Saddle point problems in liquid crystal modelling

Saddle-point problems occur frequently in liquid crystal modelling. For example, they arise whenever Lagrange multipliers are used for the pointwise-unit-vector constraints in director modelling, or in both general director and order tensor models when an electric field is present that stems from a constant voltage. Furthermore, in a director model with associated constraints and Lagrange multipliers, together with a coupled electric-field interaction, a particular ''double'' saddle-point structure arises. This talk will focus on a simple example of this type and discuss appropriate numerical solution schemes.

This is joint work with Eugene C. Gartland, Jr., Department of Mathematical Sciences, Kent State University.