Research Summary
I welcome midshipmen interested in working with me for reading courses, honors projects or trident scholarships to contact me.
My work is naturally interdisciplinary, involving topics from mathematics, physics, computer science, and engineering. My research interests can be broadly stated with the following bullet list:
- 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.
Material contained herein is made available for the purpose of peer review and discussion and does not necessarily reflect the views of the Department of the Navy or the Department of Defense.
Supersonic shock wave. Image courtesy NASA
Solution to a two-dimensional Riemann problem for the Euler system describing gas dynamics with shocks.
Wind tunnel problem with a step.
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Publications
See my Publications page for more information about my scholarly articles.
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Collaborators
Here is an incomplete list of some people that I have worked or am currently working with:
- Matt Causley, Kettering University
- Andrew Christlieb, Michigan State University
- Sigal Gottlieb, University of Massachusetts Dartmouth
- Yaman Güçlü, Max-Planck-Institut fur Plasmaphysik
- Zachary Grant, Householder Fellow, Oak Ridge National Laboratory, Oak Ridge, Tennesee
- Cory Hauck, Oak Ridge National Laboratory and University of Tennesee
- Alexander Jaust, Stuttgart University, Germany
- Stephen Pankavich, Colorado School of Mines
- James Rossmanith, Iowa State University
- Jennifer Ryan, Colorado School of Mines, Colorado
- Jochen Schütz, Hasselt University, Belgium
- Hana Cho, (PhD, MSU 2016)
- Michael Crockatt, Michigan State University
- Xiao Feng, (Expected PhD, 2016) Michigan State University
- Zachary Grant, (PhD, 2018, University of Massachusetts, Dartmouth)
- Alexander Jaust, RWTH Aachen University
- Jaylan Jones, (PhD, MSU 2013), Raytheon
- Scott Moe, University of Washington
- Qi Tang, (PhD, MSU 2015), First job is a postdoc at RPI.
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Software
An integral component of my work requires the development, testing and release of software for the purposes of investigating and validating new numerical methods.
I am one of the developers for the DoGPack software package. My primary contributions include the semi-Lagrangian sections of the code, as well as the bulk of the Lax-Wendroff time stepping options of the code. The name stands for `The Discontinuous Galerkin Software Package' and is written in C++. There are a number of choices for what the `o' between the `D' and `G' stands for.
Additionally, I am the lead developer for the software package FINESS, which is a FINite difference weighted ESSentially non-oscillatory (FD-WENO) software package. The basic structure was derived from DoGPack, and all of my work involving finite difference methods has been incorporated into the package.
