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

• K. Liu, L. Song, S. Zhao, and Y. Wu, An over-penalized weak Galerkin method with a stabilizer for second-order elliptic problems, preprint, (2019).
• H. Feng, G. Long, and S. Zhao, An augmented matched interface and boundary (MIB) method for solving elliptic interface problem, preprint, (2019).
  
• 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).
  
• 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
  

Citations

• Google Scholar Profile (Citations > 1500)
  
• Researcher ID (Citations > 1000)
  

Software

• 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. 
  

Research group

• Current group members:
  Sheik Ahmed-Ullah, PhD student.
  Siwen Wang, PhD student.
  Hongsong Feng, PhD student.
  Arum Lee, MSc student.
  Benjamin Jones, Undergraduate student.
  
  
• Recent group alumni:
  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 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.