  We study the problem of a cholesteric liquid crystal confined to an
elliptical channel. The system is geometrically frustrated because the
cholesteric prefers to adopt a uniform rate of twist deformation, but the
elliptical domain precludes this. The frustration is resolved by deformation of
the layers or introduction of defects, leading to a particularly rich family of
equilibrium configurations. To identify the solution set, we adapt and apply a
new family of algorithms, known as deflation methods, that iteratively modify
the free energy extremisation problem by removing previously known solutions. A
second algorithm, deflated continuation, is used to track solution branches as
a function of the aspect ratio of the ellipse and preferred pitch of the
cholesteric.
