{"id":"https://openalex.org/W1987187554","doi":"https://doi.org/10.1137/05063790x","title":"On a Parallel Robin\u2010Type Nonoverlapping Domain Decomposition Method","display_name":"On a Parallel Robin\u2010Type Nonoverlapping Domain Decomposition Method","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W1987187554","doi":"https://doi.org/10.1137/05063790x","mag":"1987187554"},"language":"en","primary_location":{"id":"doi:10.1137/05063790x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063790x","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080291324","display_name":"Lizhen Qin","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Lizhen Qin","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080291324"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.5444,"has_fulltext":false,"cited_by_count":42,"citation_normalized_percentile":{"value":0.87967923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"44","issue":"6","first_page":"2539","last_page":"2558"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.853753924369812},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8136961460113525},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6322664022445679},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6216344237327576},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5873191356658936},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5376651883125305},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5225502848625183},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5011811256408691},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.43922558426856995},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.36124417185783386},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35764992237091064},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3501047194004059},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09999647736549377},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.08477121591567993}],"concepts":[{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.853753924369812},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8136961460113525},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6322664022445679},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6216344237327576},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5873191356658936},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5376651883125305},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5225502848625183},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5011811256408691},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.43922558426856995},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.36124417185783386},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35764992237091064},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3501047194004059},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09999647736549377},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.08477121591567993},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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},{"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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/05063790x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/05063790x","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"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Quality Education","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W175880062","https://openalex.org/W1503942291","https://openalex.org/W1979771104","https://openalex.org/W1987152170","https://openalex.org/W1987240068","https://openalex.org/W2000582360","https://openalex.org/W2015280312","https://openalex.org/W2021037854","https://openalex.org/W2032539100","https://openalex.org/W2041523977","https://openalex.org/W2045642207","https://openalex.org/W2067497474","https://openalex.org/W2102016474","https://openalex.org/W2171622994","https://openalex.org/W2326261353","https://openalex.org/W2509362106","https://openalex.org/W2512076211","https://openalex.org/W2789204947"],"related_works":["https://openalex.org/W1857348759","https://openalex.org/W596860038","https://openalex.org/W2153233687","https://openalex.org/W2286395548","https://openalex.org/W4211094555","https://openalex.org/W2504287632","https://openalex.org/W4288364146","https://openalex.org/W2061746173","https://openalex.org/W2940897047","https://openalex.org/W2005295558"],"abstract_inverted_index":{"In":[0,145],"recent":[1],"years,":[2],"a":[3,127],"nonoverlapping":[4,62],"Robin\u2010type":[5,27],"domain":[6],"decomposition":[7],"method":[8,57],"(DDM)":[9],"for":[10,61,75],"the":[11,17,35,54,67,86,98,124,135,141,149,169,172],"finite":[12],"element":[13],"discretization":[14],"systems":[15],"of":[16,66,89,101,126,130,143,164],"second":[18],"order":[19,146],"elliptic":[20],"equations,":[21],"which":[22],"is":[23,116,134,140,162,171],"based":[24],"on":[25,34,71],"using":[26],"boundary":[28],"conditions":[29,33],"as":[30],"information":[31],"transmission":[32],"subdomain":[36],"interfaces,":[37],"has":[38],"been":[39],"developed":[40],"and":[41,138,168],"analyzed":[42],"since":[43],"it":[44],"was":[45],"first":[46],"proposed":[47],"by":[48],"P.":[49],"L.":[50],"Lions":[51],"in":[52,64,110,120,158],"[On":[53],"Schwarz":[55],"alternating":[56],"III:":[58],"A":[59],"variant":[60],"subdomains,":[63,131],"Proceedings":[65],"3rd":[68],"International":[69],"Symposium":[70],"Domain":[72],"Decomposition":[73],"Methods":[74],"Partial":[76],"Differential":[77],"Equations,":[78],"SIAM,":[79],"Philadelphia,":[80],"PA,":[81],"1990,":[82],"pp.":[83],"202\u2013223].":[84],"However,":[85],"convergence":[87,114,151],"rate":[88,115],"this":[90,111,159],"DDM":[91],"with":[92],"many":[93],"subdomains":[94],"remains":[95],"open":[96,105],"when":[97],"lower":[99],"term":[100],"equations":[102],"vanishes.":[103],"This":[104],"problem":[106],"will":[107],"be":[108],"considered":[109],"paper.":[112],"The":[113],"almost":[117],"$1-O(h^{1/2}":[118],"H^{-1/2})$":[119],"certain":[121],"cases\u2014for":[122],"example,":[123],"case":[125],"small":[128],"number":[129],"where":[132],"h":[133],"mesh":[136],"size":[137,142],"H":[139],"subdomain.":[144],"to":[147],"get":[148],"desirous":[150],"results,":[152],"two":[153],"mathematics":[154],"skills":[155],"are":[156],"introduced":[157],"paper;":[160],"one":[161],"complexification":[163],"real":[165],"linear":[166],"space":[167],"other":[170],"spectral":[173],"radius":[174],"formula.":[175]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":5}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
