Journal article
Augmented Lagrangian preconditioners for the Oseen–Frank model of nematic and cholesteric liquid crystals
- Abstract:
- We propose a robust and efficient augmented Lagrangian-type preconditioner for solving linearizations of the Oseen–Frank model arising in nematic and cholesteric liquid crystals. By applying the augmented Lagrangian method, the Schur complement of the director block can be better approximated by the weighted mass matrix of the Lagrange multiplier, at the cost of making the augmented director block harder to solve. In order to solve the augmented director block, we develop a robust multigrid algorithm which includes an additive Schwarz relaxation that captures a pointwise version of the kernel of the semi-definite term. Furthermore, we prove that the augmented Lagrangian term improves the discrete enforcement of the unit-length constraint. Numerical experiments verify the efficiency of the algorithm and its robustness with respect to problem-related parameters (Frank constants and cholesteric pitch) and the mesh size.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, 1.1MB, Terms of use)
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- Publisher copy:
- 10.1007/s10543-020-00838-9
Authors
- Publisher:
- Springer
- Journal:
- BIT Numerical Mathematics More from this journal
- Volume:
- 61
- Issue:
- 2021
- Pages:
- 607–644
- Publication date:
- 2021-03-23
- Acceptance date:
- 2020-12-11
- DOI:
- EISSN:
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1572-9125
- ISSN:
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0006-3835
- Language:
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English
- Keywords:
- Pubs id:
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1148575
- Local pid:
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pubs:1148575
- Deposit date:
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2020-12-11
Terms of use
- Copyright holder:
- Xia et al.
- Copyright date:
- 2020
- Rights statement:
- © The Author(s) 2020. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
- Licence:
- CC Attribution (CC BY)
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