Welcome to Shan
Zhao's Home Page
Contact Information
Education
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Ph.D., Scientific Computing, National
University of Singapore, Singapore, July, 2003
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B.Sc., Mathematics, Lanzhou
University, China, July, 1997
Teaching
- Fall 2008:
Calculus I (Math 125)
Applied Differential Equation I (Math 238)
Research Interests
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Mathematical biology:
Mathematical methods for structural biology, implicit solvent
modeling, molecular surface modeling;
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Scientific computing:
High order methods for PDEs, immersed interface methods, immersed boundary methods,
matched interface and boundary method, computational electromagnetics and optics,
short wave problems;
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Other interests:
nonlinear dynamics, digital signal processing, financial mathematics, and time series
analysis.
Recent grants and supports
- National Science Foundation Grant,
Fast simulation of wave scattering and propagation in inhomogeneous media with complex
geometries, (2006-2009).
- National Science Foundation Grant, Mathematical modeling of
biomolecular surfaces, (2006-2009).
- University of Alabama Startup Grant
Journal Publications
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G.W. Wei and S. Zhao, Synchronization and information
processing by an on-off coupling, Physical Review E, 65(5),
056210, (2002).
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S. Zhao and G.W. Wei, Jump process for the
trend estimation of time series, Computational Statistics and Data
Analysis, 42(1-2), pp. 219-241, (2003).
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G. Bao, G.W. Wei, and S. Zhao, Local spectral
time-domain method for electromagnetic wave propagation, Optics
Letters,
28(7), pp. 513-515, (2003).
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Z.H. Shao, G.W. Wei, and S. Zhao, DSC time-domain
solution of Maxwell's equations,
Journal of Computational Physics,
189,
pp. 427-453, (2003).
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S. Zhao and G.W. Wei, Comparison of the discrete
singular convolution and three other numerical schemes for solving Fisher's
equation, SIAM Journal on Scientific Computing,
25, pp.
127-147, (2003).
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G. Bao, G.W. Wei, and S. Zhao, Numerical solution
of the Helmholtz equation with high wavenumbers, International Journal
for Numerical Methods in Engineering, 59, pp. 389-408, (2004).
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S. Zhao and G.W. Wei, Tensor product derivative
matching for wave propagation in inhomogeneous media, Microwave
and Optical Technology Letters,
43-1, pp. 69-77, (2004).
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S. Zhao and G.W. Wei, High-order FDTD methods
via derivative matching for Maxwell's equations with material interfaces,
Journal
of Computational Physics, 200, pp. 60-103, (2004).
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S. Zhao, G.W. Wei, and Y. Xiang, DSC analysis
of free-edged beams by an iteratively matched boundary method, Journal
of Sound and Vibration, 284, pp. 487-493, (2005).
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S.N. Yu, S. Zhao, and G.W. Wei, Local spectral
time-splitting method for first and second order partial differential equations,
Journal of Computational Physics, 206, pp. 727-780, (2005).
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S. Zhao and G.W. Wei, Option valuation by using
discrete singular convolution,
Applied Mathematics and Computation,
167, pp. 383-418, (2005).
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Y.C. Zhou, S. Zhao, M. Feig, and G.W. Wei,
High order matched interface and
boundary method for elliptic equations with discontinuous coefficients and
singular sources,
Journal of Computational Physics,
213, pp. 1-30, (2006).
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Ge Wang, Haiou Shen, Wenxiang Cong, Shan Zhao and G.W. Wei,
Temperature modulated bioluminescence tomography,
Optics Express,
14(17), pp. 7852-7871, (2006).
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G.W. Wei and S. Zhao,
On the validity of ``A proof that the discrete singular convolution
(DSC)/Langrange-distributed approxiamtion function (LDAF) method is inferior to high order
finite differentces '',
Journal of Computational Physics,
226, pp. 2389-2392, (2007).
- S. Zhao,
On the spurious solutions in the high-order finite difference
methods , Computer Methods in Applied Mechanics and Engineering ,
196, pp. 5031-5046, (2007).
- P. Bates, G.W. Wei and S. Zhao, Minimal molecular surfaces and their
applications , Journal of Computational Chemistry, 29, pp. 380-391, (2008).
- S. Zhao,
Full-vectorial matched interface and boundary (MIB) method
for the modal analysis of dielectric waveguides,
IEEE/OSA Journal of Lightwave Technology , in press, (2008).
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S. Zhao and G.W. Wei,
Matched interface and boundary (MIB) for the
implementation of boundary conditions in high order central finite differences,
International Journal for Numerical Methods in Engineering
accepted, (2008).
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S. Rosencrans, X. Wang, W. Winter, and S. Zhao,
Measuring the insulating ability of anisotropic thermal conductors via
principal Dirichlet eigenvalue,
preprint, (2008).
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P. Bates, Z. Chen, Y. Sun, G.W. Wei, and S. Zhao,
Geometric flows in induced biomolecular surfaces,
preprint, (2008).
Upcoming Conferences
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International Conference on Applied Mathematics and Approximation Theory
, Oct. 11-13, 2008, University of Memphis, Memphis, TN.
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Midwest Conference on Mathematical Method for Images and Surfaces
, April 18-19, 2009, Michigan State University, East Lansing, MI.