A New Algorithm For Computing Liquid Crystal Stable Configurations: The Harmonic Mapping Case

Abstract

In this article, we propose a new algorithm for minimizing the energy of a nematic liquid crystal. Based on the equal elastic constants Oseen--Frank model, the problem reduces to finding harmonic minimizing maps that take values into the unit sphere of ${\Bbb R}^{3}$. The convergence of this algorithm is proved in a continuous setting. Then, numerous numerical results that show its efficiency are given.