Home » Publications » 2018-2022
  1. H. Zhu, Z. Wang, H. Wang, Q. Zhang, Z. Gao, Troubled-Cell Indication Using K-means Clustering with Unified Parameters. J. Sci. Comput., 93, 21, 2022.
  2. B.-S. Wang, W.S. Don, Affine-Invariant WENO Weights and Operator, Appl. Numer. Math., 181, 630-646, 2022.
  3. B.-S. Wang, P. Li, Z. Gao, High order well-balanced and positivity-preserving finite difference alternative WENO scheme with hydrostatic reconstruction for shallow water equations, Appl. Numer. Math., 181, 483-502, 2022.
  4. Y. Gu, D. Luo, Z. Gao, Y. Chen, An Adaptive Moving Mesh Method for the Five-equation Model, Commun. Comput. Phys., 32, 189-221, 2022.
  5. Q. Fu, Z. Gao, Y. Gu, P. Li, High order well-balanced conservative finite difference AWENO scheme with hydrostatic reconstruction for the Euler equations under gravitational fields, Appl. Numer. Math., 180, 1-15, 2022.
  6. Z. Gao, Y. Lin, X. Sun, X. Zeng, A reduced order method for nonlinear parameterized partial differential equations using dynamic mode decomposition coupled with k-nearest neighborhood, J. Comput. Phys., 452, 110907, 2022.
  7. Y. Shi, S. Xie, D. Liang, A Fourth-Order Block-Centered Compact Difference Scheme for Nonlinear Contaminant Transport Equations with Adsorption, Appl. Numer. Math., 171, 212-232, 2022.
  8. W.S. Don, R. Li, B.-S. Wang, Y. Wang, A novel and robust scale-invariant WENO scheme for hyperbolic conservation laws, J. Comput. Phys., 448, 110724, 2022.
  9. C. Zhang, Z. Gao, S. Ye, P. Li, Edge detectors based on PauTa criterion with application to hybrid compact-WENO finite difference scheme, Adv. Appl. Math. Mech., 2021.
  10. H. Liu, X. Zheng, H. Fu, Analysis of a multi-term variable-order time-fractional diffusion equation and its Galerkin finite element approximation, J. Comput. Math., 2021, in Press.
  11. B.-S. Wang, W.S. Don, A. Kurganov, Y. Liu, Fifth-Order A-WENO Finite-Difference Schemes Based on the Central-Upwind Rankine-Hugoniot Fluxes, Commun. Appl. Math. Comput., 2021, Accepted.
  12. C. Zhu, B. Zhang, J. Liu, H. Fu, Efficient second-order ADI difference method for three-dimensional Riesz space-fractional diffusion equations,  Comput. Math. Appl., 98, 24-39, 2021.
  13. Y. Gu, Z. Gao, G. Hu, P. Li, L. Wang, High Order Finite Difference Alternative WENO Scheme for Multi-component Flows, J. Sci. Comput., 89(3), 52, 2021.
  14. Y. Gu, F. Kwok, On the Choice of Robin Parameters for the Optimized Schwarz Method for Domains with Non-Conforming Heterogeneities, J. Sci. Comput., 89(1), 5, 2021.
  15. H. Fu, C. Zhu, X. Liang, B. Zhang, Efficient spatial second/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations, Adv. Comput. Math., 47, 58, 2021.
  16. P. Li, B.-S. Wang, W.S. Don, Sensitivity parameter-independence well-balanced finite volume WENO scheme for the Euler equations under gravitational fields, J. Sci. Comput., 88(2), 47, 2021.
  17. Y. Gu, Z. Gao, G. Hu, P. Li, L. Wang, A Robust High Order Alternative WENO Scheme for the Five-Equation Model, J. Sci. Comput., 88(1), 12, 2021.
  18. H. Zhu, H. Wang, Z. Gao, A New Troubled-Cell Indicator for Discontinuous Galerkin Methods Using K-Means Clustering, SIAM J. Sci. Comput., 43(4), A3009-A3031, 2021.
  19. F. Li, H. Fu, J. Liu, An efficient quadratic finite volume method for variable coefficient Riesz space-fractional diffusion equations, Math. Meth. Appl. Sci., 44(4), 2934-2951, 2021.
  20. H. Liu, X. Zheng, H. Fu, H. Wang, Analysis and efficient implementation of ADI finite volume method for Riesz space-fractional diffusion equations in two space dimensions, Numer. Meth. Part. Diff. Equat., 37, 818-835, 2021.
  21. X. Zheng, H. Wang, H. Fu, Optimal-order finite element approximations to variable-coefficient two-sided space-fractional advection-reaction-diffusion equations in three space dimensions, Appl. Numer. Math., 161, 1-12, 2021.
  22. J. Liu, C. Zhu, Y. Chen, H. Fu, A Crank-Nicolson ADI quadratic spline collocation method for two-dimensional Riemann-Liouville space-fractional diffusion equations, Appl. Numer. Math., 160, 331-348, 2021.
  23. Y. Shi, S.S. Xie, D. Liang, K. Fu, High Order Compact Block-Centered Finite Difference Schemes for Elliptic and Parabolic Problems, J. Sci. Comput., 87(3), 86, 2021.
  24. Z. Gao, Q. Liu, J. S. Hesthaven, B.-S. Wang, W.S. Don, X. Wen, Non-intrusive reduced order modeling of convection dominated flows using artificial neural networks with application to Rayleigh-Taylor instability, Commun. Computat. Phys., 30(1), 97-123, 2021.
  25. P. Li, Z. Gao, Simple high order well-balanced finite difference WENO schemes for the Euler equations under gravitational fields, J. Comput. Phys., 437, 110341, 2021.
  26. B.-S. Wang, W.S. Don, N.K. Garg, A. Kurganov, Fifth-Order A-WENO Finite Difference Schemes Based on a New Adaptive Diffusion Central Numerical Flux, SIAM J. Sci. Comput., 42(6), A3932-A3956, 2020.
  27. X. Wen, W.S. Don, Z. Gao, Y. Xing, Entropy Stable and Well-Balanced Discontinuous Galerkin Method for the Nonlinear Shallow Water Equations, J. Sci. Comput., 83(3), 66, 2020.
  28. X. Wen, W.S. Don, Z. Gao, J. S. Hesthaven, An edge detector based on artificial neural network with application to hybrid Compact-WENO finite difference scheme, J. Sci. Comput., 83(3), 49, 2020.
  29. P. Li, X.Q. Zhao, Z. Gao, B.-S. Wang, High Order Hybrid Weighted Compact Nonlinear Schemes for Hyperbolic Conservation Laws, Adv. Appl. Math. Mech., 12(4), 972-991, 2020.
  30. Z. Gao, L.-L. Fang, B.-S. Wang, Y.H. Wang, W.S. Don, Seventh and ninth orders alternative WENO finite difference schemes for hyperbolic conservation laws, Comput. Fluids, 202, 104519, 2020.
  31. P. Li, W.S. Don, Z. Gao, High Order Well-Balanced Finite Difference WENO Interpolation-Based Schemes for Shallow Water Equations, Comput. Fluids, 201, 104476, 2020.
  32. W.S. Don, D.M. Li, Z. Gao, B.-S. Wang, A characteristic-wise alternative WENO-Z finite difference scheme for solving the compressible multicomponent non-reactive flows in the overestimated quasi-conservative form, J. Sci. Comput., 82(2), 27, 2020.
  33. X. Zheng, H. Wang, H. Fu, Well-posedness of fractional differential equations with variable-order Caputo-Fabrizio derivative, Chaos Sol. Fract., 138, 109966, 2020.
  34. J. Liu, X. Chai, H. Fu, H. Wang, A preconditioned fast quadratic spline collocation method for two-sided space-fractional partial differential equations, J. Comput. Appl. Math., 360, 138-156, 2019.
  35. Y.H. Wang, B.-S. Wang, W.S. Don, Generalized Fifth Order WENO Finite Difference Scheme with Z-Type Weights, J. Sci. Comput. 81(3), 1329-1358, 2019
  36. H. Fu, H. Wang, A preconditioned fast parareal finite difference method for space-time fractional partial differential equation, J. Sci. Comput., 78(3), 1724-1743, 2019.
  37. H. Fu, H. Liu, H. Wang, A finite volume method for two- dimensional Riemann-Liouville space-fractional diffusion equation and its efficient implementation, J. Comput. Phys., 388, 316-334, 2019.
  38. H. Fu, Y. Sun, H. Wang, X. Zheng, Stability and convergence of a Crank-Nicolson finite volume method for space fractional diffusion equation, Appl. Numer. Math., 139, 38-51, 2019.
  39. B.W. Wissink, G.B. Jacobs, J.K. Ryan, W.S. Don, E.T.A. van der Weide, Shock Regularization with Smoothness-Increasing Accuracy-Conserving Dirac-Delta Polynomial Kernels, J. Sci. Comput. 77(1), 579-596, 2018
  40. W.S. Don, P. Li, K.Y. Wang, Z. Gao, Improved Symmetry Property of High Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws, Adv. Appl. Math. Mech. 10(6), 1418-1439, 2018
  41. P. Li, Z. Gao, W.S. Don, Hybrid Fourier-Continuation Method and WENO-Z Finite Difference Scheme for Multi-Dimensional Detonation Structure Simulations, Pure Appl. Math. Q. 14(1), 27-55, 2018
  42. B.-S. Wang, W.S. Don, Z. Gao, Y.H. Wang, X. Wen, Hybrid compact-WENO finite difference scheme with radial basis function based shock detection method for hyperbolic conservation laws, SIAM J. Sci. Comput.40(6), A3699-A3714, 2018
  43. B.-S. Wang, P. Li, Z. Gao, W.S. Don, An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws, J. Comput. Phys. 374: 469- 477, 2018.
  44. W.S. Don, B.-S. Wang, Z. Gao, Fast Iterative Adaptive Multi-quadric Radial Basis Function Method for Edges Detection of Piecewise Functions---I: Uniform Mesh, J. Sci. Comput. 75(2), 1016-1039, 2018
  45. P. Li, W.S. Don, C. Wang, Z. Gao, High order positivity- and bound-preserving hybrid Compact-WENO finite difference scheme for the compressible Euler equations, J. Sci. Comput. 74(2), 640-666, 2018
  46. Z. Gao, G.H. Hu, High order well-balanced weighted compact nonlinear schemes for the gas dynamic equations under gravitational fields, E. Asian J. Appl. Math., 7, 697-713, 2018