A preconditioned nullspace method for liquid crystal director modeling

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.

LanguageEnglish
PagesB226-B247
Number of pages22
JournalSIAM Journal on Scientific Computing
Volume35
Issue number1
DOIs
Publication statusPublished - 22 Apr 2013

Fingerprint

Unit vector
Liquid Crystal
Liquid crystals
Sparse Linear Systems
Continuum Model
Saddlepoint
Modeling
Electric Field
Discretization
Numerical Solution
Numerical Results
Linear systems
Electric fields
Model

Keywords

  • liquid crystals
  • nullspace method
  • saddle-point problems
  • unit-vector constraints

Cite this

@article{a2b527afd07c432cbe599c1c290df3d8,
title = "A preconditioned nullspace method for liquid crystal director modeling",
abstract = "We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.",
keywords = "liquid crystals, nullspace method, saddle-point problems, unit-vector constraints",
author = "Alison Ramage and {Gartland Jnr.}, {Eugene C.}",
year = "2013",
month = "4",
day = "22",
doi = "10.1137/120870219",
language = "English",
volume = "35",
pages = "B226--B247",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
number = "1",

}

A preconditioned nullspace method for liquid crystal director modeling. / Ramage, Alison; Gartland Jnr., Eugene C.

In: SIAM Journal on Scientific Computing, Vol. 35, No. 1, 22.04.2013, p. B226-B247.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A preconditioned nullspace method for liquid crystal director modeling

AU - Ramage, Alison

AU - Gartland Jnr., Eugene C.

PY - 2013/4/22

Y1 - 2013/4/22

N2 - We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.

AB - We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.

KW - liquid crystals

KW - nullspace method

KW - saddle-point problems

KW - unit-vector constraints

UR - http://www.scopus.com/inward/record.url?scp=84876256922&partnerID=8YFLogxK

U2 - 10.1137/120870219

DO - 10.1137/120870219

M3 - Article

VL - 35

SP - B226-B247

JO - SIAM Journal on Scientific Computing

T2 - SIAM Journal on Scientific Computing

JF - SIAM Journal on Scientific Computing

SN - 1064-8275

IS - 1

ER -