Constrained Optimization for Liquid Crystal Equilibria

Abstract. This paper investigates energy-minimization finite-element approaches for the computation of nematic liquid crystal equilibrium configurations. We compare the performance of these methods when the necessary unit-length constraint is enforced by either continuous Lagrange multipliers or a penalty functional. Building on previous work in [1, 2], the penalty method is derived such that the linearizations within the nonlinear iteration are well-posed under certain assumptions. In addition, the paper discusses the effects of tailored trust-region methods and nested iteration for both formulations. Such methods are aimed at increasing the efficiency and robustness of each algorithms’ nonlinear iterations. Three representative, free-elastic, equilibrium problems are considered to examine each method’s performance. The first two configurations have analytical solutions and, therefore, convergence to the true solution is considered. The third problem considers more complicate...

• Type: Journal
• Year: 2016
• Where: SIAMSC
• Authors: James H. Adler, D. B. Emerson, Scott P. MacLachlan, Thomas A. Manteuffel
• Keywords: Computer Graphics, SIAMSC 2016