Abstract
We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region.
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