高精度数值方法及应用，复杂流体，机器学习

招学生要求

1. 硕博连读生优先

2. 专业计算数学， 方向为高精度方法及其应用
3. 课程要求： 数值线性代数，数值逼近，常微和偏微分方程, 流体力学，偏微分方程数值方法等

4. 动手能力强： 熟悉C或 Fortran;  Matlab 或者 Python 等。

070102-计算数学

高精度数值方法及其应用
数据科学

2002-09--2007-07   北京大学   理学博士
1998-09--2002-07   北京大学   理学学士

微分方程数值解Ⅱ
谱方法和高精度算法

   

（1） 陈景润未来之星, 国家级, 2013

   

[1] 于海军, Itzhak Fouxon, Jianchun Wang, Xiangru Li, Li Yuan, Shipeng Mao, Michael Mond. Lyapunov exponents and Lagrangian chaos suppression in compressible homogeneous isotropic turbulence. Physics of Fluids[J]. 2023, 35(12): 1-22, [2] Jiang, Shan, Yu, Haijun. Efficient Spectral Methods for Quasi-Equilibrium Closure Approximations of Symmetric Problems on Unit Circle and Sphere. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2021, 89(2): http://dx.doi.org/10.1007/s10915-021-01646-1.
[3] Yu, Haijun, Tian, Xinyuan, Weinan, E, Li, Qianxiao. OnsagerNet: Learning stable and interpretable dynamics using a generalized Onsager principle. PHYSICAL REVIEW FLUIDS[J]. 2021, 6(11): [4] Wang, Lin, Yu, Haijun. An energy stable linear diffusive Crank-Nicolson scheme for the Cahn-Hilliard gradient flow. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2020, 377: http://dx.doi.org/10.1016/j.cam.2020.112880.
[5] Li, Bo, Tang, Shanshan, Yu, Haijun. Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units. COMMUNICATIONS IN COMPUTATIONAL PHYSICS[J]. 2020, 27(2): 379-411, http://dx.doi.org/10.4208/cicp.OA-2019-0168.
[6] Masoumnezhad, Mojtaba, Saeedi, Mohammadhossein, Yu, Haijun, Nik, Hassan Saberi. A Laguerre spectral method for quadratic optimal control of nonlinear systems in a semi-infinite interval. AUTOMATIKA[J]. 2020, 61(3): 461-474, https://doaj.org/article/5ed512ee9c2b4126ada83c731ab0eeb6.
[7] Wang Lin, Yu Haijun. An Energy Stable Linear Diffusive Crank-Nicolson Scheme for the Cahn-Hilliard Gradient Flow. 2020, http://arxiv.org/abs/2004.05163.
[8] Li, Bo, Tang, Shanshan, Yu, Haijun. PowerNet: Efficient Representations of Polynomials and Smooth Functions by Deep Neural Networks with Rectified Power Units. JOURNAL OF MATHEMATICAL STUDY[J]. 2020, 53(2): 159-191, [9] 于海军. Quasi-Potential Calculation and Minimum Action Method for Limit Cycles. J. Nonlinear Science. 2019, [10] Tang, Tao, Yu, Haijun, Zhou, Tao. ON ENERGY DISSIPATION THEORY AND NUMERICAL STABILITY FOR TIME-FRACTIONAL PHASE-FIELD EQUATIONS. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2019, 41(6): A3757-A3778, http://dx.doi.org/10.1137/18M1203560.
[11] Wan, Xiaoliang, Yu, Haijun. NUMERICAL APPROXIMATION OF ELLIPTIC PROBLEMS WITH LOG-NORMAL RANDOM COEFFICIENTS. INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION[J]. 2019, 9(2): 161-186, http://ir.amss.ac.cn/handle/2S8OKBNM/35097, http://www.irgrid.ac.cn/handle/1471x/6865671, http://ir.amss.ac.cn/handle/2S8OKBNM/35098, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000473286900005&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[12] Tang, Shanshan, Yu, Haijun. Applications of the Bounded Total Variation Denoising Method to Urban Traffic Analysis. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS[J]. 2019, 9(3): 622-642, http://ir.amss.ac.cn/handle/2S8OKBNM/34806, http://www.irgrid.ac.cn/handle/1471x/6865548, http://ir.amss.ac.cn/handle/2S8OKBNM/34807, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000470088100012&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[13] Wang, Lin, Yu, Haijun. ENERGY STABLE SECOND ORDER LINEAR SCHEMES FOR THE ALLEN-CAHN PHASE-FIELD EQUATION. COMMUNICATIONS IN MATHEMATICAL SCIENCES[J]. 2019, 17(3): 609-635, http://ir.amss.ac.cn/handle/2S8OKBNM/35536, http://www.irgrid.ac.cn/handle/1471x/6865875, http://ir.amss.ac.cn/handle/2S8OKBNM/35537, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000485624800002&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[14] Lin, Ling, Yu, Haijun, Zhou, Xiang. Quasi-Potential Calculation and Minimum Action Method for Limit Cycle. JOURNAL OF NONLINEAR SCIENCE[J]. 2019, 29(3): 961-991, http://ir.amss.ac.cn/handle/2S8OKBNM/34639, http://www.irgrid.ac.cn/handle/1471x/6865472, http://ir.amss.ac.cn/handle/2S8OKBNM/34640, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000467546000004&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[15] Wang, Lin, Yu, Haijun. On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2018, 77(2): 1185-1209, https://www.webofscience.com/wos/woscc/full-record/WOS:000446594600022.
[16] Wan, Xiaoliang, Yu, Haijun, Zhai, Jiayu. CONVERGENCE ANALYSIS OF A FINITE ELEMENT APPROXIMATION OF MINIMUM ACTION METHODS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2018, 56(3): 1597-1620, http://dx.doi.org/10.1137/17M1141679.
[17] Wang, Lin, Yu, Haijun. On Efficient Second Order Stabilized Semi-implicit Schemes for the Cahn-Hilliard Phase-Field Equation. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2018, 77(2): 1185-1209, https://www.webofscience.com/wos/woscc/full-record/WOS:000446594600022.
[18] Wan, Xiaoliang, Yu, Haijun, Zhai, Jiayu. CONVERGENCE ANALYSIS OF A FINITE ELEMENT APPROXIMATION OF MINIMUM ACTION METHODS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2018, 56(3): 1597-1620, https://www.webofscience.com/wos/woscc/full-record/WOS:000437013900018.
[19] Yang, Xiaofeng, Yu, Haijun. EFFICIENT SECOND ORDER UNCONDITIONALLY STABLE SCHEMES FOR A PHASE FIELD MOVING CONTACT LINE MODEL USING AN INVARIANT ENERGY QUADRATIZATION APPROACH. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2018, 40(3): B889-B914, https://www.webofscience.com/wos/woscc/full-record/WOS:000436986000011.
[20] Xu, Xianmin, Di, Yana, Yu, Haijun. Sharp-interface limits of a phase-field model with a generalized Navier slip boundary condition for moving contact lines. JOURNAL OF FLUID MECHANICS[J]. 2018, 849: 805-833, https://www.webofscience.com/wos/woscc/full-record/WOS:000436551300001.
[21] Wan, Xiaoliang, Yu, Haijun. A dynamic-solver-consistent minimum action method: With an application to 2D Navier-Stokes equations. JOURNAL OF COMPUTATIONAL PHYSICS[J]. 2017, 331: 209-226, http://dx.doi.org/10.1016/j.jcp.2016.11.019.
[22] Rong, Zhijian, Shen, Jie, Yu, Haijun. A NODAL SPARSE GRID SPECTRAL ELEMENT METHOD FOR MULTI-DIMENSIONAL ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS. INTERNATIONAL JOURNAL OF NUMERICAL ANALYSIS AND MODELING[J]. 2017, 14(4-5): 762-783, https://www.webofscience.com/wos/woscc/full-record/WOS:000408158100016.
[23] Yu, Haijun, Yang, Xiaofeng. Numerical approximations for a phase-field moving contact line model with variable densities and viscosities. JOURNAL OF COMPUTATIONAL PHYSICS[J]. 2017, 334: 665-686, http://dx.doi.org/10.1016/j.jcp.2017.01.026.
[24] 于海军. Efficient spectral-element methods for the electronic Schrö dinger equation. Lecture Notes in Computational Science and Engineering. 2016, [25] Wan, Xiaoliang, Yu, Haijun, Weinan, E. Model the nonlinear instability of wall-bounded shear flows as a rare event: a study on two-dimensional Poiseuille flow. NONLINEARITY[J]. 2015, 28(5): 1409-1440, https://www.webofscience.com/wos/woscc/full-record/WOS:000353562300011.
[26] Shen, Jie, Yang, Xiaofeng, Yu, Haijun. Efficient energy stable numerical schemes for a phase field moving contact line model. JOURNAL OF COMPUTATIONAL PHYSICS[J]. 2015, 284: 617-630, http://dx.doi.org/10.1016/j.jcp.2014.12.046.
[27] Shen, Jie, Wang, LiLian, Yu, Haijun. Approximations by orthonormal mapped Chebyshev functions for higher-dimensional problems in unbounded domains. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS[J]. 2014, 265: 264-275, http://dx.doi.org/10.1016/j.cam.2013.09.024.
[28] 于海军. 带时空白噪声外力不可压Navier-Stokes方程的谱方法离散. 2013, http://kns.cnki.net/KCMS/detail/detail.aspx?QueryID=0&CurRec=1053&recid=&FileName=YWJS201308001045&DbName=CPFD0914&DbCode=CPFD&yx=&pr=&URLID=&bsm=.
[29] Shen, Jie, Yu, Haijun. EFFICIENT SPECTRAL SPARSE GRID METHODS AND APPLICATIONS TO HIGH-DIMENSIONAL ELLIPTIC EQUATIONS II. UNBOUNDED DOMAINS. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2012, 34(2): A1141-A1164, http://dx.doi.org/10.1137/110834950.
[30] Chen, Feng, Shen, Jie, Yu, Haijun. A New Spectral Element Method for Pricing European Options Under the Black-Scholes and Merton Jump Diffusion Models. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2012, 52(3): 499-518, http://dx.doi.org/10.1007/s10915-011-9556-5.
[31] Shen, Jie, Yu, Haijun. ON THE APPROXIMATION OF THE FOKKER-PLANCK EQUATION OF THE FINITELY EXTENSIBLE NONLINEAR ELASTIC DUMBBELL MODEL I: A NEW WEIGHTED FORMULATION AND AN OPTIMAL SPECTRAL-GALERKIN ALGORITHM IN TWO DIMENSIONS. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2012, 50(3): 1136-1161, https://www.webofscience.com/wos/woscc/full-record/WOS:000310210700007.
[32] Shen, Jie, Yu, Haijun. EFFICIENT SPECTRAL SPARSE GRID METHODS AND APPLICATIONS TO HIGH-DIMENSIONAL ELLIPTIC PROBLEMS. SIAM JOURNAL ON SCIENTIFIC COMPUTING[J]. 2010, 32(6): 3228-3250, https://www.webofscience.com/wos/woscc/full-record/WOS:000285551800004.
[33] Yu, Haijun, Ji, Guanghua, Zhang, Pingwen. A Nonhomogeneous Kinetic Model of Liquid Crystal Polymers and Its Thermodynamic Closure Approximation. COMMUNICATIONS IN COMPUTATIONAL PHYSICS[J]. 2010, 7(2): 383-402, https://www.webofscience.com/wos/woscc/full-record/WOS:000274090600010.

   

（ 1 ） 非结构数据的统计学习:数学基础及算法. 第三子课题, 参与, 国家级, 2015-01--2019-08
（ 2 ） 科学前沿中若干具挑战性的稀有事件研究, 参与, 国家级, 2016-01--2018-12
（ 3 ） 面向中高维偏微分方程的高效谱方法, 主持, 国家级, 2018-01--2021-12
（ 4 ） 基于极小作用方法和高精度算法的湍流生成机理研究, 主持, 国家级, 2019-01--2021-12

已指导学生

李波  博士研究生  070102-计算数学  

王琳  博士研究生  070102-计算数学  

唐珊珊  博士研究生  070102-计算数学  

现指导学生

田鑫源  硕士研究生  070102-计算数学  

刘士勤  硕士研究生  070102-计算数学  

黄盛和  博士研究生  070102-计算数学  

姜姗  博士研究生  070102-计算数学