Research

Research questions that I've previously and currently exploring, focusing on the interaction and effects of numerical methods in various types and scenarios. My work is currently under Jesse Chan at the University of Texas at Austin's Oden Institute for Computational Engineering and Sciences.

Current Directions

Nonlinear stability analysis of positivity-preserving hyperbolic schemes

Developing a framework for nonlinear fully discrete stability analysis of hyperbolic PDE solvers, motivated by modified Patankar–Runge–Kutta methods that enforce positivity. The work extends classical von Neumann analysis toward state-dependent spectral behavior tracking, with the goal of analyzing how finite volume discretizations and positivity-preserving time integration interact in nonlinear settings.

  • Spectral Analysis
  • Fully Discrete Analysis
  • Partial Differential Equations
  • Finite Volume Methods
  • Runge-Kutta Methods
  • Time Integration

Spectral behavior of isogeometric analysis in comparison with finite elements

Studying the spectral behavior of isogeometric analysis relative to standard finite element methods, with emphasis on how discretization structure influences eigenvalue distributions and numerical performance. Current and planned directions include extending this comparison into nonlinear structural dynamics to understand how geometric smoothness, basis continuity, and nonlinearity affect the evolving spectrum of IGA versus FEM.

  • Isogeometric Analysis
  • Finite Element Methods
  • Spectral Analysis
  • Fully Discrete Analysis
  • Computational Structural Mechanics

Past Directions

Illustration for Solver-dependent ecological dynamics in predator–prey models

Solver-dependent ecological dynamics in predator–prey models

My first research: investigated how numerical solver choice influences the qualitative and quantitative behavior of predator–prey models fit to real ecological data. The project compared explicit, implicit, multistep, and Runge–Kutta methods in terms of stability, accuracy, and ecological realism, and later extended into spectral analysis focused on the eigensystem behavior induced by different time integrators.

  • Ordinary Differential Equations
  • Time Integration
  • Numerical Analysis
  • Spectral Analysis
  • Runge-Kutta Methods