Office Location:  Hudson Hall Annex 268
    Office Phone No:   1-919-660-5162
    Email Address:  ying@math.duke.edu
    Web Page:  http://www.math.duke.edu/~ying

Ph.D.   Applied Mathematics, Duke University (May, 2005)
           Thesis Title:  A Multilevel Adaptive Approach For Computational Cardiology ([PDF])
           Thesis Advisor:  Professor John Trangenstein

M. S.   Applied Mathematics, Tsinghua University (June, 2000)
           Thesis Title:  The MAC Scheme and Related Finite Element Methods
                                   For Nearly Incompressible Elasticity ([PDF];[PS])
           Thesis Advisor:  Professor Houde Han

B. S.   Applied Mathematics, Tsinghua University (June, 1997)
           Thesis Title:  On Artificial Boundary Conditions for Potential Flows
           Thesis Advisor:  Professor Houde Han

• The general areas of my interests include scientific computing, modeling/simulation and numerical methods for mathematical problems arising from science and engineering applications, such as mathematical biology, computational electro-physiology and computational fluid dynamics. My current specific research interests are focused on adaptive and multiscale algorithms for modeling cardiac dynamics. A few other numerical methods (other than those covered by my thesis work) that I have made intensive studies are Cartesian grid methods for elliptic boundary/interface problems, boundary integral methods accelerated by fast multipole algorithms, and composite backward differentiation formulas (CBDFs) for initial value problems.

• Linearized Gas Dynamics (1D)
• Shallow-Water Equations (1D)

• Linearized Gas Dynamics (2D)
• Shallow-Water Equations (2D)

• Compressible Euler Equations (1D)
• Compressible Euler Equations (2D)

• Supersonic Flow Around Cylinders (2D)
• A Mach 3 Wind Tunnel With a Step (2D)
• Oblique Shock Reflection with AMR (2D)

• Upwind Scheme for Burgers' Equation with AMR (1D)
• Upwind Scheme for Burgers' Equation with AMR (2D)
• Upwind Scheme for Burgers' Equation with AMR (3D)

• One-Dimensional Reaction-Diffusion Problems with AMR
• Two-Dimensional Reaction-Diffusion Problems with AMR
• Three-Dimensional Reaction-Diffusion Problems with AMR

• Rotationally Anisotropic Bidomain Model with AMR (2D)
• Bidomain Luo-Rudy Phase One Model with AMR (2D)

• FitzHugh-Nagumo Problem with AMR (1D)
• FitzHugh-Nagumo Problem with AMR (2D)
• FitzHugh-Nagumo Problem with AMR (3D)

• Spiral Waves around Obstacles with AMR (2D) (data)
• Spiral Waves around Obstacles with AMR (2D) (grids)

To view the following 3D animations, it is better to download them first and then open
with a media player such as "QuickTime Player" due to the large size of the files.

• Electrical Wave Propagation in a Virtual Ventricle with AMR (3D) (action potential)
• Electrical Wave Propagation in a Virtual Ventricle with AMR (3D) (colormapped surface grids)

• Electrical Wave Propagation in the Heart with AMR (3D) (action potential)
• Electrical Wave Propagation in the Heart with AMR (3D) (volume grids and iso-surface)
• Electrical Wave Propagation in the Heart with AMR (3D) (colormapped surface grids)
• Electrical Wave Propagation in the Heart with AMR (3D) (surface grids and isolines)

• W.-J. Ying, A multilevel adaptive approach for computational cardiology, Ph.D. Dissertation, Department of Mathematics, Duke University, May 2005 ([PDF]).

• D.G. Schaeffer, W.-J. Ying and X.P. Zhao, Asymptotic approximation of an ionic model for cardiac restitution, Nonlinear Dynamics, Vol. 51, No. 1-2, pp. 189-198, 2008 ([DOI]).

• W.-J. Ying and N. Pourtaheri and C.S. Henriquez, Field stimulation of cells in suspension: use of a hybrid finite element method, Conference Proceedings. Annual International Conference of the IEEE Engineering in Medicine and Biology Society, New York, 2006 ([DOI]).

• D.G. Schaeffer, J.W. Cain, D.J. Gauthier, S.S. Kalb, R.A. Oliver, E.G. Tolkacheva, W.-J. Ying and W. Krassowska, An ionically based mapping model with memory for cardiac restitution, Bull. in Math. Bio., Vol. 69, No. 2, pp. 459-482, 2007 ([DOI]).

• W.-J. Ying and C.S. Henriquez, Hybrid finite element method for describing the electrical response of biological cells to applied fields, IEEE Transactions on Biomedical Engineering, Vol. 54, No. 4, pp. 611-620, 2007 ([DOI]).

• M.L. Hubbard and W.-J. Ying and C.S. Henriquez, Effect of gap junction distribution on impulse propagation in a monolayer of myocytes: a model study, Europace, Vol. 9 (suppl 6), pp. vi20-vi28, 2007 ([DOI]).

• W.-J. Ying and C.S. Henriquez, A kernel-free boundary integral method for elliptic boundary value problems, Journal of Computational Physics, Vol. 227, No. 2, pp. 1046-1074, 2007 ([PDF]) ([DOI]).

• W.-J. Ying, D.J. Rose and C.S. Henriquez, Efficient fully implicit time integration methods for modeling cardiac dynamics, IEEE. Trans. Biomed. Engrg., accepted for publication, 2008. ([PDF]).

• W.-J. Ying, C.S. Henriquez and D.J. Rose, Composite backward differentiation formula: an extension of the TR-BDF2 scheme, Technical Report, Duke University, 2007 (submitted to SIAM J. Numer. Anal.) ([PDF]).

• N. Pourtaheri, W.-J. Ying, J.M. Kim and C.S. Henriquez, Local electric field perturbations around excitable fibers: effect on stimulation thresholds, Technical Report, Duke University, 2007 (submitted to IEEE. Trans. Biomed. Engrg. ).

• W.-J. Ying, D.J. Rose and C.S. Henriquez, Adaptive mesh refinement and adaptive time integration for electrical wave propagation on the Purkinje system, Technical Report, Duke University, 2007 (submitted to SIAM J. Sci. Comput.) ([PDF]).

• W.-J. Ying, J.T. Beale and C.S. Henriquez, Fast multipole accelerated high order boundary integral method for field stimulation of biological cells, in preparation, 2007.

• W.-J. Ying and C.S. Henriquez, The kernel-free boundary integral method for cardiac dynamics on a monolayer with obstacles, in preparation, 2007.

• W.-J. Ying and C.S. Henriquez, Field stimulation of biological cells with the kernel-free boundary integral method, in preparation, 2007.

• W.-J. Ying and C.S. Henriquez, Modeling cardiac dynamics with the multiscale finite element method, in preparation, 2007.