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
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
2018--2021, NSF-DMS (PI): Critical regularity, selection dynamics, and condensation in nonlinear balance laws.
2013-2017, NSF-DMS (PI): Recovery of high frequency wave fields, kinetic theory of photons and entropy satisfying methods.
2009-2013, NSF-DMS (PI): Geometrically based kinetic approach to multi-scale problems
2008-2011, NSF-DMS (PI), FRG (Focused Research Group) Collaborative Research: Kinetic Description of Multi-scale Phenomena: Modeling, Theory And Computation
2005-2008, NSF-DMS (PI), Multi-scale Wave Dynamics in Nonlinear Balance Laws
2005-2006, Ames Lab of DOE (PI), High Frequency Wave Propagation and Geometric Motion
2003-2005, PSI Grant (Co-PI), System Biology: Genome, Genetic Network, and Evolution
2001-2004, NSF-DMS (Co-PI), Critical Threshold Phenomena in Nonlinear Balance Laws
Last Revision: Sept 20, 2019.