Research interests

• Scientific computing: Computational electromagnetics and optics; Short wave problems; Material interface problems; Heat transfer; Electrostatic analysis; Biomolecular simulations.
  
  
• Mathematical biology: 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.

Preprints and publications

• L. Song, K. Liu, and S. Zhao, A relaxed weak Galerkin finite element method for low regularity elliptic interface problems, preprint, (2017).
• W. Deng, J. Xu, and S. Zhao, On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics, preprint, (2017).
  
• Z. Wei, C. Li, and S. Zhao, A spatially second order alternating direction implicit (ADI) method for three dimensional parabolic interface problems, preprint, (2017).
  
• L. Song and S. Zhao, Symmetric interior penalty Galerkin approaches for tow-dimensional parabolic interface problems with low regularity solutions, preprint, (2017).
  
• W. Geng and S. Zhao, A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation, preprint, (2017)
• Full list of journal publications

Citations

• Google Scholar Profile
• Researcher ID

Research group

• Current group members:
  Tania Hazra, PdD student.
  Zhihan Wei, PhD student.
  Sheik A. Ullah, PhD student.
  Siwen Wang, PhD student.
  Hongsong Feng, 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.