

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 macromicro models and high resolution numerical
methods.
Research Interests
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Level set methods for capturing statistics in highfrequency waves
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The Direct Discontinuous Galerkin
(DDG)
methods for higher order PDEs
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The alternating evolution (AE) methods for quasilinear and nonlinear PDEs
20132017, NSFDMS (PI): Recovery of high frequency wave fields, kinetic theory of photons and entropy satisfying methods.
20092013, NSFDMS (PI): Geometrically based kinetic approach to multiscale problems
20082011, NSFDMS (PI), FRG (Focused Research Group) Collaborative Research: Kinetic Description of Multiscale Phenomena: Modeling, Theory And Computation
20052008, NSFDMS (PI), Multiscale Wave Dynamics in Nonlinear Balance Laws
20052006, Ames Lab of DOE (PI), High Frequency Wave Propagation and Geometric Motion
20032005, PSI Grant (CoPI), System Biology: Genome, Genetic Network, and Evolution
20012004, NSFDMS (CoPI), Critical Threshold Phenomena in Nonlinear Balance Laws
Last Revision: April 20, 2010.