{"id":"https://openalex.org/W2001371530","doi":"https://doi.org/10.1080/00207169008803864","title":"The explicit block relaxation method as a grid smoother in the multigrid v-cycle scheme","display_name":"The explicit block relaxation method as a grid smoother in the multigrid v-cycle scheme","publication_year":1990,"publication_date":"1990-01-01","ids":{"openalex":"https://openalex.org/W2001371530","doi":"https://doi.org/10.1080/00207169008803864","mag":"2001371530"},"language":"en","primary_location":{"id":"doi:10.1080/00207169008803864","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169008803864","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5050075410","display_name":"David Evans","orcid":"https://orcid.org/0009-0002-2834-6700"},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"D. J. Evans","raw_affiliation_strings":["Department of Computer Studies , Loughborough University of Technology , Loughborough, Leicestershire,  UK","Dept. of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Studies , Loughborough University of Technology , Loughborough, Leicestershire,  UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Dept. of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK","institution_ids":["https://openalex.org/I143804889"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5008301700","display_name":"W.S. Yousif","orcid":null},"institutions":[{"id":"https://openalex.org/I143804889","display_name":"Loughborough University","ror":"https://ror.org/04vg4w365","country_code":"GB","type":"education","lineage":["https://openalex.org/I143804889"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"W. S. Yousif","raw_affiliation_strings":["Department of Computer Studies , Loughborough University of Technology , Loughborough, Leicestershire,  UK","Dept. of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK"],"affiliations":[{"raw_affiliation_string":"Department of Computer Studies , Loughborough University of Technology , Loughborough, Leicestershire,  UK","institution_ids":["https://openalex.org/I143804889"]},{"raw_affiliation_string":"Dept. of Computer Studies, Loughborough University of Technology, Loughborough, Leicestershire, UK","institution_ids":["https://openalex.org/I143804889"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5050075410"],"corresponding_institution_ids":["https://openalex.org/I143804889"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.1338209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"34","issue":"1-2","first_page":"71","last_page":"78"},"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":0.9991000294685364,"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":0.9991000294685364,"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":0.998199999332428,"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"}},{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.996999979019165,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.936363697052002},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7271474599838257},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.7219241857528687},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6916865110397339},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6057254672050476},{"id":"https://openalex.org/keywords/gauss\u2013seidel-method","display_name":"Gauss\u2013Seidel method","score":0.5800861120223999},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5703102946281433},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.49356353282928467},{"id":"https://openalex.org/keywords/gauss","display_name":"Gauss","score":0.45749032497406006},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3729674220085144},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3461827039718628},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.32527291774749756},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29993897676467896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2243397831916809},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.20542040467262268},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0563947856426239}],"concepts":[{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.936363697052002},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7271474599838257},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.7219241857528687},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6916865110397339},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6057254672050476},{"id":"https://openalex.org/C3828260","wikidata":"https://www.wikidata.org/wiki/Q1069090","display_name":"Gauss\u2013Seidel method","level":3,"score":0.5800861120223999},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5703102946281433},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.49356353282928467},{"id":"https://openalex.org/C161794534","wikidata":"https://www.wikidata.org/wiki/Q177493","display_name":"Gauss","level":2,"score":0.45749032497406006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3729674220085144},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3461827039718628},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.32527291774749756},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29993897676467896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2243397831916809},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.20542040467262268},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0563947856426239},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207169008803864","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207169008803864","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":4,"referenced_works":["https://openalex.org/W1530872699","https://openalex.org/W2056955017","https://openalex.org/W2127981460","https://openalex.org/W4230055019"],"related_works":["https://openalex.org/W2360606995","https://openalex.org/W2281025351","https://openalex.org/W2348990883","https://openalex.org/W1967449648","https://openalex.org/W2393794471","https://openalex.org/W2412311587","https://openalex.org/W2791022978","https://openalex.org/W2041113042","https://openalex.org/W2378486976","https://openalex.org/W2368937350"],"abstract_inverted_index":{"In":[0,15],"Yousif":[1],"and":[2,35,42],"Evans":[3],"[1],":[4],"different":[5],"explicit":[6],"block":[7],"methods":[8,24],"for":[9],"solving":[10],"elliptic":[11],"pde's":[12],"were":[13],"studied.":[14],"this":[16],"paper,":[17],"the":[18,30,38],"performance":[19],"of":[20,22],"some":[21],"these":[23],"as":[25],"a":[26],"grid":[27],"smoother":[28],"in":[29],"multigrid":[31],"method":[32],"is":[33],"investigated":[34],"compared":[36],"with":[37],"point":[39],"Gauss-Seidel":[40],"(GS)":[41],"successive":[43],"over":[44],"relaxation":[45],"(SOR)":[46],"methods.":[47]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}