Research Interests:

I work on both the theoretical and the practical sides of scientific computing and partial differential equations. One of my research focuses is nonlinearly stable and high-order numerical methods for nonlinear hyperbolic systems, including those appear in continuum mechanics and biological systems. Another one of my research topics is stabilized methods for very stiff problems, such as transient dynamics of nearly incompressible materials. Finally, I have continuous interest in fluid-structure interactions and multi-phase flow simulations.

Currently, my research focuses are:

- A new hybrid-variable (HV) discretization framework for hyperbolic and parabolic partial differential equations, which delivers higher order accuracy in comparison with conventional methods given the same computational costs.

- Numerical methods for infiltration dynamics of differential-equations based tumor growth models, including both partial differential equations and stochastic partial differential equations.

- A simple, stable, and accurate finite element method for solid dynamics of materials that are: linear or nonlinear, elastic or inelastic, compressible or nearly incompressible, and isotropic or anisotropic.

- An embedded boundary method (EBM) combined with arbitrary Lagrangian-Eulerian (ALE) flow computations for multi-material flows in the context of shock hydrodynamics or fluid-structure interactions.