Student(s): Stephanie Moreno-Rivera
Project: Optimal Number of Clusters for Spectral Clustering of 2D Unstructured Meshes | View Poster (PDF)
Major(s): Mechanical Engineering
Advisor(s): Parisa Khodabakshi
Abstract
To enable numerical solutions of the governing equations for complex physical systems, we typically employ meshes to spatially discretize a continuum into smaller domains, within which the governing equations are approximately satisfied. Often, achieving the desired accuracy in the numerical solution necessitates the use of a finely resolved mesh, which, in turn, increases the dimensionality of the resulting discretized system of equations. In this study, we focus on performing dimensional compression on meshes used in engineering analyses. Dimensional compression seeks to reduce the amount of information associated with a system while retaining the essential details for the user. We model an unstructured mesh as a graph and explore the use of spectral clustering for dimensional compression by grouping mesh elements based on the topology of the mesh. Our results demonstrate that spectral clustering effectively leverages both the geometry and topology of the mesh to generate clusters, and it is successful at clustering meshes commonly used in engineering applications. Moreover, we investigate a metric for determining the optimal number of clusters within the mesh. We demonstrate through numerical experiments that the smallest eigenvalues of the graph Laplacian can be utilized to quantify the optimal number of clusters. The resulting optimally clustered mesh can then be employed for dimensional compression in engineering simulations.
About Stephanie Moreno-Rivera
Stephanie Moreno-Rivera is a third-year student at Lehigh University majoring in Mechanical Engineering. She began research in computational mechanics under Dr. Parisa Khodabakhshi in the summer of 2024 and will continue this work in the upcoming summer. Her current work focuses on applying spectral clustering on unstructured meshes for dimensional compression aiming to enhance computational efficiency in engineering simulations. Stephanie’s research interests include the intersection of computational methods and mechanical system design. Outside of research, she dedicates time mentoring first-year students through Lehigh’s mentoring program. In her free time, she enjoys sketching, photography, and video games.