Kailiang Wu

Associate Professor of Mathematics, Southern University of Science and Technology

E-mail:  WUKL [AT] sustech [DOT] edu [DOT] cn       (I moved to SUSTech, and my OSU email may expire soon) 

Address: Block 3 Room 525, Hui Yuan (Wisdom Valley), 1088 Xueyuan Avenue, Xili, Nanshan District, Shenzhen, Guangdong 518055, P.R. China

REFEREED PAPERS

30. K. Wu, T. Qin, and D. Xiu,  Structure-preserving method for reconstructing unknown Hamiltonian systems from trajectory data

        SIAM Journal on Scientific Computing, 42(6): A3704--A3729, 2020. arXiv:1905.10396.

29. K. Wu and Y. Xing,  Uniformly high-order structure-preserving discontinuous Galerkin methods for Euler equations with gravitation: Positivity and well-balancedness 

        SIAM Journal on Scientific Computing, accepted for publication, 2020. arXiv:2005.07166.

28. K. Wu and D. Xiu,  Data-driven deep learning of partial differential equations in modal space

       Journal of Computational Physics,  408: 109307, 2020. arXiv:1910.06948 (15 Oct 2019).

27. K. Wu and C.-W. Shu,  Entropy symmetrization and high-order accurate entropy stable numerical schemes for relativistic MHD equations

       SIAM Journal on Scientific Computing, 42(4): A2230--A2261, 2020. arXiv:1907.07467 (17 July 2019). 

26. Z. Chen, K. Wu, and D. Xiu,  Methods to recover unknown processes in partial differential equations using data

       Journal of Scientific Computing, 85:23, 2020. arXiv:2003.02387.

25. K. Wu, D. Xiu, and X. Zhong,  A WENO-based stochastic Galerkin scheme for ideal MHD equations with random inputs 

       Communications in Computational Physics, accepted for publication, 2020.

24. J. Hou, T. Qin, K. Wu and D. Xiu,  A non-intrusive correction algorithm for classification problems with corrupted data

        Commun. Appl. Math. Comput., in press, 2020. arXiv:2002.04658.

23. K. Wu and C.-W. Shu,  Provably positive high-order schemes for ideal magnetohydrodynamics: Analysis on general meshes

        Numerische Mathematik,  142(4): 995--1047, 2019.

22. T. Qin, K. Wu, and D. Xiu,  Data driven governing equations approximation using deep neural networks

        Journal of Computational Physics,  395: 620--635, 2019.

21. K. Wu and D. Xiu,  Numerical aspects for approximating governing equations using data

        Journal of Computational Physics,  384: 200--221, 2019.

20. K. Wu and D. Xiu,  Sequential approximation of functions in Sobolev spaces using random samples

        Commun. Appl. Math. Comput.,  1: 449--466, 2019.

19. K. Wu and C.-W. Shu,  A provably positive discontinuous Galerkin method for multidimensional ideal magnetohydrodynamics

        SIAM Journal on Scientific Computing,  40(5):B1302--B1329, 2018.

18. Y. Shin, K. Wu, and D. Xiu,  Sequential function approximation with noisy data

        Journal of Computational Physics,  371:363--381, 2018.

17. K. Wu,  Positivity-preserving analysis of numerical schemes for ideal magnetohydrodynamics

        SIAM Journal on Numerical Analysis,  56(4):2124--2147, 2018.

16. K. Wu and D. Xiu,  Sequential function approximation on arbitrarily distributed point sets

        Journal of Computational Physics,  354:370--386, 2018.

15. K. Wu and H. Tang,  On physical-constraints-preserving schemes for special relativistic magnetohydrodynamics with a general equation of state

        Z. Angew. Math. Phys.,  69:84(24pages), 2018.

14. K. Wu, Y. Shin, and D. Xiu,  A randomized tensor quadrature method for high dimensional polynomial approximation
        SIAM Journal on Scientific Computing,  39(5):A1811--A1833, 2017. 

13. K. Wu,  Design of provably physical-constraint-preserving methods for general relativistic hydrodynamics

12. K. Wu, H. Tang, and D. Xiu,  A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
        Journal of Computational Physics,  345:224--244, 2017. 

11. K. Wu and H. Tang,  Admissible states and physical-constraints-preserving schemes for relativistic magnetohydrodynamic equations   
        Math. Models Methods Appl. Sci. (M3AS),  27(10):1871--1928, 2017. 

10. Y. Kuang, K. Wu, and H. Tang,  Runge-Kutta discontinuous local evolution Galerkin methods for the shallow water equations on the cubed-sphere grid
        Numer. Math. Theor. Meth. Appl.,  10(2):373--419, 2017. 

9. K. Wu and H. Tang,  Physical-constraint-preserving central discontinuous Galerkin methods for special relativistic hydrodynamics with a general equation of state

        Astrophys. J. Suppl. Ser. (ApJS),  228(1):3(23pages), 2017. (2015 Impact Factor of ApJS: 11.257)

8. K. Wu and H. Tang,  A direct Eulerian GRP scheme for spherically symmetric general relativistic hydrodynamics
        SIAM Journal on Scientific Computing,  38(3):B458--B489, 2016. 

7. K. Wu and H. Tang,  A Newton multigrid method for steady-state shallow water equations with topography and dry areas
        Applied Mathematics and Mechanics,  37(11):1441--1466, 2016. 

6. K. Wu and H. Tang,  High-order accurate physical-constraints-preserving finite difference WENO schemes for special relativistic hydrodynamics
        Journal of Computational Physics,  298:539--564, 2015.

5. K. Wu, Z. Yang, and H. Tang,  A third-order accurate direct Eulerian GRP scheme for one-dimensional relativistic hydrodynamics
         East Asian J. Appl. Math.,  4(2):95--131, 2014.

4. K. Wu and H. Tang,  Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
        Journal of Computational Physics,  256:277--307, 2014. 

3. K. Wu, Z. Yang, and H. Tang,  A third-order accurate direct Eulerian GRP scheme for the Euler equations in gas dynamics
        Journal of Computational Physics,  264:177--208, 2014. 

PREPRINTS

2. K. Wu and C.-W. Shu,  Provably physical-constraint-preserving discontinuous Galerkin methods for multidimensional relativistic MHD equations 

    submitted, arXiv:2002.03371, 2020.

1. K. Wu and D. Xiu,  An explicit neural network construction for piecewise constant function approximation, arXiv preprint arXiv:1808.07390.

COLLABORATORS

Zhen Chen   Jun Hou   Dr. Yangyu Kuang    Dr. Tong Qin    Dr. Yeonjong Shin 
Prof. Chi-Wang Shu   Prof. Huazhong Tang   Prof. Yulong Xing    Prof. Dongbin Xiu    Dr. Zhicheng Yang

• SISC    JCP    JSC    CiCP    SIREV    M2AN  
• FoCM   M3AS   SINUM   Numer Math   Math Comp 
• ApJS    ApJ    A&A    MNRAS    PRD 
• Recent arXiv submissions: math.NA     cs.LG    stat.ML