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Research Blurb

My research falls into the general area of computational mathematics. The main focus of this work is on the development, analysis, and implementation of numerical methods for problems that can be described, either fully or partially, by a system of nonlinear hyperbolic partial differential equations (PDEs). I am particularly interested in problems from fluid dynamics, plasma physics, and astrophysics, and I strongly believe that the interplay between applications and mathematics can lead to important advances in both.

Specifically, in my work I am interested in solving 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 Applied Mathematics.



Papers



Current Students (BS, MS, and PhD)

  • Yifan Hu (PhD, ISU, 2021 - Present)
    • Research topic: TBD
  • Jill Vesta (MS, ISU, 2020 - Present)
    • Research topic:  Asymptotic-preserving moment-closure methods for gas kinetics
  • Ian Pelakh (MS+PhD, ISU, 2018 - Present)
    • Research topic:  Lax-Wendroff DG Schemes for Magnetohydrodynamics
  • Sam Van Vleet (PhD, ISU, 2019 - Present)
    • Research topic:  Genuinely Multidimensional Lax-Wendroff DG Schemes
  • Caleb Logemann (PhD, ISU, 2015 - Present)
    • Research topic:  DG Schemes for Thin-film Models on Curved Manifold


Former Students (PhD)



Former Students (MS)



Former Students (BS)

  • Boqian Shen (BS, 2017, ISU)
    • Undergraduate Research:  A Particle-Based Numerical Method for Solving Vlasov Models in Plasma Simulations
    • Gradudate school:  Department of Computational and Applied Mathematics, Rice University
  • Scott Moe (BS, 2011, UW-Madison)
    • Undergraduate Research:  Adaptive Mesh Refinement for Discontinuous Galerkin Methods
    • Gradudate school:  Department of Applied Mathematics, University of Washington


Former Students (REU)