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A newton-penalty method for a simplified liquid crystal model

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Abstract

In this paper we are concerned with the computation of a liquid crystal model defined by a simplified Oseen-Frank energy functional and a (sphere) nonlinear constraint. A particular case of this model defines the well known harmonic maps. We design a new iterative method for solving such a minimization problem with the nonlinear constraint. The main ideas are to linearize the nonlinear constraint by Newton’s method and to define a suitable penalty functional associated with the original minimization problem. It is shown that the solution sequence of the new minimization problems with the linear constraints converges to the desired solutions provided that the penalty parameters are chosen by a suitable rule. Numerical results confirm the efficiency of the new method.

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Authors and Affiliations

  1. LSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Qiya Hu & Long Yuan

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  1. Qiya Hu
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  2. Long Yuan
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Correspondence to Qiya Hu.

Additional information

Communicated by: Silas Alben.

Qiya Hu was supported by the Major Research Plan of Natural Science Foundation of China G91130015, The Key Project of Natural Science Foundation of China G11031006 and National Basic Research Program of China G2011309702.

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Hu, Q., Yuan, L. A newton-penalty method for a simplified liquid crystal model. Adv Comput Math 40, 201–244 (2014). https://doi.org/10.1007/s10444-013-9305-4

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  • DOI: https://doi.org/10.1007/s10444-013-9305-4

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