个人简介
EDUCATION:
Ph. D. Mathematics, Duke University (May, 2005)
Thesis title: A multilevel adaptive approach for computational cardiology [PDF]
Thesis advisor: Professor John Trangenstein
M. S. Computational Mathematics, Tsinghua University (June, 2000)
Thesis title: The MAC scheme and related finite element methods for nearly incompressible elasticity
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
AWARDS AND GRANTS:
NSF-China Award DMS-91330203 (co-PI), January, 2014.
NSF-China Award DMS-11101278 (PI), January, 2012.
NSF-China Award DMS-91130012 (co-PI), January, 2012.
NSF-USA Award DMS-0915023 (single PI), August, 2009.
Outstanding Teaching Award (junior level), Math Dept., Michigan Tech, 2009-2010.
Outstanding Research Award (junior level), Math Dept., Michigan Tech, 2008-2009.
L. P. and Barbara Smith Award for Teaching Excellence, Math Dept., Duke University, 2004-2005.
NUMERICAL SIMULATIONS:
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 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)
Electrical wave propagation on a slice of mouse ventricle with the KFBI method (red colormap)
Electrical wave propagation on a slice of mouse ventricle with the KFBI method (cold-hot colormap)
Electrical wave propagation on a slice of mouse ventricle with the KFBI method (isolines)
Electrical wave propagation on a mouse ventricle with the KFBI method (3D)
Gas flow around a CIRCLE in a channel with the direct simulation Monte-Carlo method
Gas flow around a SQUARE in a channel with the direct simulation Monte-Carlo method
Gas flow around a TRIANGLE in a channel with the direct simulation Monte-Carlo method
Gas flow around a KITE (1) in a channel with the direct simulation Monte-Carlo method
Gas flow around a KITE (2) in a channel with the direct simulation Monte-Carlo method
Gas flow around a PLANE in a channel with the direct simulation Monte-Carlo method
研究领域
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.
近期论文
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W. 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, Proceedings of the 28th IEEE EMBS Annual International Conference, New York City, pp. 2276-2279, 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 ([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., Vol. 55, No. 12, pp. 2701-2711, 2008. ([DOI]).
C. S. Henriquez and W.-J. Ying, The bidomain model of cardiac tissue: from microscale to macroscale, Cardiac Bioelectric Therapy, Springer, pp. 401-421, 2009 ([DOI]).
N. Pourtaheri, W.-J. Ying, J.M. Kim and C.S. Henriquez, Thresholds for transverse stimulation: fiber bundles in a uniform field, IEEE. Trans. Biomed. Engrg., Vol 17, No. 5, pp. 478-486, 2009 ([DOI]).
W.-J. Ying and C.S. Henriquez, Adaptive mesh refinement for modeling cardiac electrical dynamics (submitted to CHAOS, an Interdisciplinary Journal of Nonlinear Science) ([PDF]).
W.-J. Ying, C.S. Henriquez and D.J. Rose, Composite backward differentiation formula: an extension of the TR-BDF2 scheme, technical report ([PDF]).
W.-J. Ying and J. T. Beale, A fast accurate boundary integral method for potentials on closely packed cells, Communications in Computational Physics, Vol. 14, No. 4, pp. 1073-1093, 2013.
Houde Han, Zhongyi Huang and W.-J. Ying, A semi-discrete tailored finite point method for a class of anisotropic diffusion problems, Computers and Mathematics with Applications, Vol. 65, No. 11, pp. 1760-1774, 2013.
W.-J. Ying and W.-C. Wang, A kernel-free boundary integral method for implicitly defined surfaces, Journal of Computational Physics, Vol. 252, pp. 606-624, 2013.
W.-J. Ying and W.-C. Wang, A kernel-free boundary integral method for variable coefficients elliptic PDEs, Communications in Computational Physics, Vol. 15, No. 4, pp. 1108-1140, 2014.
Houde Han, Min Tang and W.-J. Ying, A tailored finite point method for the discrete ordinates transport equations, Communications in Computational Physics, Vol. 15, No. 3, pp. 797-826, 2014.
W.-J. Ying and C.S. Henriquez, Adaptive mesh refinement and adaptive time integration for electrical wave propagation on the Purkinje system, (submitted to BioMed Research International), 2014 ([PDF]).
W.-J. Ying, A Cartesian grid-based boundary integral method for an elliptic interface problem on closely packed cells, submitted to Journal of Computational Physics (in revision), 2014 ([PDF]).
W.-J. Ying, A kernel-free boundary integral method for the nonlinear Poisson-Boltzmann equation, submitted to Journal of Computational Physics (in revision), 2014 ([PDF]).
W.-J. Ying, A kernel-free boundary integral method for the biharmonic equation (in preparation), 2014.
W.-J. Ying and Craig S. Henriquez, A kernel-free boundary integral method for the heat equation and its applications (in preparation), 2014.
W.-J. Ying and Craig S. Henriquez, Composite backward differentition formula for the bidomain equations (in preparation), 2014.
W.-J. Ying, Shuwang Li and Xiaofan Li, A Cartesian grid method for mean curvature flows in two and three space dimensions (in preparation), 2014.
W.-J. Ying and W.-C. Wang, A kernel-free boundary integral method for the Stokes equation (in preparation), 2014.
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