曾凡海教授主要从事分数阶微积分理论及应用方面的研究,是国内外较早从事分数阶微积分领域研究的学者之一,在分数阶微积分建模,计算和应用等领域取得了一系列成果.曾凡海博士 2014 年毕业于上海大学计算数学专业, 接着在美国布朗大学应用数学系 (合作导师: George Em Karniadakis 教授), 澳大利亚昆士兰科技大学应用数学系(合作导师: Ian Turner 教授和 Kevin Burrage 教授)和新加坡国立大学数学系(合作导师:包维柱教授)博士后研究.到目前为止,已经在计算数学及应用数学主流期刊 SIAM J. Numer. Anal., SIAM J. Sci. Comput., J. Sci. Comput., Comput. Methods Appl. Mech. Engrg. 和 J. Comput. Phys. 上发表论文 30 余篇, 2015 年合作出版专著一部, 2016 年获得上海市优秀博士论文奖, 论文 SCI 他引 1000 余次, 单篇论文引用高达到 200 余次, 成果被国内外知名学者引用与正面评价,包括 SIAM 科学计算的主编 Jan Hesthaven 教授,冯康科学计算奖获得者吴国宝教授等.目前研究领域包括谱方法及其应用,分数阶微积分的理论,数值算法及其应用.

基金

国家自然科学基金面上项目，2022.01-2025.12，51万。

代表论文

● H. Zhang, X. Jiang*, F. Zeng*, G. Karniadakis, A stabilized semi-implicit Fourier spectral method for nonlinear  space-fractional reaction-diffusion equations, JCP, 2020.

● L. Guo, F. Zeng∗, I. Turner, K. Burrage, G. Karniadakis, Efficient multistep methods for tempered fractional calculus: Algorithms and simulations, SISC, 2019.

● F. Zeng, I. Turner, K. Burrage,  S. J. Wright, A discrete least squares collocation method for two-dimensional nonlinear time-dependent partial differential equations, JCP, 2019

● F. Zeng*, I. Turner, K. Burrage, A stable fast time-stepping method for fractional integral and derivative operators, JSC, 2018.

● F. Zeng, I. Turner, K. Burrage, G. Karniadakis, A new class of semi-implicit methods with linear complexity for nonlinear fractional differential equations, SISC, 2018.

● F. Zeng, Z. Zhang,  G. Karniadakis, Second-order numerical methods for multi-term fractional differential equations: Smooth and non-smooth solutions, CMAME, 2017.

● X. Chen, F. Zeng, G. Karniadakis, A tunable finite difference method for fractional differential equations with non-smooth solutions, CMAME, 2017.

● F. Zeng, Z. Mao, G. Karniadakis, A generalized spectral collocation method with tunable accuracy for fractional differential equations with end-point singularities, SISC, 2017. 

● W. Cao, F. Zeng, Z. Zhang, G.Karniadakis, Implicit-explicit difference schemes for nonlinear fractional differential equations with non-smooth solutions, SISC, 2016.

● F. Zeng, Z. Zhang, G. Karniadakis, Fast difference schemes for solving high-dimensional time-fractional subdiffusion equations, JCP, 2016.

● F. Zeng, C. Li, F. Liu, I. Turner, Numerical algorithms for time-fractional subdiffusion equation with second-order accuracy, SISC, 2015.

● F. Zeng, Z. Zhang, G. Karniadakis, A generalized spectral collocation method with tunable accuracy for variable-order fractional differential equations, SISC, 2015.

● F. Zeng, Second-order stable finite difference schemes for the time-fractional diffusion-wave equation, JSC, 2015.

● Z. Zhang, F. Zeng, G. Karniadakis, Optimal error estimates for spectral Petrov–Galerkin and collocation methods for initial value problems for fractional differential equations, SINUM, 2015.

● F. Zeng, F. Liu, C. Li, K. Burrage, I. Turner, V. Anh, A Crank–Nicolson ADI spectral method for the two-dimensional Riesz space fractional nonlinear reaction-diffusion equation, SINUM, 2014.

● F. Zeng, C. Li, F. Liu, I. Turner, The use of finite difference/element approaches for solving the time-fractional subdiffusion equation, SISC, 2013.

● C. Li, F. Zeng, F. Liu, Spectral approximations to the fractional integral and derivative, Fract. Calc. Appl. Anal., 2012.

● C. Li, F. Zeng, Numerical Methods for Fractional Calculus, Chapman and Hall/CRC, 2015.

详情请见  https://orcid.org/0000-0003-4507-1278  或者扫描二维码

招生信息：每年招收博士研究生一名，硕士研究生两名。有意向的同学请发送简历到 fanhai_zeng@sdu.edu.cn