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Research works:

Numerical Methods:
-- a novel boundary element method -- "node patch" BEM

-- finite element menthod

-- finite difference

-- fast multipole method

Mesh generation for molecular systems, surface triangular mesh and volume tetrahedral mesh for purposes of mathematical modeling and numerical simulation (such as boundary element/finite element computation) of biomolecular systems besides of for usual visualization and structural geometric analysis.
Electrostatics, density distribution, diffusion-reaction processes described by the Poisson-Boltzmann equation, the Poisson-Nernst-Planck equations, and their modified forms.
Cellular network modeling of calcium signaling in myocyte and virus DNA/RND trafficking.
Prediction of solution structure (ions, water, and biomolecules), theory and computation of hydration, hydrophobicity, and associated entropy and free energy.
Synergistic binding in protein kinase.
Structural fluctuation and rate regulation in biomolecule.
Entropy and free energy calculations in binding and docking.
Developed a reduced Hessian method to direct calculation of entropy loss due to reduced translational and rotational motions upon molecular binding. And continue to extend this method as a domain-based coarse normal mode analysis for large conformational change prediction of supermolecule system.


Numerical solvers

AFMPB (beta version):
Boundary element method is used in modeling of electrostatics, ionic effect, solvation energy,  Work done includes the variational approach, hypersingular boundary integral technique, and interpolation method for stress tensor and force calculation, fast multipole method for speeding up the solving process.


A robust molecular surface mesh generation tool: Tracing Molecular Surface for Meshing. The MS is Gaussian type of surface. The software is designed for a general, stable, and efficient tool for qualified MS meshing for purposes of mathematical modeling and numerical simulation of biomolecular systems besides of for usual visualization and structural geometric analysis. It can now handle arbitrary size of molecula rsystem, and the generated mesh can be directly used in stable boundary element type of simulations.


PNP solver:

FE/BEM hybrid scheme or pure FEM approach for solution of the Poisson-Nernst-Planck equations, to study the nonequilibrium density and flux profiles, diffusion processes, and solvation free energy.


A comrehensive visualization and analysis tool/interface for biomolecular continuum modeling, can handle: molecule, mesh (especially unstructured mesh), and numerical results.


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