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

*    Modeling--kinetic description of small scale phenomena

Polymers

Fluid-particle flows

Collective behavior of biological agents

*    Analysis -- well-posedness and solution behavior for mathematical models

Analysis of macro-micro models for complex fluids

Critical thresholds in hyperbolic balance laws

*      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: Sept 20, 2019.