Semester of Graduation

Spring 2021

Degree

Master of Science (MS)

Department

Mathematics

Document Type

Thesis

Abstract

Liquid crystal models with the capability of capturing defects has been one of the main focus in modeling the behavior of such phase mathematically. A uni-axially constrained Landau-de Gennes one-constant model, which has this capability was modeled using three minimization schemes - standard gradient descent, Nesterov accelerated gradient descent, and heavy-ball accelerated gradient descent. The uni-axially constrained Landau-de Gennes energy is discretized using finite element method and the performance of the minimization schemes are measured using the classical gradient descent scheme as the baseline. The numerical experiments conducted indicated that the accelerated gradient descent schemes improved the convergence rate and reduced the duration of the computation while maintaining the same minimum energy.

Committee Chair

Shawn Walker

Available for download on Sunday, May 22, 2022

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