Meshfree solution of Q-tensor equations of nematostatics using the MLPG method

CMES - Computer Modeling in Engineering and Sciences

Volumn 13, Issue 2, 2006, Pages 91-101

  Pecher, Radek ^a   Elston, Steve ^a   Raynes, Peter ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Meshfree modelling; Meshless local Petrov Galerkin method; MLPG; Nematic liquid crystals; Tensor order parameter; Topological defects

Indexed keywords

FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; FREE ENERGY; PARTIAL DIFFERENTIAL EQUATIONS; PROBLEM SOLVING; TOPOLOGY;

BOUNDARY CONSTRAINTS; PETROV-GALERKIN METHOD; Q-TENSOR; TOPOLOGICAL DEFECTS;

NEMATIC LIQUID CRYSTALS;

EID: 33745003707     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (15)

1. Atluri, S.; Shen, S. (2002): The Meshless Local Petrov-Galerkin (MLPG) Method. Tech Science Press.
2. Atluri, S.; Han, Z.D.; and Rajendran, A.M. (2004): A New Implementation of the Meshless Finite Volume Method, Through the MLPG "Mixed" Approach CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. 6, pp. 491-514.
3. Atluri, S.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Computational Mechanics, vol. 22, pp. 117-127.
4. Beris, A.; Edwards, B. (1994): Thermodynamics of Flowing Systems with Internal Microstructure - Oxford Engineering Science Series. Oxford University Press, Oxford.
5. Berreman, D.; Meiboom, S. (1984): Tensor representation of Oseen-Frank strain energy in uniaxial cholesterics. Physical Review A, vol. 30, pp. 1955-1959.
6. Breitkopf, P.; Rassineux, A.; Touzot, G.; Villon, P. (2000): Explicit form and efficient computation of MLS shape functions and their derivatives. International Journal for Numerical Methods in Engineering, vol. 48, pp. 451-466.
7. de Gennes, P.; Prost, J. (1993): The Physics of Liquid Crystals (2nd edn). The International Series of Monographs on Physics. Clarendon Press, Oxford.
8. Frank, F. (1958): On the theory of liquid crystals. Discussions of the Faraday Society, vol. 25, pp. 19-28.
9. Landau, L.; Lifshitz, E. (1980): Statistical Physics (3rd edn). Pergamon Press, Oxford.
10. Li, Q.; Shen, S.; Han, Z.; Atluri, S. (2003): Application of meshless local Petrov-Galerkin (MLPG) to problems with singularities, and material discontinuities, in 3-D elasticity. CMES: Computer Modeling in Engineering & Sciences, vol. 4, pp. 571-585.
11. Liu, G. (2003): Mesh Free Methods: Moving Beyond the Finite Element Method. CRC Press.
12. Mori, H.; Gartland, E.; Kelly, J.; Bos, P. (1999): Multidimensional director modeling using the Q tensor representation in a liquid crystal cell and its application to the π cell with patterned electrodes. Japanese Journal of Applied Physics - Part 1, vol. 38, pp. 135-146.
13. Oseen, C. (1933): The theory of liquid crystals. Transactions of the Faraday Society, vol. 29, pp. 883-899.
14. Pecher, R. (2005): Efficient cubature formulae for MLPG and related methods. International Journal for Numerical Methods in Engineering, vol. 65, pp. 566-593.
15. Schopohl, N.; Sluckin, T. (1987): Defect core structure in nematic liquid crystals. Physical Review Letters, vol. 59,pp. 2582-2584.