Computational Mathematics and Scientific Computing
I am a researcher at the Oden Institute and an undergraduate at the Cockrell School of Engineering focused on computational and numerical differential equations. I develop and analyze numerical methods for ordinary and partial differential equations, with work spanning time integration, spatial discretization, and open-source implementation. I study time integration techniques that preserve mathematical and physical structure (such as stiffness, geometric preservation, and efficiency), with interests in fully implicit, stabilized, and IMEX general linear methods (RKs and LMMs) along with matrix-function and specialized methods. I additionally focus on spatial discretization such as isogeometric analysis, finite elements, finite volume, spectral, and other Galerkin methods, guided by the mathematical and numerical structure of the underlying models. I implement these methods in open-source software and am also interested in numerical linear algebra, modern techniques of scientific computing (scientific machine learning, reduced order modeling), and applications of these techniques to real problems.
MIISO: Modal Integrators for Isogeometric Stabilization of Outliers is available on arXiv and currently in review in Applied Numerical Mathematics. It introduces a new family of time integration methods based on non-holomorphic blends of Padé approximants in an exponential Rosenbrock–Krylov scheme, targeting the outlier problem in isogeometric analysis without requiring assembly.
Gave a talk at FerriteCon 2026 at TU Braunschweig covering the basics of isogeometric analysis and introducing FerriteIGA.jl to the Ferrite and Julia ecosystem ahead of its registration as a package.
Looking into stabilized Runge–Kutta methods based on orthogonal polynomials, including standard and shifted Runge–Kutta Chebyshev, Legendre, and general Gegenbauer schemes, for efficient simulation of diffusion-dominated problems. The work is based on Trixi.jl and builds on implementations I contributed into OrdinaryDiffEq.jl. Focused on efficiency analysis and exploring specialized schemes for this regime.
Developed a new class of numerical ODE methods for isogeometric analysis that target the spline space outlier problem in structural simulations. The methods are based on non-holormphic blends of Padé approximants of the exponential function and form a family of modified exponential Rosenbrock–Krylov schemes, called MIISO, constructed matrix-free for efficient implementation and backed by rigorous theoretical proofs. Available on arXiv and currently in review in Computer Methods in Applied Mechanics and Engineering.
Julia package for fully implicit Runge–Kutta methods, expanding on SciML's OrdinaryDiffEq.jl. Plans to expand this to custom collocation methods for expermentation and learning uses
Contributor to SciML's differential equation ecosystem.
