{"id":"https://openalex.org/W2000675710","doi":"https://doi.org/10.1007/s00211-011-0401-4","title":"Optimal multilevel methods for graded bisection grids","display_name":"Optimal multilevel methods for graded bisection grids","publication_year":2011,"publication_date":"2011-07-20","ids":{"openalex":"https://openalex.org/W2000675710","doi":"https://doi.org/10.1007/s00211-011-0401-4","mag":"2000675710"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-011-0401-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0401-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5100336427","display_name":"Long Chen","orcid":"https://orcid.org/0000-0003-0184-5446"},"institutions":[{"id":"https://openalex.org/I204250578","display_name":"University of California, Irvine","ror":"https://ror.org/04gyf1771","country_code":"US","type":"education","lineage":["https://openalex.org/I204250578"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Long Chen","raw_affiliation_strings":["Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of California at Irvine, Irvine, CA, 92697, USA","institution_ids":["https://openalex.org/I204250578"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5040883953","display_name":"Ricardo H. Nochetto","orcid":"https://orcid.org/0009-0002-8895-1144"},"institutions":[{"id":"https://openalex.org/I66946132","display_name":"University of Maryland, College Park","ror":"https://ror.org/047s2c258","country_code":"US","type":"education","lineage":["https://openalex.org/I66946132"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ricardo H. Nochetto","raw_affiliation_strings":["Department of Mathematics, University of Maryland, College Park, MD, 20742, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Maryland, College Park, MD, 20742, USA","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014166483","display_name":"Jinchao Xu","orcid":"https://orcid.org/0000-0002-1530-6913"},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]},{"id":"https://openalex.org/I20231570","display_name":"Peking University","ror":"https://ror.org/02v51f717","country_code":"CN","type":"education","lineage":["https://openalex.org/I20231570"]}],"countries":["CN","US"],"is_corresponding":false,"raw_author_name":"Jinchao Xu","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, University Park, PA, 16801, USA","The School of Mathematical Science, Peking University, Beijing, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, University Park, PA, 16801, USA","institution_ids":["https://openalex.org/I130769515"]},{"raw_affiliation_string":"The School of Mathematical Science, Peking University, Beijing, China","institution_ids":["https://openalex.org/I20231570"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5100336427"],"corresponding_institution_ids":["https://openalex.org/I204250578"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.7042,"has_fulltext":false,"cited_by_count":50,"citation_normalized_percentile":{"value":0.71006411,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"120","issue":"1","first_page":"1","last_page":"34"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9980999827384949,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.996999979019165,"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/bisection-method","display_name":"Bisection method","score":0.8135322332382202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7541252374649048},{"id":"https://openalex.org/keywords/bisection","display_name":"Bisection","score":0.623125433921814},{"id":"https://openalex.org/keywords/smoothing","display_name":"Smoothing","score":0.6184321045875549},{"id":"https://openalex.org/keywords/multiplicative-function","display_name":"Multiplicative function","score":0.6025536060333252},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5591200590133667},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4825822412967682},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4798423945903778},{"id":"https://openalex.org/keywords/decomposition-method","display_name":"Decomposition method (queueing theory)","score":0.44362467527389526},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.4341583549976349},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43061214685440063},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3697212338447571},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.31867459416389465},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28045374155044556},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1283136010169983},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12614211440086365},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.11596518754959106}],"concepts":[{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.8135322332382202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7541252374649048},{"id":"https://openalex.org/C31599958","wikidata":"https://www.wikidata.org/wiki/Q3128632","display_name":"Bisection","level":2,"score":0.623125433921814},{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.6184321045875549},{"id":"https://openalex.org/C42747912","wikidata":"https://www.wikidata.org/wiki/Q1048447","display_name":"Multiplicative function","level":2,"score":0.6025536060333252},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5591200590133667},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4825822412967682},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4798423945903778},{"id":"https://openalex.org/C2778258933","wikidata":"https://www.wikidata.org/wiki/Q16918986","display_name":"Decomposition method (queueing theory)","level":2,"score":0.44362467527389526},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.4341583549976349},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43061214685440063},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3697212338447571},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.31867459416389465},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28045374155044556},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1283136010169983},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12614211440086365},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.11596518754959106},{"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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s00211-011-0401-4","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-011-0401-4","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.227.9077","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.227.9077","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.umd.edu/%7Erhn/papers/pdf/multilevel.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.41999998688697815}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":70,"referenced_works":["https://openalex.org/W20824204","https://openalex.org/W48069542","https://openalex.org/W101816209","https://openalex.org/W136882936","https://openalex.org/W184188664","https://openalex.org/W393218382","https://openalex.org/W965126270","https://openalex.org/W1488071155","https://openalex.org/W1523673167","https://openalex.org/W1530115438","https://openalex.org/W1548892666","https://openalex.org/W1559891132","https://openalex.org/W1576769952","https://openalex.org/W1592589766","https://openalex.org/W1913407073","https://openalex.org/W1963991060","https://openalex.org/W1970733603","https://openalex.org/W1977851468","https://openalex.org/W1978687734","https://openalex.org/W1983072269","https://openalex.org/W1988975817","https://openalex.org/W1995479616","https://openalex.org/W1997831216","https://openalex.org/W1999953445","https://openalex.org/W2000192542","https://openalex.org/W2009985306","https://openalex.org/W2015740317","https://openalex.org/W2017085690","https://openalex.org/W2018685527","https://openalex.org/W2020626918","https://openalex.org/W2030199904","https://openalex.org/W2033698269","https://openalex.org/W2034298604","https://openalex.org/W2035450252","https://openalex.org/W2039924562","https://openalex.org/W2042491177","https://openalex.org/W2044959876","https://openalex.org/W2047586811","https://openalex.org/W2048171329","https://openalex.org/W2059340658","https://openalex.org/W2060573511","https://openalex.org/W2062246266","https://openalex.org/W2071036364","https://openalex.org/W2071182807","https://openalex.org/W2072463419","https://openalex.org/W2072811159","https://openalex.org/W2074992689","https://openalex.org/W2084743165","https://openalex.org/W2088963353","https://openalex.org/W2089704477","https://openalex.org/W2093538658","https://openalex.org/W2094820085","https://openalex.org/W2095044295","https://openalex.org/W2096545304","https://openalex.org/W2103343860","https://openalex.org/W2103576314","https://openalex.org/W2107813568","https://openalex.org/W2124214067","https://openalex.org/W2137498124","https://openalex.org/W2142467748","https://openalex.org/W2150061371","https://openalex.org/W2151317657","https://openalex.org/W2492054050","https://openalex.org/W2911695249","https://openalex.org/W3147515309","https://openalex.org/W3147602598","https://openalex.org/W4205354563","https://openalex.org/W4240495313","https://openalex.org/W4285719527","https://openalex.org/W6618464575"],"related_works":["https://openalex.org/W2329494729","https://openalex.org/W41290553","https://openalex.org/W3112697985","https://openalex.org/W1986919722","https://openalex.org/W2585516632","https://openalex.org/W2093663313","https://openalex.org/W4296983618","https://openalex.org/W2158390333","https://openalex.org/W40332083","https://openalex.org/W2577097539"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
