偏微分方程数值解

有限元方法

控制与优化

形状与拓扑优化

计算数学专业：硕士和博士研究生

070102-计算数学

偏微分方程数值解，控制与优化

2006-09--2009-07   中国科学院数学与系统科学研究院   理学博士
2003-09--2006-07   郑州大学数学系   理学硕士
1999-09--2003-07   郑州大学数学系   理学学士

偏微分方程约束优化的计算方法
微积分II习题课-B04-1
微积分I-B习题课
微积分I习题-B04-2

   

（1） 中国科学院数学与系统科学研究院陈景润之星, 其他, 2017
（2） 洪堡学者, , 其他, 2010

[1] 龚伟, 李嘉杰, 朱升峰. Improved discrete boundary type shape gradients for PDE-constrained shape optimization. SIAM Journal on Scientific Computing[J]. 2022, [2] 龚伟, Zhiyu Tan, 周兆杰. Optimal convergence of finite element approximation to an optimization problem with PDE constraint. INVERSE PROBLEMS[J]. 2022, [3] 龚伟, Mariano Mateos, John R. Singler, Yangwen Zhang. Analysis and approximations of Dirichlet boundary control of Stokes flows in the energy space. SIAM Journal on Numerical Analysis[J]. 2022, [4] 周凯烨, 龚伟. Error estimates for finite element approximation of Dirichlet boundary control for Stokes equations in L^2(Gamma). Journal of Scientific Computing[J]. 2022, [5] 龚伟, 朱升峰. On discrete shape gradient of boundary type for PDE-constrained shape optimization. SIAM Journal on Numerical Analysis[J]. 2021, [6] Gong, Wei, Hu, Weiwei, Mateos, Mariano, Singler, John R, Zhang, Yangwen. Analysis of a hybridizable discontinuous Galerkin scheme for the tangential control of the Stokes system. ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE[J]. 2020, 54(6): 2229-2264, https://www.webofscience.com/wos/woscc/full-record/WOS:000585906800003.
[7] Gong, Wei, Li, Buyang. Improved error estimates for semidiscrete finite element solutions of parabolic Dirichlet boundary control problems. IMA JOURNAL OF NUMERICAL ANALYSIS[J]. 2020, 40(4): 2898-2939, https://www.webofscience.com/wos/woscc/full-record/WOS:000610489200025.
[8] Gong, Wei, Liu, Wenbin, Tan, Zhiyu, Yan, Ningning. A convergent adaptive finite element method for elliptic Dirichlet boundary control problems. IMA JOURNAL OF NUMERICAL ANALYSIS[J]. 2019, 39(4): 1985-2015, http://ir.amss.ac.cn/handle/2S8OKBNM/35974, http://www.irgrid.ac.cn/handle/1471x/6869840, http://ir.amss.ac.cn/handle/2S8OKBNM/35975, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000491253300013&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=3a85505900f77cc629623c3f2907beab.
[9] Gong, Wei, Liu, Huipo, Yan, Ningning. Adaptive finite element method for parabolic equations with Dirac measure. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING[J]. 2018, 328: 217-241, http://dx.doi.org/10.1016/j.cma.2017.08.051.
[10] Gong, Wei, Hu, Weiwei, Mateos, Mariano, Singler, John, Zhang, Xiao, Zhang, Yangwen. A NEW HDG METHOD FOR DIRICHLET BOUNDARY CONTROL OF CONVECTION DIFFUSION PDEs II: LOW REGULARITY. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2018, 56(4): 2262-2287, https://www.webofscience.com/wos/woscc/full-record/WOS:000443291900012.
[11] Gong, Wei, Tan, Zhiyu, Zhang, Shuo. A robust optimal preconditioner for the mixed finite element discretization of elliptic optimal control problems. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS[J]. 2018, 25(1): https://www.webofscience.com/wos/woscc/full-record/WOS:000417585300008.
[12] Gong, Wei, Xie, Hehu, Yan, Ningning. Adaptive Multilevel Correction Method for Finite Element Approximations of Elliptic Optimal Control Problems. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2017, 72(2): 820-841, https://www.webofscience.com/wos/woscc/full-record/WOS:000406014800015.
[13] Gong, Wei, Yan, Ningning. Adaptive finite element method for elliptic optimal control problems: convergence and optimality. NUMERISCHE MATHEMATIK[J]. 2017, 135(4): 1121-1170, https://www.webofscience.com/wos/woscc/full-record/WOS:000398175500006.
[14] Gong, Wei, Yan, Ningning. FINITE ELEMENT APPROXIMATIONS OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD. SIAM JOURNAL ON NUMERICAL ANALYSIS[J]. 2016, 54(2): 1229-1262, https://www.webofscience.com/wos/woscc/full-record/WOS:000375488100029.
[15] Gong, Wei, Hinze, Michael, Zhou, Zhaojie. Finite Element Method and A Priori Error Estimates for Dirichlet Boundary Control Problems Governed by Parabolic PDEs. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2016, 66(3): 941-967, https://www.webofscience.com/wos/woscc/full-record/WOS:000369911500003.
[16] Chang, Lili, Gong, Wei, Yan, Ningning. Numerical analysis for the approximation of optimal control problems with pointwise observations. MATHEMATICAL METHODS IN THE APPLIED SCIENCES[J]. 2015, 38(18): 4502-4520, https://www.webofscience.com/wos/woscc/full-record/WOS:000368252300005.
[17] Yan, Ming, Gong, Wei, Yan, Ningning. Finite element methods for elliptic optimal control problems with boundary observations. APPLIED NUMERICAL MATHEMATICS[J]. 2015, 90: 190-207, [18] Chang, Lili, Gong, Wei, Sun, Guiquan, Yan, Ningning. PDE-CONSTRAINED OPTIMAL CONTROL APPROACH FOR THE APPROXIMATION OF AN INVERSE CAUCHY PROBLEM. INVERSE PROBLEMS AND IMAGING[J]. 2015, 9(3): 791-814, https://www.webofscience.com/wos/woscc/full-record/WOS:000360672300008.
[19] Gong, Wei, Wang, Gengsheng, Yan, Ningning. APPROXIMATIONS OF ELLIPTIC OPTIMAL CONTROL PROBLEMS WITH CONTROLS ACTING ON A LOWER DIMENSIONAL MANIFOLD. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2014, 52(3): 2008-2035, https://www.webofscience.com/wos/woscc/full-record/WOS:000338832300024.
[20] Gong, Wei, Hinze, Michael, Zhou, Zhaojie. A PRIORI ERROR ANALYSIS FOR FINITE ELEMENT APPROXIMATION OF PARABOLIC OPTIMAL CONTROL PROBLEMS WITH POINTWISE CONTROL. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2014, 52(1): 97-119, https://www.webofscience.com/wos/woscc/full-record/WOS:000333536500005.
[21] Gong, Wei. ERROR ESTIMATES FOR FINITE ELEMENT APPROXIMATIONS OF PARABOLIC EQUATIONS WITH MEASURE DATA. MATHEMATICS OF COMPUTATION[J]. 2013, 82(281): 69-98, https://www.webofscience.com/wos/woscc/full-record/WOS:000326285800004.
[22] Gong, Wei, Hinze, Michael. Error estimates for parabolic optimal control problems with control and state constraints. COMPUTATIONAL OPTIMIZATION AND APPLICATIONS[J]. 2013, 56(1): 131-151, https://www.webofscience.com/wos/woscc/full-record/WOS:000321590500007.
[23] Gong, W, Hinze, M, Zhou, Z J. Space-time finite element approximation of parabolic optimal control problems. JOURNAL OF NUMERICAL MATHEMATICS[J]. 2012, 20(2): 111-145, https://www.webofscience.com/wos/woscc/full-record/WOS:000305147600002.
[24] Gong, Wei, Yan, Ningning. A Mixed Finite Element Scheme for Optimal Control Problems with Pointwise State Constraints. JOURNAL OF SCIENTIFIC COMPUTING[J]. 2011, 46(2): 182-203, https://www.webofscience.com/wos/woscc/full-record/WOS:000286004700003.
[25] Gong, Wei, Yan, Ningning. MIXED FINITE ELEMENT METHOD FOR DIRICHLET BOUNDARY CONTROL PROBLEM GOVERNED BY ELLIPTIC PDES. SIAM JOURNAL ON CONTROL AND OPTIMIZATION[J]. 2011, 49(3): 984-1014, https://www.webofscience.com/wos/woscc/full-record/WOS:000291870400004.
[26] Liu, Wenbin, Gong, Wei, Yan, Ningning. A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2009, 27(1): 97-114, http://lib.cqvip.com/Qikan/Article/Detail?id=29545477.
[27] 龚伟. A posteriori error estimates for boundary control problems governed by the parabolic partial differential equations. 2009, [28] Gong, Wei, Li, Ruo, Yan, Ningning, Zhao, Weibo. An improved error analysis for finite element approximation of bioluminescence tomography. JOURNAL OF COMPUTATIONAL MATHEMATICS[J]. 2008, 26(3): 297-309, http://lib.cqvip.com/Qikan/Article/Detail?id=27610926.
[29] Gong, Wei, Xie, Hehu, Yan, Ningning. A multilevel correction method for optimal controls of elliptic equation. http://arxiv.org/abs/1410.1132.

   

（ 1 ） 状态受限最优控制问题的数值方法, 主持, 国家级, 2013-01--2015-12
（ 2 ） 两类偏微分方程最优控制问题的有限元方法, 主持, 国家级, 2014-01--2016-12
（ 3 ） 基于子空间方法的四维变分耦合同化系统及其在气候预测中的应用, 参与, 国家级, 2014-01--2014-12
（ 4 ） 空间合作目标运动再现中跨尺度控制的前沿数学问题, 参与, 国家级, 2012-09--2016-08
（ 5 ） 集合四维变分耦合同化的非线性子空间方法研究及其在年代际气候预测中的应用, 参与, 国家级, 2016-01--2018-12
（ 6 ） 偏微分方程约束最优控制问题的区域分解方法, 主持, 国家级, 2017-01--2020-12
（ 7 ） 国家材料基因工程数据汇交与管理服务技术平台, 参与, 国家级, 2018-07--2022-06
（ 8 ） 类地行星的形成演化及其宜居性, 参与, 部委级, 2020-01--2024-12
（ 9 ） 偏微分方程Dirichlet边界最优控制问题的理论与算法, 主持, 国家级, 2021-01--2024-12

已指导学生

沈玥  博士研究生  070102-计算数学  

现指导学生

刘乐  硕士研究生  070102-计算数学  

周凯烨  博士研究生  070102-计算数学  

张紫翊  硕士研究生  070102-计算数学  

陶雪霖  博士研究生  070102-计算数学