Publications (at google scholar)
 
  Refereed Journal and Conference Articles:

  • (76) Q. Chen, Z. Sun and Y. Xing, The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws, Submitted.

  • (75) Q. Sheng, C. Hauck and Y. Xing, New asymptotic preserving, hybrid discontinuous Galerkin methods the radiation transport equation with isotropic scattering and diffusive scaling, Submitted.

  • (74) Q. Sheng, C. Hauck and Y. Xing, Numerical analysis of a spherical harmonic discontinuous Galerkin method for scaled radiative transfer equations with isotropic scattering, Submitted.

  • (73) Z. Sun and Y. Xing, On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix, Submitted.

  • (72) Q. Chen, Z. Sun and Y. Xing, The Runge--Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws, SIAM Journal on Scientific Computing, in press.

  • (71) Y. Chen and Y. Xing, Optimal error estimates of ultra-weak discontinuous Galerkin methods with generalized numerical fluxes for multi-dimensional convection-diffusion and biharmonic equations, Mathematics of Computation, in press.

  • (70) G. Huang, Y. Xing and T. Xiong, High order asymptotic preserving well-balanced finite difference WENO schemes for all Mach full Euler equations with gravity, Communications in Computational Physics, in press.

  • (69) J. Hunter, Z. Sun and Y. Xing, Stability and time-step constraints of implicit-explicit Runge--Kutta methods for the linearized Korteweg--de Vries equation, Communications on Applied Mathematics and Computation, v6 (2024), pp. 658-687.

  • (68) Y. Ren, K. Wu, J. Qiu and Y. Xing, On high order positivity-preserving well-balanced finite volume methods for the Euler equations with gravitation, Journal of Computational Physics, v492 (2023), 112429.

  • (67) W. Zhang, Y. Xing, Y. Xia and Y. Xu, High order structure-preserving arbitrary Lagrangian-Eulerian discontinuous Galerkin methods for the Euler equations under gravitational fields, Computers & Mathematics with Applications, v146 (2023), pp. 339-359.

  • (66) Z. Sun and Y. Xing, On generalized Gauss-Radau projections and optimal error estimates of upwind-biased DG methods for the linear advection equation on special simplex meshes, Journal of Scientific Computing, v95 (2023), 40.

  • (65) J. Sun, C.-W. Shu and Y. Xing, Discontinuous Galerkin methods for stochastic Maxwell equations with multiplicative noise, ESAIM: Mathematical Modelling and Numerical Analysis, v57 (2023), pp. 841-864.

  • (64) Y. Ren, Y. Xing and J. Qiu, High order finite difference Hermite WENO fast sweeping methods for static Hamilton-Jacobi equations, Journal of Computational Mathematics, v41 (2023), pp. 1064-1092.

  • (63) B. Ye, S. Jin, Y. Xing and X. Zhong, Hamiltonian-preserving discontinuous Galerkin methods for the Liouville equation with discontinuous potential, SIAM Journal on Scientific Computing, v54 (2022), pp. A3317-A3340.

  • (62) W. Zhang, Y. Xing and E. Endeve, Energy conserving and well-balanced discontinuous Galerkin methods for the Euler-Poisson equations in spherical symmetry, Monthly Notices of the Royal Astronomical Society, v514 (2022), pp. 370-389. PDF

  • (61) R. Yang and Y. Xing, Energy conserving discontinuous Galerkin method with scalar auxiliary variable technique for the nonlinear Dirac equation, Journal of Computational Physics, v463 (2022), 111278. PDF

  • (60) J. Sun, C.-W. Shu and Y. Xing, Multi-symplectic discontinuous Galerkin methods for the stochastic Maxwell equations with additive noise, Journal of Computational Physics, v461 (2022), 111199. PDF

  • (59) G. Huang, Y. Xing and T. Xiong, High order well-balanced asymptotic preserving finite difference WENO schemes for the shallow water equations in all Froude numbers, Journal of Computational Physics, v463 (2022), 111255. PDF

  • (58) Y. Li, S. Wu and Y. Xing, Finite element approximations of a class of nonlinear stochastic wave equation with multiplicative noise, Journal of Scientific Computing, v91 (2022), 53. PDF

  • (57) Y. Ren, Y. Xing and J. Qiu, High order finite difference Hermite WENO fixed-point fast sweeping methods for static Hamilton-Jacobi equations, Communications in Computational Physics, v31 (2022), pp. 154-187. PDF

  • (56) W. Zhang, Y. Xing, Y. Xia and Y. Xu, High-order positivity-preserving well-balanced discontinuous Galerkin methods for Euler equations with gravitation on unstructured meshes, Communications in Computational Physics, v31 (2022), pp. 771-815. PDF

  • (55) J. Sun, S. Xie and Y. Xing, Local discontinuous Galerkin methods for the abcd nonlinear Boussinesq system, Communications on Applied Mathematics and Computation, v4 (2022), pp. 381-416. PDF

  • (54) Y. Ren, Y. Xing, D. Wang and J. Qiu, High order asymptotic preserving Hermite WENO fast sweeping method for the steady-state S_N transport equation, Journal of Scientific Computing, v93 (2022), 3.

  • (53) R. Yang, Y. Yang and Y. Xing, High order sign-preserving and well-balanced exponential Runge-Kutta discontinuous Galerkin methods for the shallow water equations with friction, Journal of Computational Physics, v444 (2021), 110543. PDF

  • (52) J. Britton, Y. T. Chow, W. Chen and Y. Xing, Recovery of a time-dependent bottom topography function from the shallow water equations via an adjoint approach, SIAM Journal on Scientific Computing, v43 (2021), pp. A2981-A3008. PDF

  • (51) Z. Sun and Y. Xing, Optimal error estimates of discontinuous Galerkin methods with generalized fluxes for wave equations on unstructured meshes, Mathematics of Computation, v90 (2021), pp. 1741-1772. PDF

  • (50) R. Guo and Y. Xing, Optimal energy conserving local discontinuous Galerkin methods for elastodynamics: Semi and fully discrete error analysis, Journal of Scientific Computing, v87 (2021), 13. PDF

  • (49) 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, v43 (2021), pp. A472-A510. PDF

  • (48) Z. Sun, S. Wang, L.-B. Chang, Y. Xing and D. Xiu, Convolution neural network shock detector for numerical solution of conservation laws, Communications in Computational Physics, v28 (2020), pp. 2075-2108. PDF

  • (47) Z. Sun and Y. Xing, On structure-preserving discontinuous Galerkin methods for Hamiltonian partial differential equations: Energy conservation and multi-symplecticity, Journal of Computational Physics, v419 (2020), 109662. PDF

  • (46) X. Li, Y. Xing and C.-S. Chou, Optimal energy conserving and energy dissipative local discontinuous Galerkin methods for the Benjamin-Bona-Mahony equation, Journal of Scientific Computing, v83 (2020), 17. PDF

  • (45) J. Britton and Y. Xing, Well-balanced discontinuous Galerkin methods for the one-dimensional blood flow through arteries model with man-at-eternal-rest and living-man equilibria, Computers and Fluids, v203 (2020), 104493. PDF

  • (44) X. Wen, W.S. Don, Z. Gao and Y. Xing, Entropy stable and well-balanced discontinuous Galerkin methods for the nonlinear shallow water equations, Journal of Scientific Computing, v83 (2020), 66. PDF

  • (43) J. Britton and Y. Xing, High order still-water and moving-water equilibria preserving discontinuous Galerkin methods for the Ripa model, Journal of Scientific Computing, v82 (2020), 30. PDF

  • (42) J. Buli and Y. Xing, A discontinuous Galerkin method for the Aw-Rascle traffic flow model on networks, Journal of Computational Physics, v406 (2020), 109183. PDF

  • (41) X. Li, W. Sun, Y. Xing and C.-S. Chou, Energy conserving local discontinuous Galerkin methods for the improved Boussinesq equation, Journal of Computational Physics, v401 (2020), 109002. PDF

  • (40) S. Qian, G. Li, F. Shao and Y. Xing, Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water flows in open channels, Advances in Water Resources, v115 (2018), pp. 172-184. PDF

  • (39) J. Buli and Y. Xing, Local discontinuous Galerkin Methods for the Boussinesq Coupled BBM System, Journal of Scientific Computing, v75 (2018), pp. 536-559. PDF

  • (38) G. Li and Y. Xing, Well-balanced discontinuous Galerkin methods with hydrostatic reconstruction for the Euler equations with gravitation, Journal of Computational Physics, v352 (2018), pp. 445-462. (Note: See paper #(56) for the update on the accuracy of the proposed method.) PDF

  • (37) G. Li and Y. Xing, Well-balanced finite difference weighted essentially non-oscillatory schemes for general equilibrium states of the Euler equations with gravitation, Computers and Mathematics with Applications, v75 (2018), pp. 2071-2085. PDF

  • (36) D. Wang, S. Xiao, Y. Xu, T. Downar, E. Shemon and Y. Xing, Stabilizing CMFD with Linear Prolongation, PHYSOR2018, Cancun, Mexico, 2018.

  • (35) C.-S. Chou, W. Sun, Y. Xing and H. Yang, Local discontinuous Galerkin methods for the Khokhlov-Zabolotskaya-Kuznetzov equation, Journal of Scientific Computing, v73 (2017), pp. 593-616. PDF

  • (34) Y. Cheng, C.-S. Chou, F. Li and Y. Xing, L2 stable discontinuous Galerkin methods for one-dimensional two-way wave equations, Mathematics of Computation, v86 (2017), pp. 121-155. PDF

  • (33) Y. Xing, Numerical methods for the nonlinear shallow water equations, Handbook of Numerical Analysis: Applied and Modern Issues, R. Abgrall and C.-W. Shu, Editors, North-Holland, Elsevier, Amsterdam, 2017, pp. 361-384. PDF

  • (32) G. Li and Y. Xing, High order finite volume WENO schemes for the Euler equations under gravitational fields, Journal of Computational Physics, v316 (2016), pp. 145-163. PDF

  • (31) X. Wen, Z. Gao, W.S. Don, Y. Xing and P. Li, Application of positivity-preserving well-balanced discontinuous Galerkin method in computational hydrology, Computers and Fluids, v139 (2016), pp. 112-119. PDF

  • (30) O. Karakashian and Y. Xing, A posteriori error estimates for conservative local discontinuous Galerkin methods for the generalized Korteweg-de Vries equation, Communications in Computational Physics, v20 (2016), pp. 250-278. PDF

  • (29) H. Liu and Y. Xing, An invariant preserving discontinuous Galerkin method for the Camassa-Holm equation, SIAM Journal on Scientific Computing, v38 (2016), pp. A1919-A1934. PDF

  • (28) Y. Xing, High order finite volume WENO schemes for the shallow water flows through channels with irregular geometry, Journal of Computational and Applied Mathematics, v299 (2016), pp. 229-244. PDF

  • (27) X. Feng, Y. Li and Y. Xing, Analysis of mixed interior penalty discontinuous Galerkin methods for the Cahn-Hilliard equation and the Hele-Shaw flow, SIAM Journal on Numerical Analysis, v54 (2016), pp. 825-847. PDF

  • (26) G. Li and Y. Xing, Well-balanced discontinuous Galerkin methods for the Euler equations under gravitational fields, Journal of Scientific Computing, v67 (2016), pp. 493-513. PDF

  • (25) M. Kelly, Y. Xing and S. Lenhart, Optimal fish harvesting for a population modeled by a nonlinear parabolic partial differential equation, Natural Resource Modeling, v29 (2016), pp. 36-70. PDF

  • (24) E. Endeve, C.D. Hauck, Y. Xing and A. Mezzacappa, Bound-preserving discontinuous Galerkin methods for conservative phase space advection in curvilinear coordinates, Journal of Computational Physics, v287 (2015), pp.151-183. PDF

  • (23) X. Liang, A. Q. M. Khaliq and Y. Xing, Fourth order exponential time differencing method with local discontinuous Galerkin approximation for coupled nonlinear Schrodinger equations, Communications in Computational Physics, v17 (2015), pp.510-541. PDF

  • (22) Y. Xing, Exactly well-balanced discontinuous Galerkin methods for the shallow water equations with moving water equilibrium, Journal of Computational Physics, v257 (2014), pp.536-553. PDF

  • (21) C.-S. Chou, C.-W. Shu and Y. Xing, Optimal energy conserving local discontinuous Galerkin methods for second-order wave equation in heterogeneous media, Journal of Computational Physics, v272 (2014), pp.88-107. PDF

  • (20) C. Hufford and Y. Xing, Superconvergence of the local discontinuous Galerkin method for the linearized Korteweg-de Vries equation, Journal of Computational and Applied Mathematics, v255 (2014), pp.441-455. PDF

  • (19) Y. Xing and C.-W. Shu, A survey of high order schemes for the shallow water equations, Journal of Mathematical Study, v47 (2014), pp. 221-249. PDF

  • (18) J.L. Bona, H. Chen, O. Karakashian and Y. Xing, Conservative, discontinuous-Galerkin methods for the generalized Korteweg-de Vries equation, Mathematics of Computation, v82 (2013), pp.1401-1432. PDF

  • (17) Y. Xing, C.-S. Chou and C.-W. Shu, Energy conserving local discontinuous Galerkin methods for wave propagation problems, Inverse Problems and Imaging, v7 (2013), pp.967-986. PDF

  • (16) Y. Xing and X. Zhang, Positivity-preserving well-balanced discontinuous Galerkin methods for the shallow water equations on unstructured triangular meshes, Journal of Scientific Computing, v57 (2013), pp.19-41. PDF

  • (15) Y. Xing and C.-W. Shu, High order well-balanced WENO scheme for the gas dynamic equations under gravitational fields, Journal of Scientific Computing, v54 (2013), pp.645-662. PDF

  • (14) X. Feng and Y. Xing, Absolutely stable local discontinuous Galerkin methods for the Helmholtz equation with large wave number, Mathematics of Computation, v82 (2013), pp.1269-1296. PDF

  • (13) Y. Xing and C.-W. Shu, High-order finite volume WENO schemes for the shallow water equations with dry states, Advances in Water Resources, v34 (2011), pp.1026-1038. PDF

  • (12) Y. Xing, C.-W. Shu and S. Noelle, On the advantage of well-balanced schemes for moving-water equilibria of the shallow water equations, Journal of Scientific Computing, v48 (2011), pp.339-349. PDF

  • (11) Y. Xing, X. Zhang and C.-W. Shu, Positivity-preserving high order well-balanced discontinuous Galerkin methods for the shallow water equations, Advances in Water Resources, v33 (2010), pp.1476-1493. PDF

  • (10) A.J. Majda, Y. Xing and M. Mohammadian, Moist multi-scale models for the hurricane embryo, Journal of Fluid Mechanics, v657 (2010), pp. 478-501. PDF

  • (9) A.J. Majda and Y. Xing, New multi-scale models on mesoscales and squall lines, Communications in Mathematical Sciences,v8 (2010), pp.113-134. PDF

  • (8) Y. Xing, A.J. Majda and W.W. Grabowski, New efficient sparse space-time algorithms for superparameterization on mesoscales, Monthly Weather Review, v137 (2009), pp.4307-4324. PDF

  • (7) A.J. Majda, M. Mohammadian and Y. Xing, Vertically sheared horizontal flow with mass sources: a canonical balanced model, Geophysical & Astrophysical Fluid Dynamics, v102 (2008), pp.543-591. PDF

  • (6) S. Noelle, Y. Xing and C.-W. Shu, High order well-balanced finite volume WENO schemes for shallow water equation with moving water, Journal of Computational Physics, v226 (2007), pp.29-58. (Note: the published paper has some typos in Section 3. Please refer to this pdf file for the correct one.) PDF

  • (5) Y. Xing and C.-W. Shu, Application of high order well-balanced schemes to a class of hyperbolic systems with source terms, Boletin de la Sociedad Espanola de Matematica Aplicada, v34 (2006), pp.69-80. PDF

  • (4) Y. Xing and C.-W. Shu, A new approach of high order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Communications in Computational Physics, v1 (2006), pp.100-134. PDF

  • (3) Y. Xing and C.-W. Shu, High order well-balanced finite volume WENO schemes and discontinuous Galerkin methods for a class of hyperbolic systems with source terms, Journal of Computational Physics, v214 (2006), pp.567-598. PDF

  • (2) Y. Xing and C.-W. Shu, High order well-balanced finite difference WENO schemes for a class of hyperbolic systems with source terms, Journal of Scientific Computing, v27 (2006), pp.477-494. PDF

  • (1) Y. Xing and C.-W. Shu, High order finite difference WENO schemes with the exact conservation property for the shallow water equations, Journal of Computational Physics, v208 (2005), pp.206-227. PDF

  Book Edited:

  • (1) X. Feng, O. Karakashian and Y. Xing, Editors, Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations, The IMA Volumes in Mathematics and its Applications, volume 157, Springer-Verlag, 2013, 278 pages. Link

  Conference Proceedings and Book Chapters:

  • (3) E. Endeve, C.D. Hauck, Y. Xing and A. Mezzacappa, Towards robust discontinuous Galerkin methods for general relativistic neutrino radiation transport, Proceedings of the 9th Annual International Conference on Numerical Modeling of Space Plasma Flows (ASTRONUM 2014), N.V. Pogorelov, E. Audit and G.P. Zank, editors, Astronomical Society of the Pacific Conference Series, v498, 2015.

  • (2) R. Archibald, E. Constantinescu, K. Evans, H. Finkel, B. Norris, M.R. Norman, A. Sandu, M. Stoyanov, M. Tokman, B. Wingate and Y. Xing, Resilient, communication-reducing, and adaptive time stepping to accelerate exascale scientific applications, DOE Applied Mathematics Research for Exascale Computings, Washington, DC, 2013.

  • (1) S. Noelle, Y. Xing and C.-W. Shu, High order well-balanced schemes, Numerical Methods for Balance Laws, G. Puppo and G. Russo, editors, Quaderni di Matematica volume 24, Dipartimento di Matematica, Seconda Universita di Napoli, Italy, 2010, pp. 1-66. PDF

  Technical Reports:

  • (1) D. Wang, T. Downar, Y. Xu, Y. Xing and E. Shemon, Development of a Novel Accelerator for Neutron Transport Solution Using the Galerkin Spectral Element Methods, U.S. DOE NEUP Final Report, Project No. 15-8208, 2019, 83 pages. Link

  Thesis:

  • (1) Y. Xing, High order well-balanced numerical schemes for hyperbolic systems with source term, Ph.D. thesis, Brown University, May 2006, 211 pages. PDF