Date on Master's Thesis/Doctoral Dissertation


Document Type

Doctoral Dissertation

Degree Name

Ph. D.



Degree Program

Applied and Industrial Mathematics, PhD

Committee Chair

Wu, Shi-Yu

Committee Co-Chair (if applicable)

Jayanthi, Chakram S.

Committee Member

Larson, Lee

Committee Member

Riedel, Thomas

Committee Member

Sahoo, Prasanna

Committee Member

Yu, Ming


Quantum field theory; Quantum theory--Mathematics


In this document I describe a novel implementation of the generalized bisection method for finding roots of highly non-linear functions of several variables. Several techniques were optimized to reduce computation time. The implementation of the bisection method allows for the calculation of heterogeneous systems with SCED-LCAO, since derivative-based methods often fail for these systems. Systems composed of Gallium and Nitrogen are currently receiving much interest due to their behavior as semi-conductors and their ability to form nano-wires. The methods developed here were employed to create a set of SCED-LCAO parameters for homogeneous Gallium and heterogeneous Gallium Nitride systems. These parameters were shown to provide SCED-LCAO with predictive power for future Gallium Nitride systems.