Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Mathematics and Statistics

First Advisor

Jung-Han Kimn


biofilm, computational science, fluid dynamics, parallel computing


The importance of computing in the natural sciences continues to grow as scientists strive to analyze complex phenomena. The dynamics of turbulence, astrophysics simulations, and climate change are just a few examples where computing is critical. These problems are computationally intractable on all computing platforms except supercomputers, necessitating the continued development of efficient algorithms and methodologies in parallel computing. This thesis investigates the use of parallel computing and mathematical modeling in the natural sciences through several applications, namely computational fluid dynamics for impinging jets in mechanical engineering, simulation of biofilms in an aqueous environment in mathematical biology, and the solution of the alternating current optimal power flow problem in electrical engineering. In this study, the Portable, Extensible Toolkit for Scientific Computing (PETSc) is utilized in the design of the numerical methods and parallel implementations.

Library of Congress Subject Headings

Parallel processing (Electronic computers)
High performance computing.
Mathematical models.
Computer algorithms.
Fluid dynamics.
Electric power transmission -- Alternating current.
Mathematical optimization.



Number of Pages



South Dakota State University



Rights Statement

In Copyright