{"id":"https://openalex.org/W2082399810","doi":"https://doi.org/10.1002/nla.1680020405","title":"Peaceman\u2014Rachford procedure and domain decomposition for finite element problems","display_name":"Peaceman\u2014Rachford procedure and domain decomposition for finite element problems","publication_year":1995,"publication_date":"1995-07-01","ids":{"openalex":"https://openalex.org/W2082399810","doi":"https://doi.org/10.1002/nla.1680020405","mag":"2082399810"},"language":"en","primary_location":{"id":"doi:10.1002/nla.1680020405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020405","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064202954","display_name":"William Layton","orcid":"https://orcid.org/0000-0002-2539-4478"},"institutions":[{"id":"https://openalex.org/I4780363","display_name":"Pittsburg State University","ror":"https://ror.org/04hteea03","country_code":"US","type":"education","lineage":["https://openalex.org/I4780363"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"William J. Layton","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Pittsburg, Pittsburg, PA 15260, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburg, Pittsburg, PA 15260, USA","institution_ids":["https://openalex.org/I4780363"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111859627","display_name":"Patrick J. Rabier","orcid":null},"institutions":[{"id":"https://openalex.org/I4780363","display_name":"Pittsburg State University","ror":"https://ror.org/04hteea03","country_code":"US","type":"education","lineage":["https://openalex.org/I4780363"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Patrick J. Rabier","raw_affiliation_strings":["Department of Mathematics and Statistics, University of Pittsburg, Pittsburg, PA 15260, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, University of Pittsburg, Pittsburg, PA 15260, USA","institution_ids":["https://openalex.org/I4780363"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5064202954"],"corresponding_institution_ids":["https://openalex.org/I4780363"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":4.3566,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.94278803,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"2","issue":"4","first_page":"363","last_page":"393"},"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":0.9997000098228455,"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":0.9997000098228455,"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":0.9995999932289124,"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/T12809","display_name":"Contact Mechanics and Variational Inequalities","score":0.9912999868392944,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.8234763741493225},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.735944926738739},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.6724928021430969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.596786618232727},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.5072035789489746},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.49121564626693726},{"id":"https://openalex.org/keywords/mortar-methods","display_name":"Mortar methods","score":0.4396754503250122},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.4020562171936035},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3679278492927551},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3606598973274231},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3347620964050293},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18227440118789673},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.1771252453327179},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.07879245281219482},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.07160589098930359},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04788526892662048}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.8234763741493225},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.735944926738739},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.6724928021430969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.596786618232727},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.5072035789489746},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.49121564626693726},{"id":"https://openalex.org/C97110765","wikidata":"https://www.wikidata.org/wiki/Q17099078","display_name":"Mortar methods","level":4,"score":0.4396754503250122},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4020562171936035},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3679278492927551},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3606598973274231},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3347620964050293},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18227440118789673},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.1771252453327179},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.07879245281219482},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.07160589098930359},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04788526892662048},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/nla.1680020405","is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.1680020405","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":17,"referenced_works":["https://openalex.org/W85719053","https://openalex.org/W1532656300","https://openalex.org/W1605975348","https://openalex.org/W1989316443","https://openalex.org/W2001196128","https://openalex.org/W2007484011","https://openalex.org/W2021810545","https://openalex.org/W2034722767","https://openalex.org/W2043581458","https://openalex.org/W2053262745","https://openalex.org/W2060170348","https://openalex.org/W2072318795","https://openalex.org/W2072835905","https://openalex.org/W2095036901","https://openalex.org/W2113486502","https://openalex.org/W2150323068","https://openalex.org/W2592623476"],"related_works":["https://openalex.org/W286248473","https://openalex.org/W2412889084","https://openalex.org/W2092836554","https://openalex.org/W3145205507","https://openalex.org/W2059321831","https://openalex.org/W1253925978","https://openalex.org/W170868261","https://openalex.org/W2045656285","https://openalex.org/W2778061477","https://openalex.org/W2077112581"],"abstract_inverted_index":{"Abstract":[0],"This":[1,97],"paper":[2],"presents":[3],"a":[4,17,74,129,156],"general":[5,102],"method":[6,44,91,144],"to":[7,127,138],"associate":[8],"the":[9,13,20,46,51,55,77,108,118,134,143],"operator":[10],"splitting":[11,109],"for":[12,64,82,103],"Peaceman\u2014Rachford":[14,56],"procedure":[15,123],"with":[16],"decomposition":[18],"of":[19,29,49,54,76,85,133],"domain":[21],"in":[22,101],"problems":[23,105],"arising":[24],"from":[25],"finite":[26,87,120],"element":[27,88,121],"discretization":[28],"partial":[30],"differential":[31],"equations.":[32],"The":[33],"algorithm":[34,110],"is":[35,69,145],"provably":[36],"convergent":[37,147],"without":[38],"any":[39],"symmetry":[40],"requirement.":[41],"Moreover,":[42],"this":[43,90],"possesses":[45],"significant":[47],"advantage":[48],"making":[50],"linear":[52],"systems":[53],"iteration":[57],"block":[58],"diagonal":[59],"and":[60,124,148],"therefore":[61],"perfectly":[62],"appropriate":[63,83],"parallel":[65],"processing.":[66,96],"Not":[67],"only":[68],"sparsity":[70],"not":[71],"affected":[72],"but":[73],"reduction":[75],"bandwidth":[78],"occurs.":[79],"In":[80,136],"fact,":[81],"choices":[84],"nonconforming":[86],"spaces,":[89],"makes":[92],"directly":[93],"possible":[94],"elementwise":[95],"option":[98],"remains":[99,149],"available":[100],"higher\u2010dimensional":[104],"by":[106],"applying":[107],"recursively.":[111],"Practical":[112],"implementation":[113],"requires":[114],"nothing":[115],"more":[116],"than":[117],"standard":[119],"assembly":[122],"some":[125],"bookkeeping":[126],"relate":[128],"few":[130],"different":[131],"orderings":[132],"nodes.":[135],"addition":[137],"all":[139],"these":[140],"attractive":[141],"features,":[142],"rapidly":[146],"highly":[150],"competitive":[151],"even":[152],"when":[153],"used":[154],"on":[155],"serial":[157],"machine.":[158]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}