- 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
- H. Feng and S. Zhao, FFT-based high order central difference schemes for the three-dimensional Poisson equation with various types of boundary conditions, preprint, (2019).
- C. Li, Z. Wei, G. Long, C. Campbell, S. Ashlyn, and S. Zhao, Alternating direction ghost-fluid methods for solving the heat equation with interfaces, preprint, (2019).
- S. Ahmed Ullah and S. Zhao, Pseudo-transient ghost fluid methods for the Poisson-Boltzmann equation with a two-component regularization, preprint, (2019).
- K. Liu, L. Song, and S. Zhao, A new over-penalized weak Galerkin method. Part I: Second order elliptic problems, preprint, (2019).
- A. Lee, W. Geng, and S. Zhao, Regularization methods for the Poisson-Boltzmann equation: comparison and accuracy recovery, preprint, (2019).
- Full list of journal publications
- Regularized Matched Interface and Boundary Poisson-Boltzmann Solver
This package contains a regularized Matched Interface and Boundary (rMIB) Poisson-Boltzmann (PB) solver and Python-based wrappers for biological applications. This package is maintained by Dr. Weihua Geng at Southern Methodist University.
- Current group members:
Siwen Wang, PhD student.
Hongsong Feng, PhD student.
Benjamin Jones, Undergraduate student.
- Recent group alumni:
Sheik Ahmed-Ullah, (PhD 2019). First position after: Assistant Professor, Stillman College.
Arum Lee, (MSc 2019). First position after: PhD student in Mathematics, Penn State University.
Zhihan Wei, (PhD 2018). First position after: Algorithm Engineer, Motionloft.
Tania Hazra, (PhD 2018). First position after: Assistant Professor, Misericordia University.
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 student 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, Nanning Normal 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.