Research

Research Interests

I am interested in numerical analysis and computational methods. Specifically, I enjoy trying to design and implement numerical algorithms on meshes approximating complex geometries. When I have time, I try to think about the linear algebra behind numerical algorithms.

Current Research

I am working on understanding Fractional Differential Equations (FDE's) and the limitations of numerical methods in solving them. We are searching for a way to apply methods from Discrete Exterior Calculus to solve FDE's on triangulated meshes approximating manifolds.

Past Research

(Fall 2017--RTG) Supervised by Andrew Gillette. We worked on understanding theoretical numerical convergence results for curved finite elements. The focus was on elements that came from rational or polynomial transformations of the unit square.

(Spring 2017--Spring Term Paper) Supervised by Rob Indik. We read and worked through The Matrix Eigenvalue Problem by David S. Watkins. During this, I implemented various structured eigenvalue solvers in Matlab and tested them on random matrices with the structure of interest.

Presentations

(June 2018--Poster Presentation) Fractional Laplacian Smoothing. I presented preliminary results for fractional Laplacian smoothing at the poster session for the ICERM workshop Fractional PDEs: Theory, Algorithms, and Applications.

(December 2017--Talk) Curved Finite Elements. I presented theoretical convergence results from the third semester research project with Andrew Gillette at the Applied Mathematics Second Year Research Conference.

(May 2017--Talk) The Eigenvalue Problem. I presented results and algorithms that were implemented during the second semester research project at the First Year Applied Math Research Workshop.