Geometric integration on spheres and some interesting applications
Journal of Computational and Applied Mathematics
IPMI '01 Proceedings of the 17th International Conference on Information Processing in Medical Imaging
Numerical methods for minimization problems constrained to S1 and S2
Journal of Computational Physics
An adaptive homotopy multi-grid method for molecule orientations of high dimensional liquid crystals
Journal of Computational Physics
Finite element approximation of nematic liquid crystal flows using a saddle-point structure
Journal of Computational Physics
A New Sobolev Gradient Method for Direct Minimization of the Gross-Pitaevskii Energy with Rotation
SIAM Journal on Scientific Computing
Mumford-Shah-Euler Flow with Sphere Constraint and Applications to Color Image Inpainting
SIAM Journal on Imaging Sciences
Beyond first-order finite element schemes in micromagnetics
Journal of Computational Physics
A newton-penalty method for a simplified liquid crystal model
Advances in Computational Mathematics
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In this article, we propose a new algorithm for minimizing the energy of a nematic liquid crystal. Based on the equal elastic constants Oseen--Frank model, the problem reduces to finding harmonic minimizing maps that take values into the unit sphere of ${\Bbb R}^{3}$. The convergence of this algorithm is proved in a continuous setting. Then, numerous numerical results that show its efficiency are given.