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.

我们提出了一种方法，用于针对两个相对于缺陷而退化的相关模型加速液晶的平衡模拟：Ericksen模型和单轴约束的Landau-de Gennes模型。退化导致两个模型中两个阶参数之间的非线性/非平滑耦合，这使得离散问题很难解决。本文描述的技术使用交替的Schwarz域分解方法，该方法可隔离退化区域并减轻某些刚度，并且易于实现。我们提供了数值结果，说明了加速及其在退化区域内使用的子域大小和子迭代次数对它的影响。