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A new algorithm for computing liquid crystal stable configurations: the harmonic mapping case. (English) Zbl 0886.35010
The author proposes a new algorithm for minimizing the energy of a nematic liquid crystal. Based on the equal elastic constants Osen-Frank model, the problem reduces to finding harmonic minimizing maps that take values into the unit sphere of \(\mathbb{R}^3\). The convergence of this algorithm is proved in a continuous setting. The author gives three different ways to numerically implement the algorithm. The first is a saddle-point technique, whereas the second is closely related to a relaxation method for solving the Poisson problem. The third appears to be a conjugate gradient method. Some comparisons in terms of computation times between these implementations are presented. Then, numerous numerical results that show its efficiency are given.
Reviewer: K.Najzar (Praha)

MSC:
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65N99 Numerical methods for partial differential equations, boundary value problems
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65C20 Probabilistic models, generic numerical methods in probability and statistics
76A15 Liquid crystals
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