{"id":"https://openalex.org/W1988546164","doi":"https://doi.org/10.2478/cmam-2012-0021","title":"Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems","display_name":"Schwarz Methods for a Preconditioned WOPSIP Method for Elliptic Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1988546164","doi":"https://doi.org/10.2478/cmam-2012-0021","mag":"1988546164"},"language":"en","primary_location":{"id":"doi:10.2478/cmam-2012-0021","is_oa":false,"landing_page_url":"https://doi.org/10.2478/cmam-2012-0021","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://ddd.uab.cat/record/181544","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063675442","display_name":"Paola F. Antonietti","orcid":"https://orcid.org/0000-0002-2138-3878"},"institutions":[{"id":"https://openalex.org/I93860229","display_name":"Politecnico di Milano","ror":"https://ror.org/01nffqt88","country_code":"IT","type":"education","lineage":["https://openalex.org/I93860229"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Paola F. Antonietti","raw_affiliation_strings":["1MOX--Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133 Milano, Italy"],"affiliations":[{"raw_affiliation_string":"1MOX--Laboratory for Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza Leondardo da Vinci 32, 20133 Milano, Italy","institution_ids":["https://openalex.org/I93860229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070027067","display_name":"Blanca Ayuso de Dios","orcid":"https://orcid.org/0000-0003-4144-6984"},"institutions":[{"id":"https://openalex.org/I4210122226","display_name":"Centre de Recerca Matem\u00e0tica","ror":"https://ror.org/020s51w82","country_code":"ES","type":"facility","lineage":["https://openalex.org/I4210122226","https://openalex.org/I4387153040"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Blanca Ayuso de Dios","raw_affiliation_strings":["2Centre de Recerca Matem\u00e1tica, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain"],"affiliations":[{"raw_affiliation_string":"2Centre de Recerca Matem\u00e1tica, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain","institution_ids":["https://openalex.org/I4210122226"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061146602","display_name":"Susanne C. Brenner","orcid":"https://orcid.org/0000-0001-8330-5667"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Susanne C. Brenner","raw_affiliation_strings":["3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA"],"affiliations":[{"raw_affiliation_string":"3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA","institution_ids":["https://openalex.org/I121820613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5106074354","display_name":"Li-yeng Sung","orcid":"https://orcid.org/0000-0002-6100-2160"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Li-yeng Sung","raw_affiliation_strings":["3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA"],"affiliations":[{"raw_affiliation_string":"3Department of Mathematics and Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803, USA","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5063675442"],"corresponding_institution_ids":["https://openalex.org/I93860229"],"apc_list":null,"apc_paid":null,"fwci":3.4976,"has_fulltext":true,"cited_by_count":19,"citation_normalized_percentile":{"value":0.9189538,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"12","issue":"3","first_page":"241","last_page":"272"},"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":1.0,"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":1.0,"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":0.9991999864578247,"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/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.8190796375274658},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8124424815177917},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.7078843116760254},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6775994300842285},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.6123078465461731},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5131838917732239},{"id":"https://openalex.org/keywords/penalty-method","display_name":"Penalty method","score":0.49441957473754883},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48345550894737244},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3800174295902252},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3505334258079529},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.32440847158432007},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.3102523684501648},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08024278283119202}],"concepts":[{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.8190796375274658},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8124424815177917},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.7078843116760254},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6775994300842285},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.6123078465461731},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5131838917732239},{"id":"https://openalex.org/C6180225","wikidata":"https://www.wikidata.org/wiki/Q3411771","display_name":"Penalty method","level":2,"score":0.49441957473754883},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48345550894737244},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3800174295902252},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3505334258079529},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.32440847158432007},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3102523684501648},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08024278283119202},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.2478/cmam-2012-0021","is_oa":false,"landing_page_url":"https://doi.org/10.2478/cmam-2012-0021","pdf_url":null,"source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:ddd.uab.cat:181544","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/181544","pdf_url":"https://ddd.uab.cat/record/181544","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":"","raw_type":"Article"},{"id":"pmh:oai:dnet:uabarcelona_::4033902caa3fce6a2da9c5703f7334a0","is_oa":true,"landing_page_url":"http://ddd.uab.cat/record/181544","pdf_url":"http://ddd.uab.cat/record/181544","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1147","is_oa":false,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/148","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:boa.unimib.it:10281/218260","is_oa":false,"landing_page_url":"http://hdl.handle.net/10281/218260","pdf_url":null,"source":{"id":"https://openalex.org/S4306401259","display_name":"BOA (University of Milano-Bicocca)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66752286","host_organization_name":"University of Milano-Bicocca","host_organization_lineage":["https://openalex.org/I66752286"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:cris.unibo.it:11585/384384","is_oa":false,"landing_page_url":"http://hdl.handle.net/11585/384384","pdf_url":null,"source":{"id":"https://openalex.org/S4306402579","display_name":"Archivio istituzionale della ricerca (Alma Mater Studiorum Universit\u00e0 di Bologna)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210117483","host_organization_name":"Istituto di Ematologia di Bologna","host_organization_lineage":["https://openalex.org/I4210117483"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:re.public.polimi.it:11311/662980","is_oa":false,"landing_page_url":"http://hdl.handle.net/11311/662980","pdf_url":null,"source":{"id":"https://openalex.org/S4306400312","display_name":"Virtual Community of Pathological Anatomy (University of Castilla La Mancha)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79189158","host_organization_name":"University of Castilla-La Mancha","host_organization_lineage":["https://openalex.org/I79189158"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:recercat.cat:2072/204379","is_oa":true,"landing_page_url":"http://hdl.handle.net/2072/204379","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"RECERCAT (Dip\u00f2sit de la Recerca de Catalunya)","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1147","is_oa":false,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/148","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:ddd.uab.cat:181544","is_oa":true,"landing_page_url":"https://ddd.uab.cat/record/181544","pdf_url":"https://ddd.uab.cat/record/181544","source":{"id":"https://openalex.org/S4306400380","display_name":"Dip\u00f2sit Digital de Documents de la UAB (Universitat Aut\u00f2noma de Barcelona)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I123044942","host_organization_name":"Universitat Aut\u00f2noma de Barcelona","host_organization_lineage":["https://openalex.org/I123044942"],"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":"","raw_type":"Article"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.7900000214576721}],"awards":[],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W1988546164.pdf"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W155934647","https://openalex.org/W1540854488","https://openalex.org/W1548589512","https://openalex.org/W1963652405","https://openalex.org/W1966869202","https://openalex.org/W1979771104","https://openalex.org/W1983110265","https://openalex.org/W1984473207","https://openalex.org/W1988228958","https://openalex.org/W1992066344","https://openalex.org/W2029591011","https://openalex.org/W2040011362","https://openalex.org/W2097060633","https://openalex.org/W2105777174","https://openalex.org/W2129977146","https://openalex.org/W2130350269","https://openalex.org/W2134819391","https://openalex.org/W2149216460","https://openalex.org/W2415509676","https://openalex.org/W2466926104"],"related_works":["https://openalex.org/W2902154408","https://openalex.org/W1515964003","https://openalex.org/W2504287632","https://openalex.org/W1994696552","https://openalex.org/W3046643187","https://openalex.org/W2286395548","https://openalex.org/W4241403127","https://openalex.org/W1423765865","https://openalex.org/W2493580937","https://openalex.org/W132556536"],"abstract_inverted_index":{"Abstract":[0],"We":[1,27],"propose":[2],"and":[3,34,53,61,70],"analyze":[4],"several":[5],"two-level":[6,83],"non-overlapping":[7],"Schwarz":[8,84],"methods":[9,85],"for":[10],"a":[11,21],"preconditioned":[12,42],"weakly":[13],"over-penalized":[14],"symmetric":[15],"interior":[16],"penalty":[17,51],"(WOPSIP)":[18],"discretization":[19],"of":[20,39,45,49,55,67,80],"second":[22],"order":[23,56],"boundary":[24],"value":[25],"problem.":[26],"show":[28],"that":[29,35,76],"the":[30,36,40,50,64,68,78,81],"preconditioners":[31],"are":[32,86],"scalable":[33],"condition":[37],"number":[38],"resulting":[41],"linear":[43],"systems":[44],"equations":[46],"is":[47,54],"independent":[48],"parameter":[52],"H/h":[57],",":[58],"where":[59],"H":[60],"h":[62],"represent":[63],"mesh":[65],"sizes":[66],"coarse":[69],"fine":[71],"partitions,":[72],"respectively.":[73],"Numerical":[74],"experiments":[75],"illustrate":[77],"performance":[79],"proposed":[82],"also":[87],"presented.":[88]},"counts_by_year":[{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
