My research interests are broad in the fields of numerical analysis and scientific computing. Generally I am interested in the development of new methods and application of cutting-edge methods to complex and coupled multiphysics problems. Currently, some of my research foci include:

• 1. Partitioned and multirate time integration for high-dimensional PDEs and multiphysics problems. A main focus here is how to apply partitioned time integration schemes to physics that do not have a natural additive separation of stiff and non-stiff behavior. 
• 2. Fully implicit time integration methods. Fully implicit (collocation) methods are some of the oldest and most effective integration schemes in terms of accuracy and stability, but are not widely used, largely due to the supposed high cost of solving the implicit equations. I have been interested in and working on developing efficient linear and nonlinear solvers for these systems, as well as developing new fully-implicit-explicit and multirate methods.
• 3. Fast simulation of radiative transfer and kinetic-like equations. Transport and kinetic-like equations are very high dimensional and in many cases must be treated implicitly. There are many parts of this that require careful attention, including linear and nonlinear solvers/preconditioners, coupling to other physics packages, and the most effective way to pose the time integration.