(39) D. Wang, S. Xiao, Y. Xu, T. Downar, E. Shemon, and Y. Xing,
Stabilizing CMFD with Linear Prolongation, submitted.
(38) J. Buli and Y. Xing,
Local discontinuous Galerkin Methods for the Boussinesq Coupled BBM System, Journal of
Scientific Computing, in press.
(37) G. Li abd 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, in press.
(36) 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. PDF
(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. 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
(33) 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
(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 to tidal bores problems,
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 paper:
(1) 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
Book Chapters:
(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
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