- Associate Professor
· High order physical property preserving numerical methods (density and pressure positivity preserving DG methods for compressible Navier-Stokes equations)
· Mathematical modeling for bio-math, Chemotaxis keller-Segel equations
· High order methods for elliptic interface problems
· Numerical methods for convection diffusion equations: discontinuous Galerkin finite element method, ENO/WENO finite difference and finite volume methods.
· Nonlinear Phenomena: dispersive wave equations, Hamilton-Jacobi equations.
· Level set methods for interface capturing.
· National Science Foundation, DMS-1620335, single PI, Positivity preserving limiter and new development on elliptic interface problems, $150,000, 2016-2019.
· National Science Foundation, DMS-0915247, single PI, ’Local’ and ‘Direct’ discontinuous Galerkin Methods: New Algorithms and Applications, $99,235, 2009-2012.