Hailiang's  Research
 Computational  & Applied  Math


 applied partial diff. eqns.  structure  & dynamics
 computational methods,   accuracy  & stability
 numerical simulation,       efficiency & applications

In recent years PDE based modeling has become an important research area in applied mathematics. In our group, we develop and analyze new PDE models and numerical techniques with cutting edge research problems in physical sciences. Our main research interests are kinetic modeling of small scale phenomena, analysis of macro-micro models and high resolution numerical methods.

Research

a.       Modeling-kinetic description of small scale phenomena

Ø  Polymers

Ø  Fluid-particle flows

Ø  Collective behavior of biological agents

a.       Analysis-well-posedness of the model and solution features

Ø  Analysis of macro-micro models for complex fluids

Ø  Critical thresholds in hyperbolic balance laws

b.       Computation-numerical methods for computing the solution

Ø  Level set methods for capturing statistics in high-frequency waves

Ø  The Direct Discontinuous Galerkin (DDG) methods for diffusion problems

Ø  The alternating evolution (AE) methods for convection-dominated problems

Publications

Active Research Projects:

Conferences

Former Graduate Students

Mathematics Search

 

Financial Support

National Science Foundation

If you are interested to find out more, or to join the group, please contact Professor Hailiang Liu.