A preconditioned nullspace method for liquid crystal director modelling

Alison Ramage, Eugene C. Gartland, Jr.

Research output: Contribution to journalArticle

11 Citations (Scopus)
42 Downloads (Pure)

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.
Original languageEnglish
Pages (from-to)B226–B247
Number of pages22
JournalSIAM Journal on Scientific Computing
Volume35
Issue number1
DOIs
Publication statusPublished - 12 Feb 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

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

Cite this

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

In: SIAM Journal on Scientific Computing, Vol. 35, No. 1, 12.02.2013, p. B226–B247.

Research output: Contribution to journalArticle

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AU - Gartland, Jr., Eugene C.

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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.

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