Research

Research Blurb

My research is on the development of numerical methods for nonlinear hyperbolic partial differential equations. In particular, I am interested in studying various mathematical models from fluid dynamics, plasma physics, and astrophysics, including the following nonlinear hyperbolic systems: (1) Magnetohydrodynamics (MHD), (2) Euler-Maxwell, (3) Vlasov-Poisson, (4) Vlasov-Maxwell, and (5) the Einstein equations of general relativity. The kinds of numerical methods that I develop include the following high-order schemes: (1) Wave Propagation Schemes, (2) Residual Distribution Schemes, (3) Discontinuous Galerkin Schemes, and (4) WENO Schemes.

I welcome graduate students with a strong background or interest in applied and/or computational mathematics. I typically accept graduate students through the ISU Graduate Program in Mathematics.


2017 Summer Math REU at ISU


Current Students

  • Caleb Logemann (PhD Student, ISU)
    • Research topic:   TBD
  • Erica Johnson (MS Student, ISU)
    • Research topic:   Numerical Methods for Regularized Quadrature-based Moment Closure Models
  • Minwoo Shin (PhD Student, ISU)
    • Research topic:   High-order Discontinuous Galerkin Schemes for the PN Equations for Radiative Transport
  • Pierson Guthrey (PhD Student, ISU)
    • Research topic:   Regionally Implicit Discontinuous Galerkin Schemes with Application to the Vlasov-Maxwell System
  • Scott Moe (PhD Student, University of Washington)
    • Co-adivsing with Prof. Randall J. LeVeque
    • Research topic:   Parallel Adaptive Discontinuous Galerkin Schemes with Application to Wave Propagation in Heterogeneous Media
    • Expected gradudation:   Spring 2016

Former Students