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Publications
Publications in Refereed Journals
- [55] Z. M. Miksis and Y.-T. Zhang, Sparse-grid implementation of fixed-point fast sweeping WENO
schemes for Eikonal equations, Communications
on Applied Mathematics and Computation, v6 (1), (2024). Published
online first: https://doi.org/10.1007/s42967-022-00209-x. [pdf]
- [54]
E. Tsybulnik, X. Zhu and Y.-T. Zhang, Efficient sparse-grid implementation of a fifth-order
multi-resolution WENO scheme for hyperbolic equations, Communications on Applied Mathematics
and Computation, v5 (4), (2023), pp. 1339-1364. Published online first: https://doi.org/10.1007/s42967-022-00202-4. [pdf]
- [53]
L. Li, J. Zhu, C.-W. Shu and Y.-T. Zhang, A fixed-point fast sweeping WENO method with inverse Lax-Wendroff
boundary treatment for steady state of hyperbolic conservation laws, Communications on Applied Mathematics
and Computation, v5 (1), (2023), pp. 403-427. Published online
first: https://doi.org/10.1007/s42967-021-00179-6. [pdf]
- [52]
Y. Yang, W. Hao and Y.-T. Zhang, A continuous finite element method with homotopy vanishing
viscosity for solving the static Eikonal equation, Communications in Computational Physics, v31, issue 5,
(2022), pp. 1402-1433. https://doi.org/10.4208/cicp.OA-2021-0164. [pdf]
- [49]
Z. Zhao, Y.-T. Zhang, Y. Chen
and J. Qiu, A Hermite WENO method with modified
ghost fluid method for compressible two-medium flow problems, Communications
in Computational Physics, v30, issue 3, (2021), pp. 851-873. https://doi.org/10.4208/cicp.OA-2020-0184. [pdf]
- [48]
Z. Zhao, Y.-T. Zhang and J. Qiu, A modified fifth order
finite difference Hermite WENO scheme for hyperbolic conservation laws,
Journal of Scientific Computing, v85, (2020), Article number: 29, pp. 1-22. https://doi.org/10.1007/s10915-020-01347-1
- [47]
Y. Liu, Y. Cheng, S. Chen and Y.-T. Zhang, Krylov implicit
integration factor discontinuous Galerkin methods on sparse grids for high
dimensional reaction-diffusion equations, Journal of Computational
Physics, v388, (2019), pp. 90-102. doi:
10.1016/j.jcp.2019.03.021 arXiv:
1810.11111
- [46]
R. Zhao, Y.-T. Zhang and S. Chen, Krylov implicit
integration factor WENO method for SIR model with directed diffusion, Discrete
and Continuous Dynamical Systems - Series B, v24 (9), (2019), pp.
4983-5001. doi: 10.3934/dcdsb.2019041
[pdf]
- [45]
R. Zhang, Y.-T. Zhang, Z. Wang, B. Chen and Y. Zhang, A
conservative numerical method for the fractional nonlinear Schrodinger
equation in two dimensions, SCIENCE CHINA Mathematics, v62,
(2019), pp. 1997-2014. doi: 10.1007/s11425-018-9388-9
[pdf]
- [43]
M. Machen and Y.-T. Zhang, Krylov implicit integration
factor methods for semilinear fourth-order equations, Mathematics, v5,
(2017), 63; doi:10.3390/math5040063
[pdf]
- [42]
D. Lu and Y.-T. Zhang, Computational complexity study on
Krylov integration factor WENO method for high spatial dimension
convection-diffusion problems, Journal of Scientific Computing, v73,
(2017), pp. 980-1027. Published online: doi: 10.1007/s10915-017-0398-7
[pdf]
- [41]
D. Lu and Y.-T. Zhang, Krylov integration factor method on
sparse grids for high spatial dimension convection-diffusion
equations, Journal of Scientific Computing,
v69, (2016), pp.
736-763. Published online: doi: 10.1007/s10915-016-0216-7
[pdf]
- [40]
T. Jiang, and Y.-T. Zhang, Krylov single-step implicit
integration factor WENO method for advection-diffusion-reaction equations,
Journal of Computational Physics, v311, (2016), pp. 22-44.
Published online: doi:
10.1016/j.jcp.2016.01.021 [pdf]
- [39]
L. Wu, Y.-T. Zhang, S. Zhang, and C.-W. Shu, High order
fixed-point sweeping WENO methods for steady state of hyperbolic
conservation laws and its convergence study, Communications in
Computational Physics, v20, (2016), pp. 835-869. doi:
10.4208/cicp.130715.010216a [pdf]
- [38]
L. Wu and Y.-T. Zhang, A third order fast sweeping method
with linear computational complexity for Eikonal equations, Journal of
Scientific Computing, v62, (2015), pp. 198-229. doi: 10.1007/s10915-014-9856-7 [pdf]
- [37]
T. Jiang and Y.-T. Zhang, Krylov implicit integration factor
WENO methods for semilinear and fully nonlinear
advection-diffusion-reaction equations, Journal of
Computational Physics, v253, (2013), pp. 368-388. doi:
10.1016/j.jcp.2013.07.015 [pdf]
- [36] W. Hao, J.D. Hauenstein, C.-W. Shu, A.J.
Sommese, Z. Xu and Y.-T. Zhang, A homotopy method based on
WENO schemes for solving steady state problems of hyperbolic conservation
laws, Journal of Computational Physics, v250, (2013), pp.
332-346. doi:
10.1016/j.jcp.2013.05.008 [pdf]
- [35]
Y.-T. Zhang, M.S. Alber, and S.A. Newman, Mathematical
modeling of vertebrate limb development, Mathematical
Biosciences, v243, (2013), pp. 1-17. doi:
10.1016/j.mbs.2012.11.003. [pdf]
- [34]
Y. Liu and Y.-T. Zhang, A robust reconstruction for unstructured WENO schemes, Journal
of Scientific Computing,
v54, (2013), pp. 603-621. [pdf]
DOI 10.1007/s10915-012-9598-3.
- [33]
S. Chen and Y.-T. Zhang, Krylov implicit integration factor
methods for spatial discretization on high dimensional unstructured
meshes: application to discontinuous Galerkin methods, Journal
of Computational Physics, v230, (2011), pp. 4336-4352. [pdf]
doi: 10.1016/j.jcp.2011.01.010
- [32] W. Hao, J.D. Hauenstein, B. Hu, Y. Liu, A.J.
Sommese and Y.-T. Zhang, Continuation along bifurcation
branches for a tumor model with a necrotic core, Journal of Scientific
Computing, v53, (2012), pp. 395-413. [pdf]
- [31]
W. Hao, J.D. Hauenstein, B. Hu, Y. Liu, A.J. Sommese and Y.-T.
Zhang, Bifurcation for a free boundary problem modeling the growth
of a tumor with a necrotic core, Nonlinear Analysis: Real World Applications, v13,
(2012), pp. 694-709. [pdf]
- [30]
Y.-T. Zhang, S. Chen, F. Li, H. Zhao and C.-W. Shu, Uniformly
accurate discontinuous Galerkin fast sweeping methods for Eikonal
equations, SIAM Journal on Scientific Computing, v33,
no. 4, (2011), pp. 1873-1896. [pdf]. DOI:
10.1137/090770291
- [29]
S. Zhao, J. Ovadia, X. Liu, Y.-T. Zhang and Q. Nie, Operator
splitting implicit integration factor methods for stiff
reaction-diffusion-advection systems, Journal of Computational
Physics, v230, (2011), pp. 5996-6009. [pdf]
- [28]
C.-S. Chou, W. Lo, K. Gokoffski, Y.-T. Zhang, F. Wan, A. Lander, A.
Calof, and Q. Nie, Spatial dynamics of multi-stage cell
lineages in tissue stratification, Biophysical Journal,
v99(10), (2010), pp. 3145-3154. Article [pdf] Supporting Material [pdf]. doi:10.1016/j.bpj.2010.09.034.
- [27]
J. Zhu, Y.-T. Zhang, M. S. Alber and S. A. Newman, Bare
bones pattern formation: a core regulatory network in varying geometries
reproduces major features of vertebrate limb development and evolution, PLoS
ONE, v5(5): e10892, (2010). doi:10.1371/journal.pone.0010892.
[pdf]
- [26]
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,
v45, (2010), pp. 514-536. [pdf]
- [25]
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, v4(6), (2011), pp. 1413-1428. [pdf]
- [24]
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]
- [23]
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]
- [22]
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]
- [21]
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
- [20]
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]
- [19]
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]
- [18]
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]
- [17]
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]
- [16]
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]
- [15]
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]
- [14] 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]
- [13] 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]
- [12] 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]
- [11] 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]
- [10] 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]
- [9] 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]
- [8] 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]
- [7] 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]
- [6] 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]
- [5] 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]
- [4] 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]
- [3] 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]
- [2] 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]
- [1] 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
- [1] 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.
- [2] 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.
- [3] 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.
- [4]
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.
- [5]
Q. Nie and Y.-T. Zhang, Cell Biology Modeling
Development, Encyclopedia of Applied and Computational
Mathematics, Bjorn Engquist, Editor, Springer-Verlag, (2015),
pp. 183-189. [pdf]
- [6]
Y.-T. Zhang and C.-W. Shu, ENO
and WENO schemes, in Handbook of Numerical Analysis, Volume
17, Handbook of Numerical Methods for Hyperbolic Problems:
Basic and Fundamental Issues. North-Holland, Elsevier,
Amsterdam, 2016, pp. 103-122. doi:
10.1016/bs.hna.2016.09.009 [pdf]
Thesis
- Y.-T. Zhang, Topics in Structured and Unstructured Weighted
ENO schemes, Ph.D. Thesis,
Division of Applied Mathematics, Brown University,
2003.