Research interests

• Mathematical biology: Mathematical methods for molecular biology; Implicit solvent models; Biomolecular solvation analysis; Ensemble averaged electrostatics; Regularization for singular charges; PDE modeling of molecular surface; Variational multiscale models; Fast molecular surface triangulation.
  
  
• Scientific computing: Material interface problems; Electrostatic analysis; Biomolecular simulations; Computational electromagnetics and optics; Short wave problems; Heat transfer.
  
  
• Numerical Methods for PDEs: O(N logN) fast algorithms for PDEs; High order finite difference methods; Discontinuous Galerkin method; Weak Galerkin method; Wavelet collocation method; Discrete singular convolution (DSC) method; Matched interface and boundary (MIB) method; Alternating direction implicit (ADI) methods; Locally one-dimensional (LOD) methods; Operator splitting methods.

Preprints and publications

• Y. Shao, Z. Chen, and S. Zhao, Modeling and analysis of ensemble average solvation energy and solute-solvent interfacial fluctuations, preprint, (2024).
• Y. Ren and S. Zhao, A multigrid-based fourth order finite difference method for elliptic interface problems with variable coefficients, preprint, (2024).
• C. Li, S. Zhao, B. Pentecost, Y. Ren, and Z. Guan, A fourth-order Cartesian grid method with FFT acceleration for elliptic and parabolic problems on irregular domains and arbitrarily curved boundaries, preprint, (2024).
• Y. Ren, C. Li, G. Long, and S. Zhao, A multigrid-based high order finite difference method for parabolic interface problems with variable coefficients, preprint, (2024).
• S. Amihere, Y. Ren, W. Geng, and S. Zhao, A new boundary condition for the nonlinear Poisson-Boltzmann equation in electrostatic analysis of proteins, preprint, (2024).
• H. Yang, G. Long, Y. Ren, and S. Zhao, A FFT accelerated fourth order domain-decomposed method for solving three-dimensional Helmholtz interface problems and its applications, preprint, (2024).
• Full list of journal publications

Research profile and citations

• Google Scholar
• Web of Science
• ORCID

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. 
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• Nonlinear electrostatic free energy of a Kirkwood sphere
  This MATLAB code solves the nonlinear Poisson-Boltzmann Equation for a Kirkwood sphere with a charge at its center, and calculates the electrostatic free energy. 
  Please cite the following when using this code in a publication:
  S. Amihere, W. Geng, and S. Zhao, Benchmarking electrostatic free energy of the nonlinear Poisson-Boltzmann model for the Kirkwood sphere, Communications in Information and Systems, 22(3), 305-315, (2022).

Research group

• Current group members:
  Yimin Ren, PhD student.
  Idowu Ijaodoro, PhD student.​
  Matthias Dogbatsey, PhD student.
  Md. Borhan Uddin, PhD student.
  Ryan Engle, Undergraduate student.
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• Recent group alumni:
  Sylvia Amihere, (PhD 2024). First position after: Postdoctoral fellow, Southern Methodist University.
  Mark McGowan, (MSc 2022). Scientist II, Dynetics, Inc.
  Hongsong Feng, (PhD 2021). First position after: Postdoctoral fellow, Michigan State University.
  Siwen Wang, (PhD 2021). Data Scientist, Regions Bank.
  Benjamin Jones, (MSc 2021). First position after: PhD student in Mathematics, Michigan State University.
  Sheik Ahmed-Ullah, (PhD 2019). Quantitative Model Validation Analyst, Regions Bank.
  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). Professor, School of Mathematics and Statistics, Lanzhou University, China.
  Chuan Li, (Postdoc 2015). Associate Professor, Department of Mathematics, West Chester University.
  Duc Nguyen, (PhD 2015). Assistant Professor, Department of Mathematics, University of Kentucky.
  Leighton Wilson, (BSc and MSc 2015). Received Randall Research Award. First position after: PhD student in Mathematics, University of Michigan.
  Wufeng Tian, (PhD 2014). Associate Professor, University of Wisconsin Eau Claire.
  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.