{"id":"https://openalex.org/W2111268954","doi":"https://doi.org/10.1137/100806485","title":"Field-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier\u2013Stokes Problem","display_name":"Field-of-Values Convergence Analysis of Augmented Lagrangian Preconditioners for the Linearized Navier\u2013Stokes Problem","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W2111268954","doi":"https://doi.org/10.1137/100806485","mag":"2111268954"},"language":"en","primary_location":{"id":"doi:10.1137/100806485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806485","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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053109099","display_name":"Michele Benzi","orcid":"https://orcid.org/0000-0001-6099-0294"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michele Benzi","raw_affiliation_strings":["benzi@mathcs.emory.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"benzi@mathcs.emory.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077985757","display_name":"Maxim A. Olshanskii","orcid":"https://orcid.org/0000-0002-9102-6833"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Maxim A. Olshanskii","raw_affiliation_strings":["Maxim.Olshanskii@mtu-net.ru#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Maxim.Olshanskii@mtu-net.ru#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.1607,"has_fulltext":false,"cited_by_count":65,"citation_normalized_percentile":{"value":0.98430264,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"49","issue":"2","first_page":"770","last_page":"788"},"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9997000098228455,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.9790080189704895},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8641102313995361},{"id":"https://openalex.org/keywords/augmented-lagrangian-method","display_name":"Augmented Lagrangian method","score":0.8118529319763184},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6566647291183472},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5697766542434692},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.5459928512573242},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.537207841873169},{"id":"https://openalex.org/keywords/generalized-minimal-residual-method","display_name":"Generalized minimal residual method","score":0.5076500177383423},{"id":"https://openalex.org/keywords/field","display_name":"Field (mathematics)","score":0.45850592851638794},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.4131524860858917},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4016900956630707},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.3550499677658081},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.269004225730896},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16887715458869934},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13022202253341675},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.08226361870765686},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07524195313453674}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.9790080189704895},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8641102313995361},{"id":"https://openalex.org/C150452318","wikidata":"https://www.wikidata.org/wiki/Q4820432","display_name":"Augmented Lagrangian method","level":2,"score":0.8118529319763184},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6566647291183472},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5697766542434692},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.5459928512573242},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.537207841873169},{"id":"https://openalex.org/C155332342","wikidata":"https://www.wikidata.org/wiki/Q1432976","display_name":"Generalized minimal residual method","level":3,"score":0.5076500177383423},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.45850592851638794},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.4131524860858917},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4016900956630707},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.3550499677658081},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.269004225730896},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16887715458869934},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13022202253341675},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.08226361870765686},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07524195313453674},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/100806485","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100806485","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:CiteSeerX.psu:10.1.1.174.6817","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.174.6817","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/bo10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.186.3252","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.186.3252","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/bo10.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.204.7890","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.204.7890","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.mathcs.emory.edu/%7Ebenzi/Web_papers/SNA000770.pdf","raw_type":"text"},{"id":"pmh:oai:ricerca.sns.it:11384/75276","is_oa":false,"landing_page_url":"http://hdl.handle.net/11384/75276","pdf_url":null,"source":{"id":"https://openalex.org/S7407050981","display_name":"Scuola Normale Superiore di Pisa","issn_l":null,"issn":[],"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":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1524324710","https://openalex.org/W1963751327","https://openalex.org/W1972100784","https://openalex.org/W1973709085","https://openalex.org/W1985050465","https://openalex.org/W2022665438","https://openalex.org/W2041523977","https://openalex.org/W2044269104","https://openalex.org/W2054034220","https://openalex.org/W2068395392","https://openalex.org/W2081523040","https://openalex.org/W2087290839","https://openalex.org/W2121613024","https://openalex.org/W2126454579","https://openalex.org/W2133248904","https://openalex.org/W2141870784","https://openalex.org/W2143228255","https://openalex.org/W2158804477"],"related_works":["https://openalex.org/W1575783825","https://openalex.org/W2964012721","https://openalex.org/W192329731","https://openalex.org/W2521297506","https://openalex.org/W2060439759","https://openalex.org/W2143228255","https://openalex.org/W2742455921","https://openalex.org/W3216172936","https://openalex.org/W3034300723","https://openalex.org/W1999074586"],"abstract_inverted_index":{"We":[0],"study":[1],"a":[2,88],"block":[3,94],"triangular":[4,95],"preconditioner":[5,16,73],"for":[6,50,60,83],"finite":[7],"element":[8],"approximations":[9,96],"of":[10,24,71,97],"the":[11,20,25,31,51,61,67,72,84,98],"linearized":[12],"Navier\u2013Stokes":[13],"equations.":[14],"The":[15],"is":[17],"based":[18,79,92],"on":[19,80,93],"augmented":[21],"Lagrangian":[22],"formulation":[23],"problem":[26],"and":[27,87],"was":[28],"introduced":[29],"by":[30],"authors":[32],"in":[33],"[SIAM":[34],"J.":[35],"Sci.":[36],"Comput.,":[37],"28":[38],"(2006),":[39],"pp.":[40],"2095\u20132113].":[41],"In":[42],"this":[43],"paper":[44],"we":[45],"prove":[46],"field-of-values":[47],"type":[48],"estimates":[49],"preconditioned":[52],"system":[53],"which":[54],"lead":[55],"to":[56,65],"optimal":[57],"convergence":[58],"bounds":[59],"GMRES":[62],"algorithm":[63],"applied":[64],"solve":[66],"system.":[68],"Two":[69],"variants":[70],"are":[74],"considered:":[75],"an":[76],"ideal":[77],"one":[78],"exact":[81],"solves":[82],"velocity":[85,99],"submatrix,":[86],"more":[89],"practical":[90],"variant":[91],"submatrix.":[100]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":6},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":19},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
