{"id":"https://openalex.org/W1970588051","doi":"https://doi.org/10.1137/100805248","title":"Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids","display_name":"Multilevel Methods for Elliptic Problems with Highly Varying Coefficients on Nonaligned Coarse Grids","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1970588051","doi":"https://doi.org/10.1137/100805248","mag":"1970588051"},"language":"en","primary_location":{"id":"doi:10.1137/100805248","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100805248","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":true,"oa_status":"green","oa_url":"https://www.osti.gov/servlets/purl/1226946","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050544926","display_name":"Robert Scheichl","orcid":"https://orcid.org/0000-0001-8493-4393"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Robert Scheichl","raw_affiliation_strings":["Department of Mathematical Sciences"],"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":["Lawrence Livermore National Laboratory"],"affiliations":[{"raw_affiliation_string":"Lawrence Livermore National Laboratory","institution_ids":["https://openalex.org/I1282311441"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074536850","display_name":"Ludmil Zikatanov","orcid":"https://orcid.org/0000-0002-5189-4230"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ludmil T. Zikatanov","raw_affiliation_strings":["Mathematics"],"affiliations":[{"raw_affiliation_string":"Mathematics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050544926"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.6958,"has_fulltext":true,"cited_by_count":35,"citation_normalized_percentile":{"value":0.97756241,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"3","first_page":"1675","last_page":"1694"},"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":1.0,"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":1.0,"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":0.9997000098228455,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9990000128746033,"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/mathematics","display_name":"Mathematics","score":0.7901400327682495},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.774781346321106},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7283159494400024},{"id":"https://openalex.org/keywords/piecewise","display_name":"Piecewise","score":0.5813271999359131},{"id":"https://openalex.org/keywords/piecewise-linear-function","display_name":"Piecewise linear function","score":0.5017132759094238},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47945013642311096},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.4692855775356293},{"id":"https://openalex.org/keywords/partition","display_name":"Partition (number theory)","score":0.46660205721855164},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33630144596099854},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.27629944682121277},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11144348978996277},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.09652358293533325}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7901400327682495},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.774781346321106},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7283159494400024},{"id":"https://openalex.org/C164660894","wikidata":"https://www.wikidata.org/wiki/Q2037833","display_name":"Piecewise","level":2,"score":0.5813271999359131},{"id":"https://openalex.org/C17095337","wikidata":"https://www.wikidata.org/wiki/Q2375229","display_name":"Piecewise linear function","level":2,"score":0.5017132759094238},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47945013642311096},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.4692855775356293},{"id":"https://openalex.org/C42812","wikidata":"https://www.wikidata.org/wiki/Q1082910","display_name":"Partition (number theory)","level":2,"score":0.46660205721855164},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33630144596099854},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.27629944682121277},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11144348978996277},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.09652358293533325},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/100805248","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100805248","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"},{"id":"pmh:oai:osti.gov:1226946","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1226946","pdf_url":"https://www.osti.gov/servlets/purl/1226946","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},{"id":"pmh:oai:opus.bath.ac.uk:31605","is_oa":false,"landing_page_url":"http://opus.bath.ac.uk/31605/1/Scheichl_SINUM_2012_50_3_1675.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401631","display_name":"The University of Bath Online Publications Store (The University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Articles"},{"id":"pmh:oai:purehost.bath.ac.uk:openaire/60ef3ed8-b8b3-4f93-b826-48f6df3c64d2","is_oa":true,"landing_page_url":"https://researchportal.bath.ac.uk/en/publications/60ef3ed8-b8b3-4f93-b826-48f6df3c64d2","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Scheichl, R, Vassilevski, P S & Zikatanov, L T 2012, 'Multilevel methods for elliptic problems with highly varying coefficients on nonaligned coarse grids', SIAM Journal on Numerical Analysis (SINUM), vol. 50, no. 3, pp. 1675-1694. https://doi.org/10.1137/100805248","raw_type":"article"},{"id":"pmh:oai:purehost.bath.ac.uk:publications/60ef3ed8-b8b3-4f93-b826-48f6df3c64d2","is_oa":false,"landing_page_url":"http://www.scopus.com/inward/record.url?scp=84865592671&partnerID=8YFLogxK","pdf_url":null,"source":{"id":"https://openalex.org/S4377196294","display_name":"Pure (University of Bath)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I51601045","host_organization_name":"University of Bath","host_organization_lineage":["https://openalex.org/I51601045"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""}],"best_oa_location":{"id":"pmh:oai:osti.gov:1226946","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1226946","pdf_url":"https://www.osti.gov/servlets/purl/1226946","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1494814522","display_name":null,"funder_award_id":"DE_AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G2917824471","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3391580208","display_name":null,"funder_award_id":"DE-AC52-07NA2","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G397776097","display_name":"Collaborative Research:    Multigrid QCD at the Petascale","funder_award_id":"0749202","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4711444667","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5816449448","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5964142490","display_name":null,"funder_award_id":"E-AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G6020043373","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G7482766386","display_name":"Collaborative Research:  Algebraic Multigrid Methods:  Multilevel Theory and Practice","funder_award_id":"0810982","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7806955302","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8374966015","display_name":null,"funder_award_id":"AC52-07NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8658770765","display_name":null,"funder_award_id":"DE-AC52-07NA27","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G930637315","display_name":null,"funder_award_id":"EP/H051503/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G991281326","display_name":null,"funder_award_id":"AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1970588051.pdf","grobid_xml":"https://content.openalex.org/works/W1970588051.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1530115438","https://openalex.org/W1548589512","https://openalex.org/W1972266198","https://openalex.org/W1972927314","https://openalex.org/W1977699116","https://openalex.org/W1998855908","https://openalex.org/W2017085690","https://openalex.org/W2018074366","https://openalex.org/W2030947573","https://openalex.org/W2042732056","https://openalex.org/W2043368701","https://openalex.org/W2062246266","https://openalex.org/W2064878022","https://openalex.org/W2065385312","https://openalex.org/W2074189597","https://openalex.org/W2117887684","https://openalex.org/W2326261353","https://openalex.org/W2557433803","https://openalex.org/W4244513512"],"related_works":["https://openalex.org/W2953303953","https://openalex.org/W3182827720","https://openalex.org/W1596838019","https://openalex.org/W1991081991","https://openalex.org/W2133947431","https://openalex.org/W2490196280","https://openalex.org/W3208509670","https://openalex.org/W2100864966","https://openalex.org/W2109304297","https://openalex.org/W2083709218"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,86],"generalize":[4],"the":[5,28,35,39,59,64,68,76,92,99,118,133,157,160,164,167],"analysis":[6],"of":[7,51,67,101,139,159,166],"classical":[8],"multigrid":[9,60],"and":[10,63,147,163],"two-level":[11],"overlapping":[12],"Schwarz":[13,69],"methods":[14],"for":[15,48],"2nd":[16],"order":[17],"elliptic":[18],"boundary":[19],"value":[20],"problems":[21,23],"to":[22,88,126],"with":[24,107,129],"large":[25,108],"discontinuities":[26,131],"in":[27,98,132],"coefficients":[29,110],"that":[30,58,91,155],"are":[31,95,111,153],"not":[32,73,124],"resolved":[33],"by":[34,113],"coarse":[36,55,93],"grids":[37,94],"or":[38,79,104],"subdomain":[40],"partition.":[41],"The":[42,135],"theoretical":[43,161],"results":[44],"provide":[45],"a":[46,114],"recipe":[47],"designing":[49],"hierarchies":[50],"standard":[52],"piecewise":[53],"linear":[54],"spaces":[56],"such":[57],"convergence":[61],"rate":[62],"condition":[65],"number":[66],"preconditioned":[70],"system":[71],"do":[72,123],"depend":[74],"on":[75,80,144],"coefficient":[77,119],"variation":[78],"any":[81],"mesh":[82],"parameters.":[83],"An":[84],"assumption":[85],"have":[87],"make":[89,137],"is":[90,120],"sufficiently":[96],"fine":[97],"vicinity":[100],"cross":[102],"points":[103],"where":[105,117],"regions":[106],"diffusion":[109],"separated":[112],"narrow":[115],"region":[116],"small.":[121],"We":[122],"need":[125],"align":[127],"them":[128],"possible":[130],"coefficients.":[134],"proofs":[136],"use":[138],"novel":[140],"stable":[141],"splittings":[142],"based":[143],"weighted":[145,148],"quasi-interpolants":[146],"Poincar\u00e9-type":[149],"inequalities.":[150],"Numerical":[151],"experiments":[152],"included":[154],"illustrate":[156],"sharpness":[158],"bounds":[162],"necessity":[165],"technical":[168],"assumptions.":[169]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":6},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":8}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}