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Hailiang's Research
Computational & Applied Math
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applied partial diff. eqns. structure &
dynamics
computational methods, accuracy & stability
numerical simulation, efficiency
& applications
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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
- Haseena
Amhed (ISU, graduated 2008) Ph.D.
- Zhongming Wang ( ISU, graduated 2008) PhD
- Xiaoliang Xie (ISU, graduated 2009) Ph.D.
- Hung Phan
( ISU, graduated, 2005) M.S.
- Eric Blabac ( ISU, graduated, 2004) M.S.
Mathematics
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Financial Support
If you are interested to find
out more, or to join the group, please contact Professor
Hailiang Liu.