A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models
•Domain decomposition approach to speed up liquid crystal simulations with defects.•Idea is to use extra gradient flow steps in (small) regions around the defect.•Examples shown for the Ericksen and uniaxially constrained Landau-de Gennes model. We present a method for speeding up equilibrium simula...
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| Veröffentlicht in: | Journal of non-Newtonian fluid mechanics 2020-09, Vol.283, p.104335, Article 104335 |
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| container_title | Journal of non-Newtonian fluid mechanics |
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| creator | Carter, Sylver Rotem, Amit Walker, Shawn W. |
| description | •Domain decomposition approach to speed up liquid crystal simulations with defects.•Idea is to use extra gradient flow steps in (small) regions around the defect.•Examples shown for the Ericksen and uniaxially constrained Landau-de Gennes model.
We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region. |
| doi_str_mv | 10.1016/j.jnnfm.2020.104335 |
| format | Article |
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We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region.</description><identifier>ISSN: 0377-0257</identifier><identifier>EISSN: 1873-2631</identifier><identifier>DOI: 10.1016/j.jnnfm.2020.104335</identifier><language>eng</language><publisher>Amsterdam: Elsevier B.V</publisher><subject>Alternating Schwarz method ; Crystal defects ; Crystal structure ; Defects ; Degenerate elliptic ; Domain decomposition methods ; Finite element method ; Liquid crystals ; Nematic crystals ; Order parameters ; Stiffness</subject><ispartof>Journal of non-Newtonian fluid mechanics, 2020-09, Vol.283, p.104335, Article 104335</ispartof><rights>2020</rights><rights>Copyright Elsevier BV Sep 2020</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c376t-5de89d55fac6706c5d4d1525b1375c13354c70468239dc04f12e033f827ac4383</citedby><cites>FETCH-LOGICAL-c376t-5de89d55fac6706c5d4d1525b1375c13354c70468239dc04f12e033f827ac4383</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jnnfm.2020.104335$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,777,781,3537,27905,27906,45976</link.rule.ids></links><search><creatorcontrib>Carter, Sylver</creatorcontrib><creatorcontrib>Rotem, Amit</creatorcontrib><creatorcontrib>Walker, Shawn W.</creatorcontrib><title>A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models</title><title>Journal of non-Newtonian fluid mechanics</title><description>•Domain decomposition approach to speed up liquid crystal simulations with defects.•Idea is to use extra gradient flow steps in (small) regions around the defect.•Examples shown for the Ericksen and uniaxially constrained Landau-de Gennes model.
We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region.</description><subject>Alternating Schwarz method</subject><subject>Crystal defects</subject><subject>Crystal structure</subject><subject>Defects</subject><subject>Degenerate elliptic</subject><subject>Domain decomposition methods</subject><subject>Finite element method</subject><subject>Liquid crystals</subject><subject>Nematic crystals</subject><subject>Order parameters</subject><subject>Stiffness</subject><issn>0377-0257</issn><issn>1873-2631</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LxDAQhoMouK7-Ai8Bz13z0TTdgwcRv2DBi55DnEw1pW26Sbqw_96u69lcBsLzzvA-hFxztuKMV7ftqh2Gpl8JJg4_pZTqhCx4rWUhKslPyYJJrQsmlD4nFym1bH5KVgsS7qkLvfUDdQihH0Py2YeB2nGMwcI3zYFaAOww2ow0-X7q7IFINDQ05ThBniLSMWLCuPPDFx2wnwmgnd9O3lGI-5RtR_vgsEuX5KyxXcKrv7kkH0-P7w8vxebt-fXhflOA1FUulMN67ZRqLFSaVaBc6bgS6pNLrYDP_UrQrKxqIdcOWNlwgUzKphbaQilruSQ3x71zje2EKZs2THGYTxpRKlYpydZ8puSRghhSitiYMfrexr3hzBzMmtb8mjUHs-Zodk7dHVNzH9x5jCaBxwHQ-YiQjQv-3_wPDYyD_w</recordid><startdate>202009</startdate><enddate>202009</enddate><creator>Carter, Sylver</creator><creator>Rotem, Amit</creator><creator>Walker, Shawn W.</creator><general>Elsevier B.V</general><general>Elsevier BV</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>7U5</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>KR7</scope><scope>L7M</scope></search><sort><creationdate>202009</creationdate><title>A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models</title><author>Carter, Sylver ; Rotem, Amit ; Walker, Shawn W.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c376t-5de89d55fac6706c5d4d1525b1375c13354c70468239dc04f12e033f827ac4383</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Alternating Schwarz method</topic><topic>Crystal defects</topic><topic>Crystal structure</topic><topic>Defects</topic><topic>Degenerate elliptic</topic><topic>Domain decomposition methods</topic><topic>Finite element method</topic><topic>Liquid crystals</topic><topic>Nematic crystals</topic><topic>Order parameters</topic><topic>Stiffness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carter, Sylver</creatorcontrib><creatorcontrib>Rotem, Amit</creatorcontrib><creatorcontrib>Walker, Shawn W.</creatorcontrib><collection>CrossRef</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Solid State and Superconductivity Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>Aerospace Database</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><jtitle>Journal of non-Newtonian fluid mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Carter, Sylver</au><au>Rotem, Amit</au><au>Walker, Shawn W.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models</atitle><jtitle>Journal of non-Newtonian fluid mechanics</jtitle><date>2020-09</date><risdate>2020</risdate><volume>283</volume><spage>104335</spage><pages>104335-</pages><artnum>104335</artnum><issn>0377-0257</issn><eissn>1873-2631</eissn><abstract>•Domain decomposition approach to speed up liquid crystal simulations with defects.•Idea is to use extra gradient flow steps in (small) regions around the defect.•Examples shown for the Ericksen and uniaxially constrained Landau-de Gennes model.
We present a method for speeding up equilibrium simulations of liquid crystals for two related models that are degenerate with respect to defects: the Ericksen model and the uniaxially constrained Landau-de Gennes model. The degeneracy induces a non-linear/non-smooth coupling between the two order parameters in both models that makes the discrete problems very stiff to solve. The technique described in this paper uses an alternating Schwarz domain decomposition method that isolates the degenerate region and alleviates some of the stiffness, and is easy to implement. We present numerical results illustrating the speed-up and how it is affected by the size of the sub-domains and the number of sub-iterations used within the degenerate region.</abstract><cop>Amsterdam</cop><pub>Elsevier B.V</pub><doi>10.1016/j.jnnfm.2020.104335</doi><oa>free_for_read</oa></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Alternating Schwarz method Crystal defects Crystal structure Defects Degenerate elliptic Domain decomposition methods Finite element method Liquid crystals Nematic crystals Order parameters Stiffness |
| title | A domain decomposition approach to accelerate simulations of structure preserving nematic liquid crystal models |
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