Research

  My primary fields of research are Numerical Analysis and Scientific and Engineering Computing. More specifically, my work is on the analysis and design of algorithms in the following areas:

• Anisotropic mesh adaptation and adaptive finite element methods.

• Fuel cell modeling.

• Phase field methods.

• Numerical solution of partial differential equations.

• Domain decomposition methods with non-matching grids.

• Numerical solution of integro-differential equations.

• Computation and Software design.

  My research interests focus on computational methods for handling large-scale and multiscale phenomena, e.g., for physical solutions having boundary layers or sharp interfaces on irregular domains in multiple spatial dimensions that involve complex boundary conditions. Applications focus of my research is widespread and includes the following practical problems:

• Convection dominated PDEs.

• A fourth order thin film flow problem with moving contact lines.

• An extreme-mass-ratio binary system arising from a black hole problem.

• Numerical models of fuel cell dynamics.

• Two-phase flow problems.

• Navier-Stokes equations.

• Elasticity and plasticity mechanics problems.

• Multiphase compressible displacement in porous media.

• Integro-differnential equation arising in population dynamics.

Collaborators

      Jinchao Xu

      Long Chen

      Center for Computational Mathematics and Applications

      The Electrochemical Engine Center (ECEC)

      College of Automotive Engineering, Tongji University