• Journal Papers

Selected Publications:

36. K. Wu, H. Jiang, and C.-W. Shu, Provably positive central DG schemes via geometric quasilinearization for ideal MHD equations

    submitted for publication, 2022.

35. Z. Sun, Y. Wei, and K. Wu*, On energy laws and stability of Runge--Kutta methods for linear seminegative problems

    SIAM Journal on Numerical Analysis,  accepted for publication, 2022.

34. K. Wu and C.-W. Shu*, Geometric quasilinearization framework for analysis and design of bound-preserving schemes

    submitted for publication, 2021. arXiv:2111.04722. 8 Nov 2021.

33. K. Wu, Minimum principle on specific entropy and high-order accurate invariant region preserving numerical methods for relativistic hydrodynamics

    SIAM Journal on Scientific Computing, accepted for publication, 2021.

32. Z. Chen, V. Churchill, K. Wu, and D. Xiu, Deep neural network modeling of unknown partial differential equations in nodal space

    Journal of Computational Physics, 110782, 2022.

31. H. Jiang, H. Tang, and K. Wu*, Positivity-preserving well-balanced central discontinuous Galerkin schemes for the Euler equations under gravitational fields

    Journal of Computational Physics, 463: 111297, 2022.

30. Y. Chen and K. Wu*, A physical-constraint-preserving finite volume method for special relativistic hydrodynamics on unstructured meshes

    Journal of Computational Physics, 466: 111398, 2022.

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

    Numerische Mathematik, 148: 699--741, 2021.

28. 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, A472--A510, 2021.

27. 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.

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

    Journal of Computational Physics, 408: 109307, 2020.

25. 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.

24. 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.

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

    Communications in Computational Physics, 30(2): 423--447, 2021.

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

    Commun. Appl. Math. Comput., 3: 337--356, 2021.

21. 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.

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

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

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

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

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

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

17. 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.

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

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

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

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

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

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

13. 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.

12. 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.

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

    Physical Review D, 95, 103001, 2017.

10. 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.

9. 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.

8. 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.

7. 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)

6. 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.

5. 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.

4. 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.

3. 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.

2. K. Wu and H. Tang, Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics

    Journal of Computational Physics, 256:277--307, 2014.

1. 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.

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