic nonlinearity based on the H−1-gradient flow approach. Numerical Algorithms, 2021, 87(2): 633-650.

21. Liu Z, Cheng A, Wang H. An hp-Galerkin method with fast solution for linear peridynamic models in one dimension. Computers & Mathematics with Applications, 2017, 73(7): 1546-1565.

22. Liu Z, Cheng A, Li X. A second order Crank–Nicolson scheme for fractional Cattaneo equation based on new fractional derivative. Applied Mathematics and Computation, 2017, 311: 361-374.

23. Liu Z, Cheng A, Li X, et al. A fast solution technique for finite element discretization of the space–time fractional diffusion equation. Applied Numerical Mathematics, 2017, 119: 146-163.

24. Liu Z, Cheng A, Li X. A novel finite difference discrete scheme for the time fractional diffusion-wave equation. Applied Numerical Mathematics, 2018, 134: 17-30.

25. Liu Z, Cheng A, Li X. A fast discontinuous finite element discretization for the space-time fractional diffusion-wave equation. Numerical Methods for Partial Differential Equations, 2017, 33(6): 2043-2061.

26. Liu Z, Cheng A, Li X. A fast‐high order compact difference method for the fractional cable equation. Numerical Methods for Partial Differential Equations, 2018, 34(6): 2237-2266.

27. Liu Z, Li X, Zhang X. A fast high-order compact difference method for the fractal mobile/immobile transport equation. International Journal of Computer Mathematics, 2020, 97(9): 1860-1883.

28. Liu Z, Cheng A, Li X. A second-order finite difference scheme for quasilinear time fractional parabolic equation based on new fractional derivative. International Journal of Computer Mathematics, 2018, 95(2): 396-411.

29. Liu Z, Li X. A Crank–Nicolson difference scheme for the time variable fractional mobile–immobile advection–dispersion equation. Journal of Applied Mathematics and Computing, 2018, 56(1): 391-410.

30. Liu Z, Li X. A novel equivalent definition of Caputo fractional derivative without singular kernel and superconvergent analysis. Journal of Mathematical Physics, 2018, 59(5): 051503.