Publication Date

12-2024

Date of Final Oral Examination (Defense)

7-17-2024

Type of Culminating Activity

Dissertation

Degree Title

Doctor of Philosophy in Computing

Department

Computer Science

Supervisory Committee Chair

Donna Calhoun, Ph.D.

Supervisory Committee Member

Michal Kopera, Ph.D.

Supervisory Committee Member

Grady Wright, Ph.D.

Abstract

We introduce the quadtree-adaptive Hierarchical Poincaré-Steklov (QAHPS) method, an adaptive direct method for solving elliptic partial differential equations on a hierarchy of adaptively refined finite volume meshes. The QAHPS method builds up a solution operator set with O(N^3/2) complexity that acts as the factorization of the system matrix, with linear O(N) complexity for the application of the solution operator set to any number of right-hand side vectors. As the solution operator set is built up by merging local subdomains, it can be adapted as the mesh is refined and coarsened. The method is an adaptive extension to the Hierarchical Poincaré-Steklov method by Gillman & Martinsson (2014). In this dissertation, we motivate, derive, and analyze the QAHPS method for use with the mesh management library p4est (Burstedde et al., 2011). Through scaling runs on the Polaris supercomputer, we show strong and weak scaling performance. Finally, we apply the QAHPS method to the Laplace, Poisson, and Helmholtz equations, with comparisons to iterative solvers for elliptic partial differential equations.

Comments

https://orcid.org/0000-0001-6600-3720

DOI

https://doi.org/10.18122/td.2285.boisestate

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