My research interests are in the area of scientific computing, particularly in the area of computational mathematics and physics. Simulation has become an integral part of the scientific process as more advanced theories and experiments are developed for studying various physical phenomena. Many physical systems involve large time and spatial scales that need to be resolved. Therefore, advanced techniques in numerical methods are needed to resolve these scales in a reasonable amount of compute time. My research focuses on the numerical computation of nonlinear partial differential equations (PDEs) that are used to model multi-scale physical systems, such as in plasma physics, particle transport, magnetohydrodynamics, and other complex fluid problems. The goals of my research are to develop methods for solving PDEs that yield accurate solutions (i.e. preserve the important physics of the problem) and that are efficient. More specifically, I develop adaptive finite-element discretizations and multigrid solvers for such problems. The fun and excitement comes from analyzing, which flavor of these methods is best suited for a particular problem, so that you can preserve mathematical and physical properties such as conservation of energy, while also using an optimal amount of computational work
