My Projects
Senior Thesis: High Dimensional Spectral Solver for Partial Differential Equations
May 2024 - Present
This research focuses on constructing a general-purpose solver to approximate solutions of high-dimensional partial differential equations (PDEs) with exponential convergence under the guidance of Dr. Paul Fischer. Leveraging Legendre and Chebyshev polynomials on Gauss-Lobatto sparse grids, the project aims to address challenges in scalability and computational efficiency. Significant progress has been made in developing solvers for 1D, 2D, and 3D domains using polynomial basis functions on full Gauss-Lobatto grids. Current efforts include implementing sparse grids that exploit the nested property of Chebyshev nodes, which will enable scalability to hundreds of dimensions. Future work involves parallelizing computations to enhance solver performance and conducting a comprehensive performance analysis to evaluate speed, accuracy, and scalability. This study's ultimate goal is to develop a solver optimized for practical high-dimensional applications, offering insights into the power and limitations of spectral element methods for PDEs.
Cardgames
May 2024 - Present
Side project to keep score in card games I play.
TunedIn
Dec 2023 - May 2024
My friends and I launched an iOS app for you to curate personalized news feeds that you can listen to on your commute to work or class. Also launched a web app for podcast creators to design episodes that mirror their style, voice, and previously published content.
Quantum Computing Algorithms in Python
May 2022 - Oct 2022
Fundamental concepts behind quantum technology.