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 Interests

a.       Modeling--kinetic description of small scale phenomena

  Polymers

  Fluid-particle flows

  Collective behavior of biological agents

b.       Analysis -- well-posedness and solution behavior for mathematical models

  Analysis of macro-micro models for complex fluids

  Critical thresholds in hyperbolic balance laws

c.       Computation-- development of high resolution numerical methods

  Level set methods for capturing statistics in high-frequency waves

  The Direct Discontinuous Galerkin (DDG) methods for higher order PDEs 

  The alternating evolution (AE) methods for quasilinear and nonlinear PDEs

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Last Revision: April 20, 2010.