{"id":"https://openalex.org/W2084073638","doi":"https://doi.org/10.1137/s106482759732678x","title":"A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems","display_name":"A Restricted Additive Schwarz Preconditioner for General Sparse Linear Systems","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2084073638","doi":"https://doi.org/10.1137/s106482759732678x","mag":"2084073638"},"language":"en","primary_location":{"id":"doi:10.1137/s106482759732678x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759732678x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5006367748","display_name":"Xiao\u2010Chuan Cai","orcid":"https://orcid.org/0000-0003-0296-8640"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xiao-Chuan Cai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5025777901","display_name":"Marcus Sarkis","orcid":null},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Marcus Sarkis","raw_affiliation_strings":["Worcester Polytechnic Institute"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.741,"has_fulltext":false,"cited_by_count":603,"citation_normalized_percentile":{"value":0.99246082,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"21","issue":"2","first_page":"792","last_page":"797"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.8192576169967651},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7806237936019897},{"id":"https://openalex.org/keywords/additive-schwarz-method","display_name":"Additive Schwarz method","score":0.640560507774353},{"id":"https://openalex.org/keywords/schwarz-alternating-method","display_name":"Schwarz alternating method","score":0.6403200626373291},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47107449173927307},{"id":"https://openalex.org/keywords/domain-decomposition-methods","display_name":"Domain decomposition methods","score":0.3955634534358978},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.36573559045791626},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.22182920575141907},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.11761030554771423}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8192576169967651},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7806237936019897},{"id":"https://openalex.org/C174819683","wikidata":"https://www.wikidata.org/wiki/Q4681340","display_name":"Additive Schwarz method","level":4,"score":0.640560507774353},{"id":"https://openalex.org/C31278502","wikidata":"https://www.wikidata.org/wiki/Q7433186","display_name":"Schwarz alternating method","level":4,"score":0.6403200626373291},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47107449173927307},{"id":"https://openalex.org/C198880260","wikidata":"https://www.wikidata.org/wiki/Q5289813","display_name":"Domain decomposition methods","level":3,"score":0.3955634534358978},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.36573559045791626},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.22182920575141907},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.11761030554771423},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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":7,"locations":[{"id":"doi:10.1137/s106482759732678x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759732678x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.wpi.edu:mathematicalsciences-pubs-1037","is_oa":false,"landing_page_url":"https://digitalcommons.wpi.edu/cgi/viewcontent.cgi?article=1037&context=mathematicalsciences-pubs","pdf_url":null,"source":{"id":"https://openalex.org/S4377196141","display_name":"Digital WPI","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Sciences Faculty Publications","raw_type":"text"},{"id":"pmh:ADA448279","is_oa":false,"landing_page_url":"http://oai.dtic.mil/oai/oai?&amp;verb=getRecord&amp;metadataPrefix=html&amp;identifier=ADA448279","pdf_url":null,"source":{"id":"https://openalex.org/S4406923043","display_name":"Defense Technical Information Center (DTIC)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"DTIC","raw_type":"Text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.132.4138","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.132.4138","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.colorado.edu/~cai/papers/ras.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.46.1448","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.46.1448","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.colorado.edu/homes/cai/public_html/papers/ras.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.595.1062","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.595.1062","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://users.wpi.edu/~msarkis/papers/CDS03.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.850.5217","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.850.5217","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://digitalcommons.wpi.edu/cgi/viewcontent.cgi?article%3D1041%26context%3Dmathematicalsciences-pubs","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1534237538","https://openalex.org/W1542243431","https://openalex.org/W1647103664","https://openalex.org/W1830282431","https://openalex.org/W1976538983","https://openalex.org/W2010521901","https://openalex.org/W2049664825","https://openalex.org/W2074062009","https://openalex.org/W2077157253","https://openalex.org/W2093052046","https://openalex.org/W2104126767","https://openalex.org/W2140153041","https://openalex.org/W2509362106","https://openalex.org/W4239804747"],"related_works":["https://openalex.org/W2140013918","https://openalex.org/W2008215882","https://openalex.org/W1623009832","https://openalex.org/W2050028993","https://openalex.org/W2953099512","https://openalex.org/W2963172443","https://openalex.org/W2040702578","https://openalex.org/W1033826287","https://openalex.org/W2082742450","https://openalex.org/W2219976283"],"abstract_inverted_index":{".":[0],"We":[1],"introduce":[2,104],"some":[3,105],"cheaper":[4],"and":[5,20,39,67,78,132],"faster":[6],"variants":[7],"of":[8,35,69],"the":[9,26,45],"classical":[10],"additive":[11,108,117],"Schwarz":[12,109,118],"preconditioner":[13],"(AS)":[14,120],"for":[15,58,111,123],"general":[16],"sparse":[17,91,112],"linear":[18,65,113],"systems":[19,66,68],"show,":[21],"by":[22],"numerical":[23],"examples,":[24],"that":[25],"new":[27],"methods":[28],"are":[29,81],"superior":[30],"to":[31,136],"AS":[32],"in":[33],"terms":[34],"both":[36],"iteration":[37],"counts":[38],"CPU":[40],"time,":[41],"as":[42,44,62],"well":[43],"communication":[46],"cost":[47],"when":[48],"implemented":[49],"on":[50],"distributed":[51],"memory":[52],"computers.":[53],"This":[54],"is":[55],"especially":[56],"true":[57],"harder":[59],"problems":[60],"such":[61],"indefinite":[63],"complex":[64],"convection-di#usion":[70],"equations":[71],"from":[72],"three-dimensional":[73],"compressible":[74],"flows.":[75],"Both":[76],"sequential":[77],"parallel":[79],"results":[80],"reported.":[82],"Key":[83],"words.":[84],"Overlapping":[85],"domain":[86],"decomposition,":[87],"preconditioner,":[88],"iterative":[89],"method,":[90],"matrix":[92],"AMS(MOS)":[93],"subject":[94],"classifications.":[95],"65N30,":[96],"65F10":[97],"1.":[98],"Introduction.":[99],"In":[100],"this":[101],"paper,":[102],"we":[103],"modified":[106],"overlapping":[107],"preconditioners":[110],"systems.":[114],"The":[115],"original":[116],"method":[119],"was":[121,133],"introduced":[122],"solving":[124],"symmetric":[125],"positive":[126],"definite":[127],"elliptic":[128],"finite":[129],"element":[130],"problems,":[131],"later":[134],"extended":[135],"many...":[137]},"counts_by_year":[{"year":2026,"cited_by_count":13},{"year":2025,"cited_by_count":21},{"year":2024,"cited_by_count":27},{"year":2023,"cited_by_count":32},{"year":2022,"cited_by_count":38},{"year":2021,"cited_by_count":28},{"year":2020,"cited_by_count":38},{"year":2019,"cited_by_count":35},{"year":2018,"cited_by_count":33},{"year":2017,"cited_by_count":42},{"year":2016,"cited_by_count":50},{"year":2015,"cited_by_count":30},{"year":2014,"cited_by_count":34},{"year":2013,"cited_by_count":28},{"year":2012,"cited_by_count":29}],"updated_date":"2026-06-13T07:54:00.901334","created_date":"2025-10-10T00:00:00"}
