{"id":"https://openalex.org/W2081624895","doi":"https://doi.org/10.1137/s0036142901388081","title":"Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients","display_name":"Dual-Primal FETI Methods for Three-Dimensional Elliptic Problems with Heterogeneous Coefficients","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2081624895","doi":"https://doi.org/10.1137/s0036142901388081","mag":"2081624895"},"language":"en","primary_location":{"id":"doi:10.1137/s0036142901388081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901388081","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://publica.fraunhofer.de/documents/B-73146.html","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041978201","display_name":"Axel Klawonn","orcid":"https://orcid.org/0000-0003-4765-7387"},"institutions":[{"id":"https://openalex.org/I4210098248","display_name":"Fraunhofer Institute for Algorithms and Scientific Computing","ror":"https://ror.org/00trw9c49","country_code":"DE","type":"facility","lineage":["https://openalex.org/I4210098248","https://openalex.org/I4923324"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Axel Klawonn","raw_affiliation_strings":["Fraunhofer Institute for Algorithms and Scientific Computing"],"affiliations":[{"raw_affiliation_string":"Fraunhofer Institute for Algorithms and Scientific Computing","institution_ids":["https://openalex.org/I4210098248"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113456504","display_name":"Olof B. Widlund","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Olof B. Widlund","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5111838056","display_name":"Maksymilian Dryja","orcid":null},"institutions":[{"id":"https://openalex.org/I4654613","display_name":"University of Warsaw","ror":"https://ror.org/039bjqg32","country_code":"PL","type":"education","lineage":["https://openalex.org/I4654613"]}],"countries":["PL"],"is_corresponding":false,"raw_author_name":"Maksymilian Dryja","raw_affiliation_strings":["University of Warsaw"],"affiliations":[{"raw_affiliation_string":"University of Warsaw","institution_ids":["https://openalex.org/I4654613"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5041978201"],"corresponding_institution_ids":["https://openalex.org/I4210098248"],"apc_list":null,"apc_paid":null,"fwci":14.4081,"has_fulltext":false,"cited_by_count":233,"citation_normalized_percentile":{"value":0.99357562,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"40","issue":"1","first_page":"159","last_page":"179"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9994999766349792,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9980999827384949,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/feti","display_name":"FETI","score":0.9327883720397949},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7713068127632141},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.7604537010192871},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.6199061870574951},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5527148842811584},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.48278701305389404},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.47666504979133606},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4749317765235901},{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.46190744638442993},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.4563009440898895},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4518142342567444},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3948887288570404},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21419757604599},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11359551548957825}],"concepts":[{"id":"https://openalex.org/C171609451","wikidata":"https://www.wikidata.org/wiki/Q5425382","display_name":"FETI","level":4,"score":0.9327883720397949},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7713068127632141},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7604537010192871},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.6199061870574951},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5527148842811584},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.48278701305389404},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.47666504979133606},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4749317765235901},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.46190744638442993},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.4563009440898895},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4518142342567444},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3948887288570404},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21419757604599},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11359551548957825},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/s0036142901388081","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0036142901388081","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:hdl:10068/182695","is_oa":false,"landing_page_url":"http://hdl.handle.net/10068/182695","pdf_url":null,"source":{"id":"https://openalex.org/S4377196900","display_name":"OpenGrey (Institut de l'Information Scientifique et Technique)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1295345811","host_organization_name":"Institut de l'Information Scientifique et Technique","host_organization_lineage":["https://openalex.org/I1295345811"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"R - Report"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.460.2449","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.460.2449","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://cs1.cs.nyu.edu/web/Research/TechReports/TR2001-815/TR2001-815.pdf","raw_type":"text"},{"id":"pmh:oai:fraunhofer.de:B-73146","is_oa":true,"landing_page_url":"http://publica.fraunhofer.de/documents/B-73146.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer SCAI","raw_type":"Report"},{"id":"pmh:oai:fraunhofer.de:N-16839","is_oa":false,"landing_page_url":"http://publica.fraunhofer.de/documents/N-16839.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400801","display_name":"Publikationsdatenbank der Fraunhofer-Gesellschaft (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer SCAI","raw_type":"Journal Article"},{"id":"pmh:oai:publica.fraunhofer.de:publica/202715","is_oa":false,"landing_page_url":"https://publica.fraunhofer.de/handle/publica/202715","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"journal article"}],"best_oa_location":{"id":"pmh:oai:fraunhofer.de:B-73146","is_oa":true,"landing_page_url":"http://publica.fraunhofer.de/documents/B-73146.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306400318","display_name":"Fraunhofer-Publica (Fraunhofer-Gesellschaft)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4923324","host_organization_name":"Fraunhofer-Gesellschaft","host_organization_lineage":["https://openalex.org/I4923324"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Fraunhofer SCAI","raw_type":"Report"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W51910955","https://openalex.org/W224358741","https://openalex.org/W1596095530","https://openalex.org/W1971812145","https://openalex.org/W1979436246","https://openalex.org/W1988570599","https://openalex.org/W1992110290","https://openalex.org/W1994934002","https://openalex.org/W2018834578","https://openalex.org/W2021257096","https://openalex.org/W2024179839","https://openalex.org/W2042248875","https://openalex.org/W2051588145","https://openalex.org/W2052706416","https://openalex.org/W2063806054","https://openalex.org/W2077157253","https://openalex.org/W2082804737","https://openalex.org/W2159959193","https://openalex.org/W2509362106","https://openalex.org/W2557433803","https://openalex.org/W2568960970","https://openalex.org/W2622475459","https://openalex.org/W2624162218","https://openalex.org/W2750235028","https://openalex.org/W3166595295","https://openalex.org/W4232240772"],"related_works":["https://openalex.org/W2074745806","https://openalex.org/W2084064164","https://openalex.org/W2091647599","https://openalex.org/W4229577910","https://openalex.org/W2008273138","https://openalex.org/W2800324324","https://openalex.org/W2063806054","https://openalex.org/W2640255794","https://openalex.org/W2019221864","https://openalex.org/W2255375681"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"certain":[3],"iterative":[4,147],"substructuring":[5,148],"methods":[6,32,103,149],"with":[7,73],"Lagrange":[8],"multipliers":[9],"are":[10,123],"considered":[11],"for":[12,41,51,62],"elliptic":[13,42],"problems":[14,43,118],"in":[15,44,136],"three":[16,52],"dimensions.":[17],"The":[18,47],"algorithms":[19,50,72],"belong":[20],"to":[21,70],"the":[22,45,63,82,87,94,100,112,115,121,127,131,137],"family":[23,48],"of":[24,49,86,97,99,111,114,126,129,144,150],"dual-primal":[25,88,101],"finite":[26],"element":[27],"tearing":[28],"and":[29,38,56,119,134],"interconnecting":[30],"(FETI)":[31],"which":[33],"recently":[34],"have":[35],"been":[36],"introduced":[37],"analyzed":[39],"successfully":[40],"plane.":[46],"dimensions":[53],"is":[54,60,68,91],"extended":[55],"a":[57,74,109],"full":[58],"analysis":[59],"provided":[61],"new":[64],"algorithms.":[65],"Particular":[66],"attention":[67],"paid":[69],"finding":[71],"small":[75],"primal":[76,151],"subspace":[77,80],"since":[78],"that":[79,93,120],"represents":[81],"only":[83],"global":[84],"part":[85],"preconditioner.":[89],"It":[90],"shown":[92],"condition":[95],"numbers":[96],"several":[98],"FETI":[102],"can":[104],"be":[105],"bounded":[106],"polylogarithmically":[107],"as":[108,152,154],"function":[110],"dimension":[113],"individual":[116],"subregion":[117],"bounds":[122],"otherwise":[124],"independent":[125],"number":[128],"subdomains,":[130],"mesh":[132],"size,":[133],"jumps":[135],"coefficients.":[138],"These":[139],"results":[140],"closely":[141],"parallel":[142],"those":[143],"other":[145],"successful":[146],"well":[153],"dual":[155],"type.":[156]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":8},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":7},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":12},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":10},{"year":2013,"cited_by_count":18},{"year":2012,"cited_by_count":14}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}