Research

My work is naturally interdisciplinary, involving topics from mathematics, physics, computer science, and engineering.  Broadly stated, my research interests include the following:

• Numerical analysis and scientific computing.

• Numerical methods for plasma physics:

  • Kinetic plasma models (Vlasov-Poisson and Vlasov-Maxwell), and

  • Fluid plasma models (single and two-fluid magnetohydrodynamics (MHD)).

• High-order numerical methods for hyperbolic conservation laws:

  • Discontinuous Galerkin (DG) FEM schemes.

  • Weighted essentially non-oscillatory (WENO) finite difference and finite volume methods.

• Time stepping methods (for PDEs):

  • Lax-Wendroff (Taylor) methods,

  • Multiderivative (strong stability preserving) methods,

  • Method of lines transpose, and

  • Integral/spectral deferred correction methods.

• High-order positivity preserving schemes.

• Limiters for DG and FD-WENO methods.

The primary domain I work in is the development of numerical algorithms for the purposes of solving problems of scientific merit, including plasma and gas dynamics. My research statement (current as of Fall 2014) describes a more in depth overview of the above mentioned methods.