• 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

    SIAM Journal on Numerical Analysis,  accepted 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,  60(5): 2448–2481, 2022.

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

    SIAM Review,  2022. 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, 43(6): B1164–B1197, 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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