{"id":"https://openalex.org/W2048752392","doi":"https://doi.org/10.1007/s002110100300","title":"Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations","display_name":"Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations","publication_year":2002,"publication_date":"2002-02-01","ids":{"openalex":"https://openalex.org/W2048752392","doi":"https://doi.org/10.1007/s002110100300","mag":"2048752392"},"language":"en","primary_location":{"id":"doi:10.1007/s002110100300","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110100300","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/A5086424147","display_name":"Howard C. Elman","orcid":"https://orcid.org/0000-0002-8886-9901"},"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":"Howard C. Elman","raw_affiliation_strings":["Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA; e-mail: elman@cs.umd.edu\n, , , , , , US","Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA; e-mail: elman@cs.umd.edu , US"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA; e-mail: elman@cs.umd.edu\n, , , , , , US","institution_ids":["https://openalex.org/I66946132"]},{"raw_affiliation_string":"Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742, USA; e-mail: elman@cs.umd.edu , US","institution_ids":["https://openalex.org/I66946132"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007116796","display_name":"David J. Silvester","orcid":"https://orcid.org/0000-0002-0652-5444"},"institutions":[{"id":"https://openalex.org/I28407311","display_name":"University of Manchester","ror":"https://ror.org/027m9bs27","country_code":"GB","type":"education","lineage":["https://openalex.org/I28407311"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David J. Silvester","raw_affiliation_strings":["Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester M601QD, UK; e-mail: djs@lanczos.ma.umist.ac.uk\n, , , , , , GB","Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester M601QD, UK; e-mail: djs@lanczos.ma.umist.ac.uk , GB"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester M601QD, UK; e-mail: djs@lanczos.ma.umist.ac.uk\n, , , , , , GB","institution_ids":["https://openalex.org/I28407311"]},{"raw_affiliation_string":"Department of Mathematics, University of Manchester, Institute of Science and Technology, Manchester M601QD, UK; e-mail: djs@lanczos.ma.umist.ac.uk , GB","institution_ids":["https://openalex.org/I28407311"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110146377","display_name":"Andrew J. Wathen","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Andrew J. Wathen","raw_affiliation_strings":["Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, UK; e-mail: Andy.Wathen@comlab.ox.ac.uk\n, , , , , , GB","Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, UK; e-mail: Andy.Wathen@comlab.ox.ac.uk , GB"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, UK; e-mail: Andy.Wathen@comlab.ox.ac.uk\n, , , , , , GB","institution_ids":["https://openalex.org/I40120149"]},{"raw_affiliation_string":"Oxford University, Computing Laboratory, Wolfson Building, Parks Road, Oxford OX13QD, UK; e-mail: Andy.Wathen@comlab.ox.ac.uk , GB","institution_ids":["https://openalex.org/I40120149"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":14.6985,"has_fulltext":false,"cited_by_count":219,"citation_normalized_percentile":{"value":0.99463252,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"90","issue":"4","first_page":"665","last_page":"688"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9998999834060669,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9995999932289124,"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.848220705986023},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7590112686157227},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.7021428346633911},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.6560747027397156},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5906094908714294},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5179861783981323},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.5065454244613647},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5035092234611511},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.4815092980861664},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4423687756061554},{"id":"https://openalex.org/keywords/preconditioner","display_name":"Preconditioner","score":0.4381631910800934},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4307246208190918},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.31978631019592285},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.2685941159725189},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.24137219786643982},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.15667396783828735},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07695573568344116}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.848220705986023},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7590112686157227},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.7021428346633911},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.6560747027397156},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5906094908714294},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5179861783981323},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.5065454244613647},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5035092234611511},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.4815092980861664},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4423687756061554},{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.4381631910800934},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4307246208190918},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.31978631019592285},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.2685941159725189},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.24137219786643982},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.15667396783828735},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07695573568344116},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"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/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s002110100300","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s002110100300","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:pure.atira.dk:openaire_cris_publications/36222fff-2809-4e10-8fad-69666d1d2753","is_oa":false,"landing_page_url":"https://research.manchester.ac.uk/en/publications/36222fff-2809-4e10-8fad-69666d1d2753","pdf_url":null,"source":{"id":"https://openalex.org/S4306400662","display_name":"Research Explorer (The University of Manchester)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I28407311","host_organization_name":"University of Manchester","host_organization_lineage":["https://openalex.org/I28407311"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Elman, H C, Silvester, D J & Wathen, A J 2002, 'Performance and analysis of saddle point preconditioners for the discrete steady-state Navier-Stokes equations', NUMERISCHE MATHEMATIK, vol. 90, no. 4, pp. 665-688. https://doi.org/10.1007/s002110100300","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.145.3554","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.145.3554","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.umd.edu/~elman/papers/esw-numermath.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.36.3794","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.36.3794","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.cs.umd.edu/pub/papers/papers/ncstrl.umcp/CS-TR-4164/CS-TR-4164.ps.Z","raw_type":"text"},{"id":"pmh:oai:ora.ox.ac.uk:uuid:cc46d6e1-5bad-44b4-9950-a9943ac32149","is_oa":false,"landing_page_url":"https://ora.ox.ac.uk/objects/uuid:cc46d6e1-5bad-44b4-9950-a9943ac32149","pdf_url":null,"source":{"id":"https://openalex.org/S4306402636","display_name":"Oxford University Research Archive (ORA) (University of Oxford)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40120149","host_organization_name":"University of Oxford","host_organization_lineage":["https://openalex.org/I40120149"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symplectic Elements at Oxford","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":24,"referenced_works":["https://openalex.org/W1678750361","https://openalex.org/W1683056966","https://openalex.org/W1965741417","https://openalex.org/W1966158133","https://openalex.org/W1993531511","https://openalex.org/W1999331305","https://openalex.org/W2005293667","https://openalex.org/W2007322305","https://openalex.org/W2008893060","https://openalex.org/W2022852340","https://openalex.org/W2029367872","https://openalex.org/W2033986961","https://openalex.org/W2050206349","https://openalex.org/W2055116131","https://openalex.org/W2056253747","https://openalex.org/W2064727561","https://openalex.org/W2069601896","https://openalex.org/W2078843646","https://openalex.org/W2081523040","https://openalex.org/W2085581918","https://openalex.org/W2101743932","https://openalex.org/W2133480447","https://openalex.org/W2140153041","https://openalex.org/W2802365918"],"related_works":["https://openalex.org/W2401310550","https://openalex.org/W2381322109","https://openalex.org/W1189497506","https://openalex.org/W3146410598","https://openalex.org/W2218557851","https://openalex.org/W1970706285","https://openalex.org/W2767153625","https://openalex.org/W1982069796","https://openalex.org/W2999046577","https://openalex.org/W1251548615"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":14},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":15},{"year":2014,"cited_by_count":26},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":15}],"updated_date":"2026-06-16T07:32:37.131356","created_date":"2025-10-10T00:00:00"}