Department of Mathematics
503 Boston Avenue
Medford, MA 02155
Scientific computing and numerical analysis: Efficient computational
methods for complex fluids, plasma physics, electromagnetism and other
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.