Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals

Abstract We propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic cholesteric liquid crystals. By applying Lagrangian method, Schur complement director block can be better approximated by weighted mass matrix Lagrange multiplier, at cost making harder to solve. In order solve block, we develop multigrid algorithm which includes an additive Schwarz relaxation that captures pointwise version kernel semi-definite term. Furthermore, prove term improves discrete enforcement unit-length constraint. Numerical experiments verify efficiency its robustness with respect problem-related parameters (Frank constants pitch) mesh size.