- 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
- 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.