Open Access

ARTICLE

Meshfree Solution of Q-tensor Equations of Nematostatics Using the MLPG Method

by Radek Pecher¹, Steve Elston, Peter Raynes

1 Department of Engineering Science, University of Oxford, Parks Road, Oxford, OX1, 3PJ, U.K. tel: +44 (0)1865 273044, fax: +44 (0)1865 273905, email: radek.pecher@eng.ox.ac.uk

Computer Modeling in Engineering & Sciences 2006, 13(2), 91-102. https://doi.org/10.3970/cmes.2006.013.091

Abstract

Meshfree techniques for solving partial differential equations in physics and engineering are a powerful new alternative to the traditional mesh-based techniques, such as the finite difference method or the finite element method. The elimination of the domain mesh enables, among other benefits, more efficient solutions of nonlinear and multi-scale problems. One particular example of these kinds of problems is a Q-tensor based model of nematic liquid crystals involving topological defects.
This paper presents the first application of the meshless local Petrov-Galerkin method to solving the Q-tensor equations of nematostatics. The theoretical part introduces the Landau -- de Gennes free-energy functional and its meshfree minimisation subject to the given boundary constraints. The theory is followed by two example models with simple distortion profiles, including a twisted chiral nematic. The resulting profiles exhibit large local gradients and a high degree of continuity even for few semi-regularly distributed nodes, indicating the high accuracy of the meshfree approach used.

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