Software
- FEM_MATLAB: A Matlab software that implements the multilevel correction method.
- Full_Eigen_Multigrid: A baltamatica software that implements the multilevel correction method for solving eigenvalue problems.
- GCGE: a software for solving large scale eigenvalue problems.
- 北太天元版本的GCGE插件: 基于北太天元SDK建立的特征值解法器GCGE_bex, 计算效率请见GCGE_bex的测试报告
- OpenPFEM: a parallel finite element analysis software(1D,2D,3D).
- PASE: a parallel augmented subspace eigensolver.
- 特征值问题数值算法讲义: 课程特征值问题数值算法的讲义, 相应的视频如下: 特征值问题数值算法视频1 (Bilibili网站) 特征值问题数值算法视频2 (Bilibili网站)
- TNN_MachineLearning: A Pytorch software for tensor neural network (TNN) and its corresponding machine learning methods for solving hihg dimensional partial differential equations. About TNN, please check its introudction: English Version (中文版)
Curriculum Vitae
Working experience
- 2016, March - Now, Professor,
Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- 2011, March - 2016, February, Associate Professor,
Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
- 2008, July-2011, February, Assistant Professor,
Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Education
- 2003,Sep.-2008,June Ph.D candidate
Academy of Mathematics and Systems Science, Chinese Academy of Sciences
Supervisor: Professor Qun Lin
- 1999,Sep.-2003,July B.Sc.
Peking University, Beijing, China
Research Topics
- Numerical Methods for Eigenvalue Problems
- Neural Networks and Machine Learning Methods(TNN算法获得2023年"大湾区"粤港澳AI for Science科技竞赛 特等奖(获得了最好的精度))
- Numerical Methods for Partial Differential Equations
- Finite Element Methods: Accuracy and Improvement
- Computational Softwares and Theirs Applications
- Numerical Method for Differential-Integral Equations and Ordinary Differential Equations For more information, plear check my research introduction (关于本人研究更详细的介绍, 请参看右边网页): Research Introduction:
Research Reports
- Zhongshuo Lin, Yifan Wang and Hehu Xie, Adaptive neural network subspace method for solving partial differential equations with high accuracy, arXiv:2412.02586, 2024.
- Yangfei Liao, Zhongshuo Lin, Jianghao Liu, Qingyuan Sun, Yifan Wang, Teng Wu and Hehu Xie, Solving Schrödinger equation using tensor neural network. arXiv:2209.12572, 2022.
- Yifan Wang and Hehu Xie, Solving high dimensional partial differential equations using tensor type discretization and optimization process, arXiv:2211.16548, 2022.
- Yunhui He, Qichen Hong, Hehu Xie, Meiling Yue and Chunguang You, Energy Error Estimates of Subspace Method and Multigrid Algorithm for Eigenvalue Problems. arXiv:1705.03038.
- Hehu Xie and Chunguang You, A Small Note About Lower Bound of Eigenvalues, report, 2016.
- Hehu Xie and Zhimin Zhang, A multilevel correction scheme for nonsymmetric eigenvalue problems by finite element methods, arXiv:1505.06288
- Hehu Xie, A Multigrid Method for Nonlinear Eigenvalue Problems, arXiv:1405.7158， 2014.
- Xiaole Han and Hehu Xie, Local a Priori Estimate on the General Scale Subdomains, arXiv:1401.5373, 2014.
Some Publications
34. Yu Li, Qun Lin and Hehu Xie, A parallel method for population balance equations based on the method of characteristics, Proceedings of the International Conference Applications of Mathematics, 2013, pp. 140-149.
33. Ran Zhang, Benxi Zhu and Hehu Xie, Spectral methods for weakly singular Volterra integral equations with pantograph delays，Frontiers of Mathematics in China, Vol. 8, Issue 2, 2013, pp 281-299
32. Tao Tang, Hehu Xie and Xiaobo Yin, High-Order Convergence of Spectral Deferred Correction Methods on General Quadrature Nodes, Journal of Scientific Computing Volume 56, Issue 1, 2013, pp 1-13
31. Qiumei Huang, Hehu Xie and Hermann Brunner, The $hp$ Discontinuous Galerkin Method for Delay Differential Equations with Nonlinear Vanishing Delay, SIAM J. Sci. Comput., 35(3), 2013, A1604–A1620.
30. Qin Li, Qun Lin and Hehu Xie,Nonconforming finite element approximations of the Steklov eigenvalue problem and its lower bound approximations, Applications of Mathematics, Volume 58, Issue 2, 2013, pp 129-151.
29. Shanghui Jia， Hongtao Chen and Hehu Xie, A posteriori error estimator for eigenvalue problems by mixed finite element method, Science China Mathematics,Volume 56, Issue 5, 2013, pp 887-900
28. Qun Lin and Hehu Xie, Extrapolation of the finite element method on general meshes, International Journal of Numerical Analysis and Modeling Computing and Information, Vol. 10, Number 1, 2013, pp. 139-153.
27. Qun Lin and Hehu Xie, Recent results on Lower bounds of eigenvalue problems by nonconforming finite element methods, Inverse Problems and Imaging, Volume 7, No. 3, 2013, 795-811.
26. F.Luo, Qun Lin and Hehu Xie (谢和虎), Computing the lower and upper bounds of Laplace eigenvalue problem: by combining conforming and nonconforming finite element methods, Science China Mathematics, Volume 55, Issue 5, pp 1069-1082, 2012.
25. Qun Lin and Hehu Xie (谢和虎), A Superconvergence result for mixed finite element approximations of the eigenvalue problem, ESAIM: Mathematical Modelling and Numerical Analysis, Volume 46/Issue 04, pp 797-812, 2012.
24、 Qun Lin and Hehu Xie (谢和虎), A multilevel correction type of adaptive finite element method for Steklov eigenvalue problems, Proceedings of the International Conference Applications of Mathematics 2012, pp. 134-143.
23. Q. Lin and H. Xie, The asymptotic lower bounds of eigenvalue problems by nonconforming finite element methods, Mathematics in Practice and Theory, 42 (11) (2012), 219–226.(In Chinese with English title and abstract)
22. H. Xie, R. Zhang and H. Brunner, Collocation Methods for General Volterra Functional Integral Equations with Vanishing Delays, SIAM Journal on Scientific Computing, 33(6) (2011), 3303-3332.
21. Qun Lin and Hehu Xie, An observation on Aubin-Nitsche Lemma and its applications, Mathematics in Practice and Theory, 41(17) (2011), 247-258.(In Chinese, English title and abstract)
20. Qun Lin and Hehu Xie, A type of finite element gradient recovery method based on vertex-edge-face interpolation: The recovery rechnique and superconvergence property, East Asian Journal on Applied Mathematics, 1(3) (2011), 248-263.
19. S. Jia, H. Xie and X. Yin, A type of finite element gradient recovery method based on vertex-edge interpolation, Mathematics in Practice and Theory, 41(6) (2011), 239-243. (In Chinese, English title and abstract)
18. Q. Huang, H. Xie and H. Brunner, Superconvergence of a discontinuous Galerkin solutions for delay differential equations of pantograph type, SIAM Journal on Scientific Computing， 33(5) (2011), 2664–2684.
17. Qun Lin and Hehu Xie, Superconvergence measurement for General meshes by linear finite element method, Mathematics in Practice and Theory, 41(1)(2011), 138-152. (In Chinese, English title and abstract)
16. N. Ahmed, G. Matthies, L. Tobiska and H. Xie, Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reactionproblems，Comput. Methods Appl. Mech. Engrg., 200 (2011), 1747-1756.
15. H. Eichel, L. Tobiska and H. Xie, Supercloseness and superconvergence of stabilized low order finite element discretizations of the Stokes problem, Mathematics of Computation, 80(274)(2011), 697–722.
14. H. Brunner, Q. Huang and H. Xie, Discontinuous Galerkin methods for delay differential equations of pantograph type, SIAM J. NUMER. ANAL., Vol. 48, No. 5, pp. 1944–1967, 2010.
13. Q. Lin, H. Xie, F. Luo, Y. Li and Y. Yang, Stokes eigenvalue approximations from below with nonconforming mixed finite element methods, Mathematics in Practice and Theory, 40(19)(2010), 157-168. (In Chinese, English title and abstract)
12. H. Brunner, Hehu Xie and R. Zhang, Analysis of collocation solutions for a class of functional equations with vanishing delays, IMA Journal of Numerical Analysis, 31(2011), 698-718.
11. Qun Lin and Hehu Xie, New expansions of numerical eigenvalue for $-\Delta u = \lambda\rho u$ by linear finite element on different triangular meshes, International Journal of Information and Systems Sciences, 6(1)(2010), 10-34
10. Qun Lin and Hehu Xie, Asymptotic error expansion and Richardson extrapolation of eigenvalue approximations for second order elliptic problems by the mixed finite element method, Applied Numerical Mathematics, 59 (8)(2009), 1884—1893.
9. Q. Huang and Hehu Xie, Superconvergence of Galerkin solutions for Hammerstein equations, International Journal of Numerical Analysis & Modeling, 2009， Volume 6, Number 4, Pages: 696-710.
8. H. Chen, S. Jia and Hehu Xie, Postprocessing and higher order convergence for the mixed finite element approximations of the Stokes eigenvalue problems, Application of Mathematics, 54(3)(2009), 237-250.
7. S. Jia, Hehu Xie, X. Yin and S. Gao, Approximation and eigenvalue extrapolation of Stokes eigenvalue problem by nonconforming finite element methods, Applications of Mathematics, 54(1)(2009), 1-15.
6. Hehu Xie and S. Jia, Extrapolation for the second order elliptic problems by mixed finite element methods in three dimensions, International Journal of Numerical Analysis and Modeling, 5(1)(2008), 112-131.
5. S. Jia, Hehu Xie, X. Yin and S. Gao, Approximation and eigenvalue extrapolation of biharmonic eigenvalue problem by nonconforming finite element methods, Numerical Methods for Partial Differential Equations, 24(2) ,435-448,2008.
4. X. Yin, Hehu Xie, S. Jia and S. Gao, Asymptotic expansions and extrapolations of eigenvalues for the stokes problem by mixed finite element methods, Journal of Computational and Applied Mathematics, 215(1)(2008), 127-141
3. Hehu Xie, Extrapolation of the Nédélec element for the Maxwell equations by the mixed finite element method, Advances in Computational Mathematics, 29(2) (2008), 135-145.
2. Hehu Xie and S. Gao, Superconvergence of the least-squares mixed finite element approximations for the second order elliptic problems, International Journal of Information and Systems Sceiences, Vol.3 (2) (2007), 277-282.
1. V. Shaidurov and Hehu Xie, Richardson extrapolation for eigenvalue of discrete spectral problem on general mesh, Computational Technologies, Vol. 12 No. 3(2007), 24-37.