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Publications

Publications in Refereed Journals

[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, Submitted, 2018. 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, Accepted, 2018. [pdf]

[45] R. Zhang, Y.-T. Zhang, Z. Wang, B. Chen and Y. Zhang, A conservative numerical method for the fractional nonlinear Schrödinger equation in two dimensions, SCIENCE CHINA Mathematics, Accepted, 2018. [pdf]

[44] D. Lu, S. Chen and Y.-T. Zhang, Third order WENO scheme on sparse grids for hyperbolic equations, Pure and Applied Mathematics Quarterly, Accepted, 2017. arXiv: 1804.00725

[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.