A Preconditioned Nullspace Method for Liquid Crystal Director Modeling

• DOI: 10.1137/120870219
• Publication Date: 2013-02-12T17:40:21Z
• Authors: Alison Ramage; Eugene C. Gartland
• Keywords: 0101 mathematics; QA; 01 natural sciences; Mathematics; 510

We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.