Current research · Scientific computing
Tensor Methods for Partial Differential Equations
My current work explores tensor-network methods for solving partial differential equations on classical computers. The aim is to establish reliable classical tensor-method benchmarks that can be used when evaluating emerging quantum approaches to PDEs.
This work involves matrix product states and operators, tensor-train representations, singular-value decomposition, finite-difference discretizations, and optimization methods for linear systems. Current numerical experiments focus on the heat equation and related parabolic problems.
Research notes and code are being developed alongside the project.
2022–2023 · Mathematical modeling
Crop Per Drop
Working with Chippewa Valley Bean, our team developed a coupled differential-equation model of water in the soil, canopy development, and reproductive biomass in dark red kidney beans. The model was used to investigate irrigation requirements and the relationship between water use and predicted crop yield.
The work was presented at the MAA Wisconsin Conference, the National Conference on Undergraduate Research, and Research in the Rotunda.
Wisconsin Freshwater Collaborative · Project information for farmers
Published research · Algebra and graph theory
On Magic Type Labelings of Zero-Divisor Graphs
In this work, we investigate semi-magic, magic, and super-magic labelings of zero-divisor graphs. We construct infinite families of commutative rings that admit these labelings, as well as families that do not, and classify the magic-type properties of zero-divisor graphs with up to 14 vertices.
M = n(n² + 1) / 2
Feggestad, J., Halvorson, J., Mooney, C. P., Royce, N., & Wanta, N. (2024). On Magic Type Labelings of Zero-Divisor Graphs. International Electronic Journal of Algebra.
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