About

Our group focuses on computational mechanics and the efficient numerical solution of time-dependent partial differential equations. Recent work focuses on provably stable and high order accurate methods for time-dependent compressible fluid dynamics, as well as their efficient implementation on high performance computing platforms.

Research topics

• Applied mathematics
• Mathematical analysis
• Mathematics
• Geometry
• Computer Science
• Physics
• Programming language
• Computational science
• Theoretical computer science
• Statistical physics
• Parallel computing

Selected publications

• Adaptive numerical simulations with Trixi.jl: A case study of Julia for scientific computing

  JuliaCon Proceedings · 2022 · 50 citations

  • Computer Science
  • Computer Science
  • Computational science

  We present Trixi.jl, a Julia package for adaptive high-order numerical simulations of hyperbolic partial differential equations. Utilizing Julia's strengths, Trixi.jl is extensible, easy to use, and fast. We describe the main design choices that enable these features and compare Trixi.jl with a mature open source Fortran code that uses the same numerical methods. We conclude with an assessment of Julia for simulation-focused scientific computing, an area that is still dominated by traditional high-performance computing languages such as C, C++, and Fortran.

  DOI

• High-order entropy stable discontinuous Galerkin methods for the shallow water equations: Curved triangular meshes and GPU acceleration

  Computers & Mathematics with Applications · 2020 · 22 citations

  Senior authorCorresponding
  • Mathematics
  • Applied mathematics
  • Mathematical analysis
  DOI

• Entropy stable reduced order modeling of nonlinear conservation laws

  Journal of Computational Physics · 2020 · 40 citations

  1st authorCorresponding
  • Mathematics
  • Applied mathematics
  • Statistical physics
  DOI

Recent grants

• Collaborative Research: Improved Algorithms for Multiwave Imaging in Complex Media: Theory and Computation

  NSF · $200k · 2017–2021

• CAREER: Tailored Entropy Stable Discretizations of Nonlinear Conservation Laws

  NSF · $450k · 2020–2026

• Bernstein-Bezier Techniques for High Order Time-Domain Discontinuous Galerkin Methods

  NSF · $200k · 2017–2022

Frequent coauthors

• Tim Warburton

  41 shared

• Axel Modave

  Propagation des Ondes : Étude Mathématique et Simulation

  22 shared

• Khemraj Shukla

  Providence College

  12 shared

• Hendrik Ranocha

  Johannes Gutenberg University Mainz

  12 shared

• Gregor J. Gassner

  University of Cologne

  10 shared

• Andreas Atle

  9 shared

• Ettore Vulcano

  Mount Sinai Medical Center

  9 shared

• Andrés M. Rueda-Ramírez

  University of Cologne

  9 shared

Labs

• Jesse Chan LabPI

Education

• PhD, Oden Institute for Computational Engineering and Sciences

  The University of Texas at Austin

  2013

• B.A., Computational and Applied Mathematics

  Rice University

  2008

Awards & honors

• NSF CAREER Award

Similar researchers at University of Texas at Austin

• Carlos Caldash-218
• Thomas J. Hughesh-154
• George Georgiouh-107
• Keith Johnstonh-106
• Jeffrey Andrewsh-104