Welcome to Shan
Zhao's Home Page
Professor, 2015 - , Department of Mathematics,
University of Alabama,
Associate Professor, 2011 - 2015, Department of Mathematics,
University of Alabama,
Assistant Professor, 2006 - 2011, Department of Mathematics,
University of Alabama,
Postdoc, 2003 - 2006, Department of Mathematics,
Michigan State University,
Ph.D., Scientific Computing, National
University of Singapore, Singapore, July, 2003
B.Sc., Mathematics, Lanzhou
University, China, July, 1997
Computational electromagnetics and optics; Short wave problems; Material interface problems;
Heat transfer; Electrostatic analysis; Biomolecular simulations.
Mathematical methods for molecular biology; Implicit Solvent models;
Biomolecular solvation analysis; PDE modeling of molecular surface; Variational
multiscale models; Fast molecular surface triangulation.
Numerical Methods for PDEs:
High order finite difference methods; Discontinuous Galerkin method;
Weak Galerkin method; Wavelet collocation method; Discrete singular convolution (DSC) method;
Immersed interface methods; Matched interface and boundary (MIB) method;
Fast time stepping schemes; Alternating direction implicit (ADI) methods;
Locally one-dimensional (LOD) methods; Operator splitting methods.
Google Scholar Profile
Recent Grants and Supports
NSF Computational Mathematics Program (2006 - 2016)
NSF Mathematical Biology Program (2006 - 2010)
University of Alabama RSP Award (2014 - 2016)
University of Alabama RGC Award (2010 - 2012)
Professional Services and Activities
- NSF Panelist and Proposal Reviewer,
Program of Computational Mathematics
and Program of Mathematical Biology, 2007, 2009, 2011, 2012, 2014.
- Minisymposium Organizer,
"Numerical PDEs for Interface Problems and Their Applications",
SIAM Conference on Computational Science and Engineering,
Reno, Nevada, March 2011.
"Modeling complex biological systems: theoretical and computational studies",
36th Annual SIAM South East Atlantic Section Conference,
University of Alabama in Huntsville, March 2012.
"Modeling and Computation of Macromolecular Structures and Interactions",
The Society for Mathematical Biology Annual Meeting and Conference,
NIMBioS, University of Tennessee, July 2012.
"Molecular Biosciences: Macromolecular Structures and Interactions",
SIAM Conference on Life Science, Charlotte, NC, August 2014.
"Accurate and efficient time integration methods for unsteady PDEs",
SIAM Southeastern Atlantic Section Conference (SIAM-SEAS 2015),
University of Alabama at Birmingham, March 2015.
"Molecular Biosciences and Biophysics - Macromolecular Structures and Interactions",
SIAM Conference on Life Science, Boston, July 2016.
- Journal Article Reviewer,
for 47 international journals.
- Outstanding Reviewer,
Journal of Computational Physics, Elsevier, 2015.
Preprints and Publications
- L. Song, K. Liu, and S. Zhao,
A relaxed weak Galerkin finite element method for low regularity elliptic interface problems,
- W. Deng, J. Xu, and S. Zhao
On developing stable finite element methods for pseudo-time simulation
of biomolecular electrostatics,
- L. Song, K. Liu, and S. Zhao, A weak Galerkin method with an over-relaxed stabilization
for low regularity elliptic problems,
- C. Li and S. Zhao,
A matched Peaceman-Rachford ADI method for solving parabolic interface problems,
- L. Song and S. Zhao,
Symmetric interior penalty Galerkin approaches for tow-dimensional
parabolic interface problems with low regularity solutions,
- L. Mu, J. Wang, X. Ye, and S. Zhao,
A new weak Galerkin finite element method for elliptic interface problems,
Journal of Computational Physics,
- L. Wilson and S. Zhao,
Unconditionally stable time splitting methods for the electrostatic
analysis of solvated biomolecules,
International Journal of Numerical Analysis and Modeling,
- Journal Publications
The second Annual Meeting of SIAM Central States Section,
Sept. 30 - Oct. 2, 2016, Little Rock, Arkansas, USA.
- Conference and Workshop Invited Speaker,
Midwest Conference on Mathematical Methods for Images and Surfaces,
Michigan State University, April 2009.
The Second International Conference on Mathematical Modeling and Analysis
of Populations in Biological Systems,
University of Alabama in Huntsville, October, 2009.
Modeling and Computation of Biomolecular Structure and Dynamics,
Mathematical Biosciences Institute, Ohio State University, April, 2011.
Eighth International Conference on Scientific Computing and Applications,
Unveristy of Nevada, Las Vegas, April, 2012.
The Second International Conference on Scientific Computing, Nanjing,
China, May, 2012.
Workshop on Aplied Mathematics and Scientific Computing, Lanzhou
University, China, June, 2012.
Mathematical Challenges in Biomolecular/Biomedical Imaging and
Visualization, Mathematical Biosciences Institute, Ohio State University, Feb. 2013.
South Central Conference on Advanced Numerical Methods and
Applications, University of Arkansas at Little Rock, April 2013.
International Conference on Computational Mathematics and Sciences,
Xi'an Jiaotong University, China, June, 2015.
Mathematics of Biological Charge Transport: Molecules and Beyond,
Insititute for Mathematics and its Applications, University of Minnesota,
Geometric and Topological Modeling of Biomolecules,
Mathematical Biosciences Instititue, Ohio State University,
The Tenth International Conference on Scientific Computing and Applications,
Fields Institute, Toronto, Canada, June 2016.
- Past conferences
- Current group members:
Tania Hazra, PdD student.
Zhihan Wei, PhD student.
Sheik A. Ullah, PhD student.
Siwen Wang, PhD student.
- Recent group alumni:
Lunji Song, (Visitor 2015, Postdoc 2016). Permanent position: Associate Professor,
School of Mathematics and Statistics, Lanzhou University, China.
Chuan Li, (Postdoc 2015). First position after: Assistant Professor,
Department of Mathematics, West Chester University.
Duc Nguyen, (PhD 2015). First position after:
Postdoctoral fellow, Department of Mathematics, Michigan State University.
Leighton Wilson, (BSc and MSc 2015).
Received Randall Research Award.
First position after:
PhD candidate in Mathematics, University of Michigan.
Wufeng Tian, (PhD 2014). First position after: Assistant Professor, Broward College.
Guangqing Long, (Visitor 2013). Permanent position: Professor, School of Mathematics Sciences,
Guangxi Teachers Education University, China.
Pengfei Yao, (PhD 2011). First position after: Assistant Professor, Southwest Tennessee College
Guoqiao Wang, (MSc 2010). First position after:
PhD candidate in Biostatistics, University of Alabama at Birmingham.
- Positions available:
Graduate research and teaching assistantship positions are
available in our group. Qualified students should have a background in
applied mathematics, computational mathematics, scientific computing,
or a closely related area. Preference is given to self-motivated students who have
research experience in the aforementioned areas and effective oral communication skills
in English. Please contact me if you are qualified and interested.