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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, (2018).
  • Full list of journal publications

Citations

  • Google Scholar Profile
  • Researcher ID

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

    Arum Lee, 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.
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