Adaptive grid methods for Q-tensor theory of liquid crystals: a one-dimensional feasibility study

A. Ramage, C.J.P. Newton

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples.
LanguageEnglish
Pages160-181
Number of pages22
JournalMolecular Crystals and Liquid Crystals
Volume480
Issue number1
DOIs
Publication statusPublished - 1 Jan 2008

Fingerprint

Liquid Crystals
Liquid crystals
Partial differential equations
Tensors
liquid crystals
grids
tensors
partial differential equations
mesh

Keywords

  • nematic liquid crystals
  • order reconstruction
  • adaptive grids
  • moving meshes
  • statistics

Cite this

@article{b4d2389a62654316afcc48d3708cfe2f,
title = "Adaptive grid methods for Q-tensor theory of liquid crystals: a one-dimensional feasibility study",
abstract = "This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples.",
keywords = "nematic liquid crystals, order reconstruction, adaptive grids, moving meshes, statistics",
author = "A. Ramage and C.J.P. Newton",
year = "2008",
month = "1",
day = "1",
doi = "10.1080/15421400701826225",
language = "English",
volume = "480",
pages = "160--181",
journal = "Molecular Crystals and Liquid Crystals",
issn = "1542-1406",
number = "1",

}

Adaptive grid methods for Q-tensor theory of liquid crystals : a one-dimensional feasibility study. / Ramage, A.; Newton, C.J.P.

In: Molecular Crystals and Liquid Crystals, Vol. 480, No. 1, 01.01.2008, p. 160-181.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Adaptive grid methods for Q-tensor theory of liquid crystals

T2 - Molecular Crystals and Liquid Crystals

AU - Ramage, A.

AU - Newton, C.J.P.

PY - 2008/1/1

Y1 - 2008/1/1

N2 - This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples.

AB - This paper illustrates the use of moving mesh methods for solving partial differential equation (PDE) problems in Q-tensor theory of liquid crystals. We present the results of an initial study using a simple one-dimensional test problem which illustrates the feasibility of applying adaptive grid techniques in such situations. We describe how the grids are computed using an equidistribution principle, and investigate the comparative accuracy of adaptive and uniform grid strategies, both theoretically and via numerical examples.

KW - nematic liquid crystals

KW - order reconstruction

KW - adaptive grids

KW - moving meshes

KW - statistics

U2 - 10.1080/15421400701826225

DO - 10.1080/15421400701826225

M3 - Article

VL - 480

SP - 160

EP - 181

JO - Molecular Crystals and Liquid Crystals

JF - Molecular Crystals and Liquid Crystals

SN - 1542-1406

IS - 1

ER -