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.
Recommended Citation
Chukwuemeka, Edison E., "Accelerated Gradient Descent Methods For the Uniaxially Constrained Landau-de Gennes Model" (2021). LSU Master's Theses. 5264.
https://repository.lsu.edu/gradschool_theses/5264
Committee Chair
Shawn Walker
DOI
10.31390/gradschool_theses.5264