{"id":"https://openalex.org/W2148028437","doi":"https://doi.org/10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","title":"Downwind Gau\u00df-Seidel Smoothing for Convection Dominated Problems","display_name":"Downwind Gau\u00df-Seidel Smoothing for Convection Dominated Problems","publication_year":1997,"publication_date":"1997-03-01","ids":{"openalex":"https://openalex.org/W2148028437","doi":"https://doi.org/10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","mag":"2148028437"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","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/A5084653980","display_name":"Wolfgang Hackbusch","orcid":"https://orcid.org/0000-0002-4801-6189"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Wolfgang Hackbusch","raw_affiliation_strings":["Praktische Mathematik, Christian-Albrechts-Universita\u0308t zu Kiel, D-24098 Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Praktische Mathematik, Christian-Albrechts-Universita\u0308t zu Kiel, D-24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5031578653","display_name":"Thomas Probst","orcid":"https://orcid.org/0000-0002-2213-104X"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Kiel University","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Thomas Probst","raw_affiliation_strings":["Praktische Mathematik, Christian-Albrechts-Universita\u0308t zu Kiel, D-24098 Kiel, Germany"],"affiliations":[{"raw_affiliation_string":"Praktische Mathematik, Christian-Albrechts-Universita\u0308t zu Kiel, D-24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5084653980"],"corresponding_institution_ids":["https://openalex.org/I32021983"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":6.2542,"has_fulltext":false,"cited_by_count":47,"citation_normalized_percentile":{"value":0.97152245,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"4","issue":"2","first_page":"85","last_page":"102"},"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9966999888420105,"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":0.9904000163078308,"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/smoothing","display_name":"Smoothing","score":0.8507646918296814},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8105015754699707},{"id":"https://openalex.org/keywords/numbering","display_name":"Numbering","score":0.6833183765411377},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5642598271369934},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5240552425384521},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4983341693878174},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4864025413990021},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43306270241737366},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.43305355310440063},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.345308780670166},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.24622291326522827},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.16064578294754028},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1029936671257019}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.8507646918296814},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8105015754699707},{"id":"https://openalex.org/C191916993","wikidata":"https://www.wikidata.org/wiki/Q362019","display_name":"Numbering","level":2,"score":0.6833183765411377},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5642598271369934},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5240552425384521},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4983341693878174},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4864025413990021},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43306270241737366},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.43305355310440063},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.345308780670166},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.24622291326522827},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.16064578294754028},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1029936671257019},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199703/04)4:2<85::aid-nla100>3.0.co;2-2","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.42.503","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.42.503","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cerfacs.fr/~douglas/mgnet/www/mgnet/www/mgnet/Conferences/P6/proceedings/hackbusch-probst.ps.gz","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1484796445","https://openalex.org/W1528831725","https://openalex.org/W2032641095","https://openalex.org/W2126036157","https://openalex.org/W2480154215","https://openalex.org/W2577784986","https://openalex.org/W4230055019","https://openalex.org/W6633037889","https://openalex.org/W6635142151","https://openalex.org/W6678923562"],"related_works":["https://openalex.org/W2380905223","https://openalex.org/W2316187651","https://openalex.org/W2791022978","https://openalex.org/W2041113042","https://openalex.org/W1987155966","https://openalex.org/W2051913886","https://openalex.org/W2040023267","https://openalex.org/W2001371530","https://openalex.org/W2463445492","https://openalex.org/W1989504412"],"abstract_inverted_index":{"In":[0],"the":[1,30,44,50,58,63,67,71,104,119,122],"case":[2,45],"of":[3,29,46,114,121],"convection":[4,48,72],"dominated":[5],"problems,":[6],"multigrid":[7,51],"methods":[8],"require":[9],"an":[10,101],"appropriate":[11],"smoothing":[12,24],"to":[13,91],"ensure":[14],"robustness.":[15],"As":[16],"a":[17,22,26,35,78,95,111],"first":[18],"approach":[19],"we":[20,76],"discuss":[21],"Gauss\u2013Seidel":[23,97],"with":[25],"correct":[27],"numbering":[28,79],"unknowns":[31],"and":[32],"if":[33],"necessary":[34],"special":[36,92],"block":[37],"partitioning.":[38],"Numerical":[39],"experiments":[40],"show":[41],"that,":[42],"in":[43,54,62,118],"general":[47],"directions,":[49],"algorithms":[52],"obtained":[53],"this":[55],"way":[56],"have":[57],"same":[59],"properties":[60],"as":[61],"model":[64],"situation.":[65],"If":[66],"graph":[68],"arising":[69],"from":[70],"part":[73],"is":[74,82],"acyclic,":[75],"describe":[77,100],"algorithm":[80,102,109],"which":[81],"valid":[83],"for":[84,94,103],"all":[85],"spatial":[86],"dimensions.":[87],"Cycles":[88],"give":[89],"rise":[90],"blocks":[93],"blockwise":[96],"smoothing.":[98],"We":[99],"two-dimensional":[105],"case.":[106],"The":[107],"proposed":[108],"requires":[110],"computational":[112],"work":[113],"optimal":[115],"order":[116],"(linear":[117],"size":[120],"problem).":[123],"\u00a9":[124],"1997":[125],"by":[126],"John":[127],"Wiley":[128],"&":[129],"Sons,":[130],"Ltd.":[131]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}