Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems
We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into m × m × m subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally...
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| Veröffentlicht in: | Computational mechanics 2023-02, Vol.71 (2), p.333-347 |
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| container_title | Computational mechanics |
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| creator | Dostál, Zdeněk Brzobohatý, Tomáš Vlach, Oldřich Meca, Ondřej Sadowská, Marie |
| description | We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into
m
×
m
×
m
subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to
m
. The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with
m
6
while the number of iterations increases only proportionally to
m
. Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems. |
| doi_str_mv | 10.1007/s00466-022-02242-2 |
| format | Article |
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m
×
m
×
m
subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to
m
. The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with
m
6
while the number of iterations increases only proportionally to
m
. Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems.</description><identifier>ISSN: 0178-7675</identifier><identifier>EISSN: 1432-0924</identifier><identifier>DOI: 10.1007/s00466-022-02242-2</identifier><language>eng</language><publisher>Berlin/Heidelberg: Springer Berlin Heidelberg</publisher><subject>Algorithms ; Classical and Continuum Physics ; Computational Science and Engineering ; Decomposition ; Domain decomposition methods ; Engineering ; Estimates ; Experiments ; Mechanics ; Methods ; Original Paper ; Partial differential equations ; Rigid structures ; Theoretical and Applied Mechanics</subject><ispartof>Computational mechanics, 2023-02, Vol.71 (2), p.333-347</ispartof><rights>The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</rights><rights>COPYRIGHT 2023 Springer</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c355t-70788b704d0f4db54d1bba6000245d6c5447360dd1948c4005c55c3c33a521863</citedby><cites>FETCH-LOGICAL-c355t-70788b704d0f4db54d1bba6000245d6c5447360dd1948c4005c55c3c33a521863</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1007/s00466-022-02242-2$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1007/s00466-022-02242-2$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,776,780,27901,27902,41464,42533,51294</link.rule.ids></links><search><creatorcontrib>Dostál, Zdeněk</creatorcontrib><creatorcontrib>Brzobohatý, Tomáš</creatorcontrib><creatorcontrib>Vlach, Oldřich</creatorcontrib><creatorcontrib>Meca, Ondřej</creatorcontrib><creatorcontrib>Sadowská, Marie</creatorcontrib><title>Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems</title><title>Computational mechanics</title><addtitle>Comput Mech</addtitle><description>We describe the three-level hybrid domain decomposition TFETI method and show that the condition number of an elastic cluster defined on a fixed cube domain, decomposed into
m
×
m
×
m
subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to
m
. The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with
m
6
while the number of iterations increases only proportionally to
m
. Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems.</description><subject>Algorithms</subject><subject>Classical and Continuum Physics</subject><subject>Computational Science and Engineering</subject><subject>Decomposition</subject><subject>Domain decomposition methods</subject><subject>Engineering</subject><subject>Estimates</subject><subject>Experiments</subject><subject>Mechanics</subject><subject>Methods</subject><subject>Original Paper</subject><subject>Partial differential equations</subject><subject>Rigid structures</subject><subject>Theoretical and Applied Mechanics</subject><issn>0178-7675</issn><issn>1432-0924</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2023</creationdate><recordtype>article</recordtype><sourceid>BENPR</sourceid><recordid>eNp9kc-KFDEQxhtRcFx9AU8BTx56rfzr9ByX9c8OLAi6nkM6Sfdk6O6MqbTr3HyNfb19ErO2IHuRIhQVfl99BV9VvaZwTgHUOwQQTVMDYw9PsJo9qTZU8DJumXhabYCqtlaNks-rF4gHACpbLjfV7dWpS8GRm48fbnbExcmEmThv43SMGHKIM7kNeU_y3hM7Lph9QnKIYfaOdCfSG-vx_tcdSWEoW6boPJI-JoJx_BHmgeyXwRP-nvjRYA6WHFPsRj_hy-pZb0b0r_72s-pbueDyqr7-_Gl3eXFdWy5lrhWotu0UCAe9cJ0UjnadaQCACekaK4VQvAHn6Fa0VgBIK6XllnMjGW0bfla9WfcW4--Lx6wPcUlzsdRMNVvB22JRqPOVGszodZj7mJOxpZyfgo2z70P5v1BcKGgl3RbB20eCwmT_Mw9mQdS7r18es2xlbYqIyff6mMJk0klT0A_p6TU9XZLTf9LTrIj4KsICz4NP_-7-j-o3gWWb6A</recordid><startdate>20230201</startdate><enddate>20230201</enddate><creator>Dostál, Zdeněk</creator><creator>Brzobohatý, Tomáš</creator><creator>Vlach, Oldřich</creator><creator>Meca, Ondřej</creator><creator>Sadowská, Marie</creator><general>Springer Berlin Heidelberg</general><general>Springer</general><general>Springer Nature B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>ISR</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>AFKRA</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope></search><sort><creationdate>20230201</creationdate><title>Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems</title><author>Dostál, Zdeněk ; 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m
×
m
×
m
subdomains interconnected by the face’s rigid body modes and discretized by a regular grid, increases proportionally to
m
. The estimates are plugged into the analysis of the unpreconditioned H-TFETI (hybrid) method and used to prove its numerical scalability for linear problems. The estimates show that the cost of the coarse problem decreases with
m
6
while the number of iterations increases only proportionally to
m
. Numerical experiments show a large scope of scalability of H-TFETI. The results are also essential for solving huge contact problems.</abstract><cop>Berlin/Heidelberg</cop><pub>Springer Berlin Heidelberg</pub><doi>10.1007/s00466-022-02242-2</doi><tpages>15</tpages></addata></record> |
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| subjects | Algorithms Classical and Continuum Physics Computational Science and Engineering Decomposition Domain decomposition methods Engineering Estimates Experiments Mechanics Methods Original Paper Partial differential equations Rigid structures Theoretical and Applied Mechanics |
| title | Hybrid TFETI domain decomposition with the clusters joined by faces’ rigid modes for solving huge 3D elastic problems |
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