Dissertation Proposal - Damyn Chipman

Implementation of a Fast and Scalable Direct Solver for Elliptic Partial Differential Equations and Applications

Presented by Damyn Chipman – Computational Math Science and Engineering Emphasis

Hybrid Presentation – CCP Room 368 and via Zoom

Abstract

This proposal lays out the background, tasks, and proposed results for my dissertation of the Ph.D. in Computing program at Boise State University. I propose to implement a novel, O(N) direct solver for elliptic partial differential equations called the Hierarchical Poincaré-Steklov method. I detail both the proposed serial and parallel implementations of the HPS method. In addition, I show applications that will benefit from a fast, scalable direct solver for elliptic PDEs such as Poisson’s equation, the incompressible Navier-Stokes equations via a projection method, and a modified Serre-Green-Naghdi model for the dispersive shallow water equations. A literature review is given to provide context and open research questions. I propose a timeline for all project and task completion as well as show current progress on these projects.

Committee

Donna Calhoun, Ph.D. (Chair), Michal Kopera, Ph.D. Cathie Olschanowsky, Ph.D.