Research areas

1. Strong stability preserving time stepping methods for  hyperbolic PDEs
2. Positivity preserving and asymptotic preserving time evolution methods for kinetic equations with hyperbolic limits
3. Error inhibiting time-discretizations
4. Developing energy and power-efficient numerical methods
5. Weighted essentially non-oscillatory methods for problems with sharp gradients and shocks
6. Reduced order methods in a collocation setting
7. Spectral collocation methods

My research interests lie primarily in the development of numerical algorithms for the simulation of hyperbolic PDEs. I am best known for my research in strong stability preserving (SSP) time discretizations. These comprise many types of time-evolution methods including Runge–Kutta methods, GLMs, multi-derivative methods, and integrating factor methods. Such methods can be explicit or implicit, and semi-implicit (IMEX) extensions have also been useful. I am also interested in spatial discretization techniques such as spectral and pseudospectral methods and WENO methods. More recently, I have been developing reduced basis methods in a collocation context.