Nonoverlapping discretization methods for partial differential equations
Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. How...
Gespeichert in:
| Veröffentlicht in: | Numerical methods for partial differential equations 2014-09, Vol.30 (5), p.1427-1454 |
|---|---|
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| container_end_page | 1454 |
|---|---|
| container_issue | 5 |
| container_start_page | 1427 |
| container_title | Numerical methods for partial differential equations |
| container_volume | 30 |
| creator | Herrera, Ismael de la Cruz, Luis M. Rosas-Medina, Alberto |
| description | Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse‐mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector‐space‐framework. Using it, it is possible to develop algorithms that satisfy the DDM‐paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 1427–1454, 2014 |
| doi_str_mv | 10.1002/num.21852 |
| format | Article |
| fullrecord | <record><control><sourceid>proquest_cross</sourceid><recordid>TN_cdi_proquest_miscellaneous_1559657006</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><sourcerecordid>1559657006</sourcerecordid><originalsourceid>FETCH-LOGICAL-c4732-2557f4fbf9c3dc0f7506ae3502f9abd15006b086aeaea9ee13c6804fce98f5753</originalsourceid><addsrcrecordid>eNp10EFLwzAUB_AgCs7pwW9Q8KKHbknbNM1RhtuEbV4cegtZ-6KZbVOTVp2f3mxTD4IEEl74_R-Ph9A5wQOCcTSsu2oQkYxGB6hHMM_CKInSQ9TDLOEhofzxGJ04t8aYEEp4D00XpjZvYEvZNLp-Cgrtcgut_pStNnVQQftsChcoY4NG2lbL0hOlwEK9K-C120l3io6ULB2cfb99tBzf3I-m4exucju6noV5wuIojChlKlErxfO4yLFiFKcSYoojxeWqIBTjdIUz_-cPByBxnmY4UTnwTFFG4z663PdtrHntwLWi8iNDWcoaTOcEoZSnlPk2nl78oWvT2dpP51WSJf5Kt-pqr3JrnLOgRGN1Je1GECy2OxV-p2K3U2-He_uuS9j8D8ViOf9JhPuEdi18_CakfREpixkVD4uJ4GwyH2U8EeP4C0rOiEk</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>1548415466</pqid></control><display><type>article</type><title>Nonoverlapping discretization methods for partial differential equations</title><source>Wiley Online Library All Journals</source><creator>Herrera, Ismael ; de la Cruz, Luis M. ; Rosas-Medina, Alberto</creator><creatorcontrib>Herrera, Ismael ; de la Cruz, Luis M. ; Rosas-Medina, Alberto</creatorcontrib><description>Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse‐mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector‐space‐framework. Using it, it is possible to develop algorithms that satisfy the DDM‐paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 1427–1454, 2014</description><identifier>ISSN: 0749-159X</identifier><identifier>EISSN: 1098-2426</identifier><identifier>DOI: 10.1002/num.21852</identifier><language>eng</language><publisher>New York: Blackwell Publishing Ltd</publisher><subject>100%-parallel algorithms ; Algorithms ; Coarsening ; Construction ; DDM with constraints ; Discretization ; Domain decomposition methods ; Mathematical models ; nonoverlapping DDM ; Numerical analysis ; parallel-computation ; Partial differential equations ; PDE-solution-methods</subject><ispartof>Numerical methods for partial differential equations, 2014-09, Vol.30 (5), p.1427-1454</ispartof><rights>2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c4732-2557f4fbf9c3dc0f7506ae3502f9abd15006b086aeaea9ee13c6804fce98f5753</citedby><cites>FETCH-LOGICAL-c4732-2557f4fbf9c3dc0f7506ae3502f9abd15006b086aeaea9ee13c6804fce98f5753</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://onlinelibrary.wiley.com/doi/pdf/10.1002%2Fnum.21852$$EPDF$$P50$$Gwiley$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://onlinelibrary.wiley.com/doi/full/10.1002%2Fnum.21852$$EHTML$$P50$$Gwiley$$Hfree_for_read</linktohtml><link.rule.ids>314,780,784,1416,27923,27924,45573,45574</link.rule.ids></links><search><creatorcontrib>Herrera, Ismael</creatorcontrib><creatorcontrib>de la Cruz, Luis M.</creatorcontrib><creatorcontrib>Rosas-Medina, Alberto</creatorcontrib><title>Nonoverlapping discretization methods for partial differential equations</title><title>Numerical methods for partial differential equations</title><addtitle>Numer. Methods Partial Differential Eq</addtitle><description>Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse‐mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector‐space‐framework. Using it, it is possible to develop algorithms that satisfy the DDM‐paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 1427–1454, 2014</description><subject>100%-parallel algorithms</subject><subject>Algorithms</subject><subject>Coarsening</subject><subject>Construction</subject><subject>DDM with constraints</subject><subject>Discretization</subject><subject>Domain decomposition methods</subject><subject>Mathematical models</subject><subject>nonoverlapping DDM</subject><subject>Numerical analysis</subject><subject>parallel-computation</subject><subject>Partial differential equations</subject><subject>PDE-solution-methods</subject><issn>0749-159X</issn><issn>1098-2426</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><sourceid>24P</sourceid><sourceid>WIN</sourceid><recordid>eNp10EFLwzAUB_AgCs7pwW9Q8KKHbknbNM1RhtuEbV4cegtZ-6KZbVOTVp2f3mxTD4IEEl74_R-Ph9A5wQOCcTSsu2oQkYxGB6hHMM_CKInSQ9TDLOEhofzxGJ04t8aYEEp4D00XpjZvYEvZNLp-Cgrtcgut_pStNnVQQftsChcoY4NG2lbL0hOlwEK9K-C120l3io6ULB2cfb99tBzf3I-m4exucju6noV5wuIojChlKlErxfO4yLFiFKcSYoojxeWqIBTjdIUz_-cPByBxnmY4UTnwTFFG4z663PdtrHntwLWi8iNDWcoaTOcEoZSnlPk2nl78oWvT2dpP51WSJf5Kt-pqr3JrnLOgRGN1Je1GECy2OxV-p2K3U2-He_uuS9j8D8ViOf9JhPuEdi18_CakfREpixkVD4uJ4GwyH2U8EeP4C0rOiEk</recordid><startdate>201409</startdate><enddate>201409</enddate><creator>Herrera, Ismael</creator><creator>de la Cruz, Luis M.</creator><creator>Rosas-Medina, Alberto</creator><general>Blackwell Publishing Ltd</general><general>Wiley Subscription Services, Inc</general><scope>BSCLL</scope><scope>24P</scope><scope>WIN</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>H8D</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>201409</creationdate><title>Nonoverlapping discretization methods for partial differential equations</title><author>Herrera, Ismael ; de la Cruz, Luis M. ; Rosas-Medina, Alberto</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c4732-2557f4fbf9c3dc0f7506ae3502f9abd15006b086aeaea9ee13c6804fce98f5753</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2014</creationdate><topic>100%-parallel algorithms</topic><topic>Algorithms</topic><topic>Coarsening</topic><topic>Construction</topic><topic>DDM with constraints</topic><topic>Discretization</topic><topic>Domain decomposition methods</topic><topic>Mathematical models</topic><topic>nonoverlapping DDM</topic><topic>Numerical analysis</topic><topic>parallel-computation</topic><topic>Partial differential equations</topic><topic>PDE-solution-methods</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Herrera, Ismael</creatorcontrib><creatorcontrib>de la Cruz, Luis M.</creatorcontrib><creatorcontrib>Rosas-Medina, Alberto</creatorcontrib><collection>Istex</collection><collection>Wiley-Blackwell Open Access Titles</collection><collection>Wiley Free Content</collection><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>Aerospace 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 methods for partial differential equations</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Herrera, Ismael</au><au>de la Cruz, Luis M.</au><au>Rosas-Medina, Alberto</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Nonoverlapping discretization methods for partial differential equations</atitle><jtitle>Numerical methods for partial differential equations</jtitle><addtitle>Numer. Methods Partial Differential Eq</addtitle><date>2014-09</date><risdate>2014</risdate><volume>30</volume><issue>5</issue><spage>1427</spage><epage>1454</epage><pages>1427-1454</pages><issn>0749-159X</issn><eissn>1098-2426</eissn><abstract>Ideally, domain decomposition methods (DDMs) seek what we call the DDM‐paradigm: “constructing the ‘global' solution by solving ‘local' problems, exclusively”. To achieve it, it is essential to disconnect the subdomain problems. This explains in part the success of nonoverlapping DDMs. However, in this kind of methods, different subdomains are linked by interface nodes that are shared by several subdomains. Discretization procedures for partial differential equations of a new kind, in which each node belongs to one and only one coarse‐mesh subdomain, are here introduced and analyzed. A discretization method of this type was very successfully used to develop the derived vector‐space‐framework. Using it, it is possible to develop algorithms that satisfy the DDM‐paradigm. Other enhanced numerical and computational properties of them are also discussed. © 2014 The Authors. Numerical Methods for Partial Differential Equations Published by Wiley Periodicals, Inc. 30: 1427–1454, 2014</abstract><cop>New York</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1002/num.21852</doi><tpages>28</tpages><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0749-159X |
| ispartof | Numerical methods for partial differential equations, 2014-09, Vol.30 (5), p.1427-1454 |
| issn | 0749-159X 1098-2426 |
| language | eng |
| recordid | cdi_proquest_miscellaneous_1559657006 |
| source | Wiley Online Library All Journals |
| subjects | 100%-parallel algorithms Algorithms Coarsening Construction DDM with constraints Discretization Domain decomposition methods Mathematical models nonoverlapping DDM Numerical analysis parallel-computation Partial differential equations PDE-solution-methods |
| title | Nonoverlapping discretization methods for partial differential equations |
| url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-01-12T13%3A23%3A01IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_cross&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=Nonoverlapping%20discretization%20methods%20for%20partial%20differential%20equations&rft.jtitle=Numerical%20methods%20for%20partial%20differential%20equations&rft.au=Herrera,%20Ismael&rft.date=2014-09&rft.volume=30&rft.issue=5&rft.spage=1427&rft.epage=1454&rft.pages=1427-1454&rft.issn=0749-159X&rft.eissn=1098-2426&rft_id=info:doi/10.1002/num.21852&rft_dat=%3Cproquest_cross%3E1559657006%3C/proquest_cross%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=1548415466&rft_id=info:pmid/&rfr_iscdi=true |