Solution of the Landau-de-Gennes Equations of Liquid Crystal Physics on a SIMD Computer

We will describe a scalable parallel finite difference algorithm for computing the equilibrium configurations, of the order-parameter tensor field for nematic liquid crystals, in rectangular and ellipsoidal regions, but minimization of the Landau-de-Gennes free energy functional. In this formulation, we solve for a symmetric traceless 3 {times} 3 tensor at each point. Our implementation of the free energy functional includes surface, gradient and scalar bulk terms, together with the effects of electric or magnetic fields. Boundary conditions can include both strong and weak surface anchoring. The target architectures for our implementation are primarily SIMD machines, with 2 or 3 dimensional rectangular grid networks, such as the Wavetracer DTC or the MasPar MP-1 as opposed to hypercube networks such as the Thinking Machines Corporation CM-2.