Research Statement

PDF of Research Statement

Current Research Interests:

Fuel Cell Modeling and Computation

A fuel cell directly converts chemical energy from a fuel to electrical energy. Essentially, an electrical current is produced while hydrogen and oxygen ions meet through an electrolyte and combine to form water. The conversion is more efficient and cleaner than combustion.

Although this process is quite simple, the variety of materials and shapes of fuel cells, as well as the total system of preparing the fuel, managing the waste, and harnessing and distributing the resulting power, can be mathematically complicated. Multiple scales in both time and space occur in fuel cells.

Many existing mathematical investigations of fuel cells focus on the structure of the fuel cell itself, effectiveness of certain materials, efficiency of power production, and water management, but there is still much more to learn. In particular, the study of fuel cell degradation over long periods of use is of present interest.

Previous Research Interests:

Integral Deferred Correction Methods, Semi-implicit Methods, Splitting Methods

Integral Deferred Correction (IDC) methods are high order numerical time integrators whose structure leads to simple construction of arbitrary order integrators. IDC methods involve a low order prediction step and correction of the prediction to higher order. A key component is the solution of an error equation in integral form.

Certain modifications to IDC allow high order numerical solutions to multi-scale and/or nonlinear problems in plasma physics, such as the Vlasov-Poisson (VP) system. These modifications include incorporating semi-implicit methods to solve an IVP (arising from method of lines discretization) with a stiff and nonstiff term, or employing operator splitting into IDC’s prediction and correction steps. Incorporation of split IDC with conservative semi-Lagrangian WENO interpolation results in well-resolved solutions to classic plasma physics problems such as Landau damping and two stream instability.