Publications
Submitted
Journal Papers
- Y.-T.
Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu, Uniformly accurate discontinuous Galerkin
fast sweeping methods for Eikonal equations, submitted to SIAM Journal on
Scientific Computing, (2009). [pdf]
- J.
Zhu, Y.-T. Zhang,
M. S. Alber and S. A. Newman, Bare bones
pattern formation: a core cell-molecular network in appropriate
geometric settings accounts for major features of vertebrate limb
development and evolution, submitted, (2009).
Publications in Refereed Journals (Appeared or
Accepted)
- T. Xiong,
M. Zhang, Y.-T. Zhang and
C.-W. Shu, Fast
sweeping fifth order WENO scheme for static Hamilton-Jacobi equations
with accurate boundary treatment, Journal
of Scientific
Computing, to appear,
(2010). [pdf]
- W.
Hao, J.D. Hauenstein, B. Hu, Y. Liu, A.J. Sommese and Y.-T. Zhang, Multiple stable steady states of a
reaction-diffusion model on zebrafish dorsal-ventral patterning, Discrete
and Continuous Dynamical Systems - Series S, to appear, (2010). [pdf]
- S.
Zhang, S.
Jiang, Y.-T. Zhang and C.-W.
Shu, The mechanism of sound
generation in the interaction between a shock wave and two
counter rotating vortices, Physics
of Fluids, v21, (2009), article number 076101. [pdf]
- J.
Zhu, Y.-T. Zhang, S.A. Newman and M. S. Alber, A finite element
model based on discontinuous
Galerkin methods on moving grids for vertebrate limb
pattern formation, Mathematical
Modelling of Natural Phenomena, v4, no. 4, (2009), pp. 131-148. [pdf]
- A.
Lander, Q. Nie, F. Wan and
Y.-T. Zhang, Localized ectopic expression
of Dpp receptors in a Drosophila embryo, Studies in Applied
Mathematics, v123, issue 2, (2009), pp. 175-214. [pdf]
- J.
Zhu, Y.-T. Zhang, S.A. Newman and M. Alber, Application
of Discontinuous Galerkin Methods for reaction-diffusion systems in developmental biology, Journal
of Scientific Computing, v40, (2009), pp. 391-418. [pdf]
DOI:
http://dx.doi.org/10.1007/s10915-008-9218-4
- Y.-T.
Zhang and C.-W. Shu, Third order WENO schemes on three
dimensional tetrahedral meshes, Communications
in Computational
Physics, v5, (2009), pp. 836-848. [pdf]
- F.
Li, C.-W. Shu, Y.-T. Zhang and
H.-K. Zhao, A second order discontinuous Galerkin fast
sweeping method for Eikonal equations, Journal
of Computational
Physics, v227, issue 17,
(2008), pp. 8191-8208. [pdf]
- Q. Nie, F.
Wan,
Y.-T. Zhang and X.-F. Liu, Compact integration factor methods in high
spatial dimensions, Journal of Computational
Physics, v227,
issue 10, (2008), pp. 5238-5255.
[pdf]
- M.
Alber, T. Glimm, H.G.E. Hentschel, B.
Kazmierczak, Y.-T. Zhang, J. Zhu and S.A. Newman,
The morphostatic limit for a model of
skeletal pattern formation in the vertebrate limb, Bulletin of Mathematical Biology,
v70, (2008), pp.460-483. [pdf]
- Y.-T.
Zhang, A. Lander and Q. Nie, Computational
analysis of BMP gradients in
dorsal-ventral patterning of the zebrafish embryo, Journal of Theoretical
Biology, v248, issue 4, (2007), pp. 579-589. [pdf]
- C.-S.
Chou, Y.-T. Zhang,
R. Zhao and Q. Nie, Numerical
methods for stiff reaction-diffusion systems, Discrete and Continuous
Dynamical Systems - Series B, v7,
(2007), pp. 515-525. [pdf]
- J.
Qian, Y.-T. Zhang and H.-K. Zhao, A
fast sweeping
method for static convex Hamilton-Jacobi equations, Journal
of Scientific Computing, v31, (2007), pp. 237-271. [pdf]
- J. Qian, Y.-T. Zhang and H.-K.
Zhao, Fast sweeping methods for Eikonal equations
on triangular meshes, SIAM Journal on Numerical
Analysis, v45, (2007), pp. 83-107. [pdf]
- S. Zhang, Y.-T. Zhang and C.-W.
Shu, Interaction of an oblique shock wave with a pair of
parallel vortices: shock dynamics and mechanism of sound generation, Physics
of Fluids, v18, (2006), article number 126101. [pdf]
- D. Levy, S. Nayak, C.-W. Shu and Y.-T.
Zhang, Central WENO schemes for Hamilton-Jacobi equations
on triangular meshes, SIAM Journal on Scientific
Computing, v28, (2006), pp. 2229-2247. [pdf]
- Y.-T. Zhang, H.-K. Zhao and S. Chen,
Fixed-point iterative sweeping methods for static
Hamilton-Jacobi equations, Methods and Applications of
Analysis, v13, (2006), pp. 299-320. [pdf]
- Y.-T. Zhang, C.-W. Shu and Y. Zhou,
Effects of Shock
Waves on Rayleigh-Taylor Instability, Physics
of Plasmas, v13, (2006), article
number 062705. [pdf]
- Q. Nie, Y.-T. Zhang and R.
Zhao, Efficient semi-implicit
schemes for stiff systems, Journal of Computational
Physics, v214 (2006), pp.
521-537. [pdf]
- Y.-T. Zhang, H.-K. Zhao and J.
Qian, High order fast sweeping methods for static
Hamilton-Jacobi equations, Journal of Scientific Computing,
v29 (2006), pp. 25-56. Appeared online, DOI:
10.1007/s10915-005-9014-3. [pdf]
- S. Zhang, Y.-T. Zhang and
C.-W. Shu, Multi-stage Interaction
of a Shock Wave and a Strong
Vortex, Physics of Fluids,
v17, (2005), article number
116101. [pdf]
- C.M. Mizutani, Q. Nie, F. Wan, Y.-T. Zhang, P. Vilmos, R.
Sousa-Neves, E. Bier, L. Marsh and A. Lander, Formation
of the BMP activity gradient in the Drosophila embryo, Developmental
Cell, v8, June (2005), pp. 915-924. [paper] , [supplement]
- Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Numerical viscosity and
resolution of high-order weighted
essentially nonoscillatory schemes for compressible
flows with high Reynolds numbers , Physical Review E, v 68, 046709 (2003). [pdf]
- J. Shi, Y.-T. Zhang, and C.-W. Shu, Resolution of High Order WENO
Schemes for Complicated Flow Structures, Journal of Computational
Physics, v186
(2003), pp.690-696. [pdf]
- Y.-T. Zhang and C.-W. Shu, High order WENO schemes for
Hamilton-Jacobi equations on triangular meshes, SIAM Journal on
Scientific Computing, v24 (2003), pp.1005-1030. [pdf]
- Y.-T. Zhang and C. Sun, Two Notes on Petrov-Galerkin
Methods, Acta
Sci. Nat. Univer. Nankai, Vol. 33, No. 1, (2000), pp.
88-93.
Publications
in Refereed Conference Proceedings and Book Chapters
- Y.-T. Zhang, J. Shi, C.-W. Shu and Y. Zhou, Resolution of high order WENO
schemes and Navier-Stokes simulation of the Rayleigh-Taylor instability
problem , in
Computational Fluid and Solid Mechanics 2003, K.J.
Bathe, Editor, the Proceedings of the Second
MIT Conference on Computational Fluid and Solid Mechanics, June 17-20,
2003, volume 1, pp.1216-1218, Elsevier Science.
- Y.-T. Zhang and C.-W. Shu, Third and Fourth Order
Weighted ENO Schemes for Hamilton-Jacobi Equations on 2D Unstructured
Meshes, in Hyperbolic Problems:
Theory, Numerics, Applications, T.Y. Hou and E. Tadmor,
editors, Springer-Verlag, Berlin, 2003, pp.941-950.
- Y.-T. Zhang, H.-K. Zhao and J. Qian, High order fast sweeping
methods for Eikonal equations, in SEG 74, volume
23, 2004,
pp.1901-1904.
- S.A.
Newman, S. Christley, T. Glimm, H.G.E. Hentschel, B. Kazmierczak, Y.-T.
Zhang, J. Zhu and M. Alber, Multiscale models for Vertebrate limb
development, Current Topics in
Developmental Biology, volume
81, 2008,
pp. 311-340.
Thesis
- Y.-T. Zhang, Topics in Structured and
Unstructured Weighted ENO schemes, Ph.D. Thesis, Division of
Applied Mathematics, Brown
University,
2003.