A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems
Summary In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence‐free velocity field independent of the n...
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| Veröffentlicht in: | Numerical linear algebra with applications 2018-05, Vol.25 (3), p.n/a |
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| creator | Coley, Christopher Benzaken, Joseph Evans, John A. |
| description | Summary
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence‐free velocity field independent of the number of pre‐smoothing steps, postsmoothing steps, grid levels, or cycles in a V‐cycle implementation, provided that the initial velocity guess is also divergence free. The methodology relies upon Scwharz‐style smoothers in conjunction with specially defined overlapping subdomains that respect the underlying topological structure of the generalized Stokes and Oseen problems. Numerical results in both two‐ and three‐dimensions demonstrate the robustness of the methodology through the invariance of convergence rates with respect to grid resolution and flow parameters for the generalized Stokes problem and the generalized Oseen problem, provided that it is not advection dominated. |
| doi_str_mv | 10.1002/nla.2145 |
| format | Article |
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In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence‐free velocity field independent of the number of pre‐smoothing steps, postsmoothing steps, grid levels, or cycles in a V‐cycle implementation, provided that the initial velocity guess is also divergence free. The methodology relies upon Scwharz‐style smoothers in conjunction with specially defined overlapping subdomains that respect the underlying topological structure of the generalized Stokes and Oseen problems. Numerical results in both two‐ and three‐dimensions demonstrate the robustness of the methodology through the invariance of convergence rates with respect to grid resolution and flow parameters for the generalized Stokes problem and the generalized Oseen problem, provided that it is not advection dominated.</description><identifier>ISSN: 1070-5325</identifier><identifier>EISSN: 1099-1506</identifier><identifier>DOI: 10.1002/nla.2145</identifier><language>eng</language><publisher>Oxford: Wiley Subscription Services, Inc</publisher><subject>Computational fluid dynamics ; Discretization ; Divergence ; generalized Oseen flow ; generalized Stokes flow ; geometric multigrid ; isogeometric compatible discretizations ; isogeometric divergence‐conforming discretizations ; Methodology ; overlapping Schwarz smoothers ; Robustness (mathematics) ; Stokes law (fluid mechanics) ; Velocity distribution</subject><ispartof>Numerical linear algebra with applications, 2018-05, Vol.25 (3), p.n/a</ispartof><rights>Copyright © 2018 John Wiley & Sons, Ltd.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c2935-fcfba14c11fc547822f1f5e003bd41d9676b6008f4646fa36cbd1d478b8c62ca3</citedby><cites>FETCH-LOGICAL-c2935-fcfba14c11fc547822f1f5e003bd41d9676b6008f4646fa36cbd1d478b8c62ca3</cites><orcidid>0000-0001-7306-496X</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnla.2145$$EPDF$$P50$$Gwiley$$H</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnla.2145$$EHTML$$P50$$Gwiley$$H</linktohtml><link.rule.ids>314,780,784,1416,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Coley, Christopher</creatorcontrib><creatorcontrib>Benzaken, Joseph</creatorcontrib><creatorcontrib>Evans, John A.</creatorcontrib><title>A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems</title><title>Numerical linear algebra with applications</title><description>Summary
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence‐free velocity field independent of the number of pre‐smoothing steps, postsmoothing steps, grid levels, or cycles in a V‐cycle implementation, provided that the initial velocity guess is also divergence free. The methodology relies upon Scwharz‐style smoothers in conjunction with specially defined overlapping subdomains that respect the underlying topological structure of the generalized Stokes and Oseen problems. Numerical results in both two‐ and three‐dimensions demonstrate the robustness of the methodology through the invariance of convergence rates with respect to grid resolution and flow parameters for the generalized Stokes problem and the generalized Oseen problem, provided that it is not advection dominated.</description><subject>Computational fluid dynamics</subject><subject>Discretization</subject><subject>Divergence</subject><subject>generalized Oseen flow</subject><subject>generalized Stokes flow</subject><subject>geometric multigrid</subject><subject>isogeometric compatible discretizations</subject><subject>isogeometric divergence‐conforming discretizations</subject><subject>Methodology</subject><subject>overlapping Schwarz smoothers</subject><subject>Robustness (mathematics)</subject><subject>Stokes law (fluid mechanics)</subject><subject>Velocity distribution</subject><issn>1070-5325</issn><issn>1099-1506</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp10E1LAzEQBuAgCtYq-BMCXrxsnSSbtHssxS8o9qCeQzYfberupiZbpP31plbw5CmT4ZkZeBG6JjAiAPSua9SIkpKfoAGBqioIB3F6qMdQcEb5ObpIaQ0AgldsgLZTvLShtX30GrfbpvfL6A3OjVUw2IWIfQp_Qod2o3pfNxYbn3S0vd_nf-gSDg73K5u3dTaqxu-twa99-LAJq87gRbK2w5sY8mibLtGZU02yV7_vEL0_3L_Nnor54vF5Np0XmlaMF067WpFSE-I0L8cTSh1x3AKw2pTEVGIsagEwcaUohVNM6NoQk2E90YJqxYbo5rg3H_7c2tTLddjGLp-UFCiDklSMZHV7VDqGlKJ1chN9q-JOEpCHUGUOVR5CzbQ40i_f2N2_Tr7Mpz_-G1tSelQ</recordid><startdate>201805</startdate><enddate>201805</enddate><creator>Coley, Christopher</creator><creator>Benzaken, Joseph</creator><creator>Evans, John A.</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><orcidid>https://orcid.org/0000-0001-7306-496X</orcidid></search><sort><creationdate>201805</creationdate><title>A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems</title><author>Coley, Christopher ; Benzaken, Joseph ; Evans, John A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2935-fcfba14c11fc547822f1f5e003bd41d9676b6008f4646fa36cbd1d478b8c62ca3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Computational fluid dynamics</topic><topic>Discretization</topic><topic>Divergence</topic><topic>generalized Oseen flow</topic><topic>generalized Stokes flow</topic><topic>geometric multigrid</topic><topic>isogeometric compatible discretizations</topic><topic>isogeometric divergence‐conforming discretizations</topic><topic>Methodology</topic><topic>overlapping Schwarz smoothers</topic><topic>Robustness (mathematics)</topic><topic>Stokes law (fluid mechanics)</topic><topic>Velocity distribution</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Coley, Christopher</creatorcontrib><creatorcontrib>Benzaken, Joseph</creatorcontrib><creatorcontrib>Evans, John A.</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Numerical linear algebra with applications</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Coley, Christopher</au><au>Benzaken, Joseph</au><au>Evans, John A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems</atitle><jtitle>Numerical linear algebra with applications</jtitle><date>2018-05</date><risdate>2018</risdate><volume>25</volume><issue>3</issue><epage>n/a</epage><issn>1070-5325</issn><eissn>1099-1506</eissn><abstract>Summary
In this paper, we present a geometric multigrid methodology for the solution of matrix systems associated with isogeometric compatible discretizations of the generalized Stokes and Oseen problems. The methodology provably yields a pointwise divergence‐free velocity field independent of the number of pre‐smoothing steps, postsmoothing steps, grid levels, or cycles in a V‐cycle implementation, provided that the initial velocity guess is also divergence free. The methodology relies upon Scwharz‐style smoothers in conjunction with specially defined overlapping subdomains that respect the underlying topological structure of the generalized Stokes and Oseen problems. Numerical results in both two‐ and three‐dimensions demonstrate the robustness of the methodology through the invariance of convergence rates with respect to grid resolution and flow parameters for the generalized Stokes problem and the generalized Oseen problem, provided that it is not advection dominated.</abstract><cop>Oxford</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/nla.2145</doi><tpages>24</tpages><orcidid>https://orcid.org/0000-0001-7306-496X</orcidid></addata></record> |
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| subjects | Computational fluid dynamics Discretization Divergence generalized Oseen flow generalized Stokes flow geometric multigrid isogeometric compatible discretizations isogeometric divergence‐conforming discretizations Methodology overlapping Schwarz smoothers Robustness (mathematics) Stokes law (fluid mechanics) Velocity distribution |
| title | A geometric multigrid method for isogeometric compatible discretizations of the generalized Stokes and Oseen problems |
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