Education

• Fall 2020 – Present: Ph.D. Mathematics, Texas A&M University
  • Research areas: Numerical PDEs, Finite Element Methods, Computational Fluid Dynamics, Hyperbolic Conservation Laws, Computational Magnetohydrodynamics
  • Advisor: Dr. Matthias Maier
• Fall 2015 – Fall 2019: B.S. Applied Mathematical Sciences, Texas A&M University
  • Magna Cum Laude
  • 4.0 Major GPA, 3.71 Overall GPA

Research Interests

• Computational fluid dynamics: hyperbolic conservation laws
• Finite element methods and finite element software
• Computational magnetohydrodynamics: Euler-Maxwell equations
• Ejecta modeling

Research Projects

• Fall 2021 – Present: Structure-preserving finite element schemes for the Euler-Maxwell equations
  • Advisor: Dr. Matthias Maier
  • Ph.D. research
  • Developing provably robust, high-performance, large-scale finite element schemes to numerically approximate solutions to the Euler-Maxwell equations
  • Part of larger work to develop finite element schemes for nonlinear hyperbolic systems that are coupled with other PDE systems
• Summer 2023: Modeling ejecta from shocked metals
  • Mentors: Bryan Kaiser and Jesse Canfield
  • Los Alamos National Lab Computational Physics Summer Workshop
  • Used high-performance large-scale multiphysics simulations to model ejecta formation in shocked metal surfaces with various defects
• Spring 2020: Numerical study of decay rates of the 1D Klein-Gordon equations
  • Advisors: Dr. Matthias Maier and Dr. Jonas Lührmann
  • Undergraduate research project
  • Implemented finite difference techniques in Julia to numerically study the decay rates of solutions to the 1D Klein-Gordon equations with various different nonlinearities in the model

Preprints and Publications

• Jordan Hoffart, Matthias Maier, John N. Shadid, and Ignacio Tomas
  Structure-preserving finite-element approximations of the magnetic Euler–Poisson equations
  Submitted October 2025
  arXiv preprint

Posters and Presentations

• October 2024: A comparison of finite element spaces for the discontinuous Galerkin approximation of the Maxwell eigenvalue problem in first-order form, SIAM TX–LA 2024, Baylor University, Waco, TX, USA
• March 2024: Towards an involution-preserving solver for the time-dependent Maxwell equations, Finite Element Rodeo 2024, Rice University, Houston, TX, USA
• November 2023: Towards an involution-preserving solver for the time-dependent Maxwell equations, SIAM TX–LA 2023, University of Louisiana at Lafayette, Lafayette, LA, USA
• March 2023: Structure-preserving finite element schemes for the Euler–Poisson equations, Finite Element Rodeo 2023, Texas A&M University, College Station, TX, USA
• November 2022: Structure-preserving finite element schemes for the Euler–Poisson equations, SIAM TX–LA 2022, University of Houston, 4800 Calhoun Rd, Houston, TX, USA

Service and Outreach

• Fall 2023 – Present: Officer in the student SIAM chapter at Texas A&M University
  • Treasurer since Summer 2025
  • Vice President from Fall 2023 to Fall 2025
  • President since Fall 2025
• Summer 2025: Modeling and Simulation with PDEs Undergraduate Summer School
  • Teaching assistant
  • Assisted students with programming and theory exercises during organized lab sessions.
  • Mentored a group of 3 students in a project using finite difference methods to study nonlinear dispersive waves.
• January 2025: Texas Junior Science and Humanities Symposium
  • Judge in the Mathematics and Computer Science category
• Summer 2024: Modeling and Simulation with PDEs Undergraduate Summer School
  • Teaching assistant
  • Assisted students with programming and theory exercises during organized lab sessions.
  • Mentored a group of 4 students in a project using finite difference methods to study nonlinear dispersive waves.
• Fall 2023: Directed Reading Program Mentor, Texas A&M University
  • Topic: Compartmental models in epidemiology
• Spring 2022: Directed Reading Program Mentor, Texas A&M University
  • Topic: Time Complexity of Algorithms
• February 2020: Change for a Dollar, K12 Math Club, Texas A&M University, College Station, TX, USA

Conferences Attended

• October 2024: SIAM TX–LA 2024, Baylor University, Waco, TX
  • Co-organized minisymposium MS34: Advances in Numerical Methods for Electromagnetism
• March 2024: Finite Element Rodeo 2024, Rice University, Houston, TX
• November 2023: SIAM TX–LA 2023, University of Louisiana at Lafayette, Lafayette, LA
  • Co-organized minisymposium MS04: Recent developments in electromagnetics and related eigenvalue problems
• May 2023: Frontiers of Numerical PDEs, Brin Mathematics Research Center, University of Maryland, College Park, MD
• March 2023: Finite Element Rodeo 2023, Texas A&M University, College Station, TX
• November 2022: SIAM TX–LA 2022, University of Houston, Houston, TX

Teaching

• Fall 2025: Principles of Numerical Analysis (MATH 437, 8 students), Texas A&M University
  • Teaching assistant
  • Undergraduate level course covering mathematical principles of numerical analysis and their application to the study of particular methods; fixed-point iteration, Newton's method; normed vector spaces and operators, Schur decomposition, convergent matrices, minimization methods, conjugate gradient method; polynomial interpolation of Lagrange and Hermite; best approximation, Bernstein and Weierstrass Theorems, numerical quadrature.
• Fall 2024: Engineering Mathematics II (MATH 152, 100 students), Texas A&M University
  • Teaching assistant
  • Undergraduate level course covering differentiation and integration techniques and their applications (area, volumes, work), improper integrals, approximate integration, analytic geometry, vectors, infinite series, power series, Taylor series, computer algebra.
• Spring 2024: Numerical Partial Differential Equations (MATH 610, 10 students), Texas A&M University
  • Teaching assistant
  • Graduate level introduction to finite difference and finite element methods for solving partial differential equations; stability and convergence of methods and error bounds.
• Fall 2022: Numerical Partial Differential Equations (MATH 610, 8 students), Texas A&M University
  • Teaching assistant
• Spring 2022: Numerical Partial Differential Equations (MATH 610, 7 students), Texas A&M University
  • Teaching assistant
• Fall 2021: Functions, Trigonometry, and Linear Systems (MATH 150, 100 students), Texas A&M University
  • Teaching assistant
  • Undergraduate level course covering functions, trigonometry, linear systems, graphs, college algebra, and vectors.

Programming, Software, and Operating System Experience

• Python, MATLAB, Julia, C++, LaTeX, HTML, CSS, GNU/Linux, ParaView, VTK, MPI