{"id":"https://openalex.org/W2008893060","doi":"https://doi.org/10.1137/s1064827596312547","title":"Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity","display_name":"Preconditioning for the Steady-State Navier--Stokes Equations with Low Viscosity","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2008893060","doi":"https://doi.org/10.1137/s1064827596312547","mag":"2008893060"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827596312547","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596312547","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":true,"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,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park, MD 20742,","institution_ids":["https://openalex.org/I66946132"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5086424147"],"corresponding_institution_ids":["https://openalex.org/I66946132"],"apc_list":null,"apc_paid":null,"fwci":11.7472,"has_fulltext":false,"cited_by_count":251,"citation_normalized_percentile":{"value":0.99114204,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":100},"biblio":{"volume":"20","issue":"4","first_page":"1299","last_page":"1316"},"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":0.9980000257492065,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9973999857902527,"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/preconditioner","display_name":"Preconditioner","score":0.8849117755889893},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.8255267143249512},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8067160248756409},{"id":"https://openalex.org/keywords/viscosity","display_name":"Viscosity","score":0.6401050090789795},{"id":"https://openalex.org/keywords/navier\u2013stokes-equations","display_name":"Navier\u2013Stokes equations","score":0.6340066194534302},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5520258545875549},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5395208597183228},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5098813772201538},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4900556802749634},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.48125097155570984},{"id":"https://openalex.org/keywords/steady-state","display_name":"Steady state (chemistry)","score":0.48040059208869934},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4802699089050293},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.41870713233947754},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.23744520545005798},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.12822961807250977},{"id":"https://openalex.org/keywords/compressibility","display_name":"Compressibility","score":0.1097293496131897},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.08455550670623779},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07954239845275879},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07319363951683044}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.8849117755889893},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.8255267143249512},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8067160248756409},{"id":"https://openalex.org/C127172972","wikidata":"https://www.wikidata.org/wiki/Q128709","display_name":"Viscosity","level":2,"score":0.6401050090789795},{"id":"https://openalex.org/C2781278361","wikidata":"https://www.wikidata.org/wiki/Q201321","display_name":"Navier\u2013Stokes equations","level":3,"score":0.6340066194534302},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5520258545875549},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5395208597183228},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5098813772201538},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4900556802749634},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.48125097155570984},{"id":"https://openalex.org/C8171440","wikidata":"https://www.wikidata.org/wiki/Q903414","display_name":"Steady state (chemistry)","level":2,"score":0.48040059208869934},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4802699089050293},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.41870713233947754},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.23744520545005798},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.12822961807250977},{"id":"https://openalex.org/C84655787","wikidata":"https://www.wikidata.org/wiki/Q8067817","display_name":"Compressibility","level":2,"score":0.1097293496131897},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.08455550670623779},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07954239845275879},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07319363951683044},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C147789679","wikidata":"https://www.wikidata.org/wiki/Q11372","display_name":"Physical chemistry","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/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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/s1064827596312547","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827596312547","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.25.1665","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.25.1665","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/Library/TRs/CS-TR-3712/CS-TR-3712.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.307.9787","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.307.9787","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/bfbt.pdf","raw_type":"text"},{"id":"pmh:oai:drum.lib.umd.edu:1903/856","is_oa":false,"landing_page_url":"http://hdl.handle.net/1903/856","pdf_url":null,"source":{"id":"https://openalex.org/S4306402644","display_name":"Digital Repository at the University of Maryland (University of Maryland College Park)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66946132","host_organization_name":"University of Maryland, College Park","host_organization_lineage":["https://openalex.org/I66946132"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Technical Report"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1156531067","display_name":"Mathematical Sciences:  Numerical Solution of Algebraic     Problems Arising in Fluids Models","funder_award_id":"9423133","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W1488435683","https://openalex.org/W1964628681","https://openalex.org/W1966158133","https://openalex.org/W1982093974","https://openalex.org/W1987001136","https://openalex.org/W1995582592","https://openalex.org/W1999331305","https://openalex.org/W2007322305","https://openalex.org/W2022396725","https://openalex.org/W2022665438","https://openalex.org/W2041876368","https://openalex.org/W2051259409","https://openalex.org/W2053295724","https://openalex.org/W2060884666","https://openalex.org/W2068585339","https://openalex.org/W2078843646","https://openalex.org/W2081523040","https://openalex.org/W2085259167","https://openalex.org/W2085581918","https://openalex.org/W2085759042","https://openalex.org/W2098174699","https://openalex.org/W2119121660","https://openalex.org/W2140153041","https://openalex.org/W2143755249","https://openalex.org/W2336720422","https://openalex.org/W2402147915","https://openalex.org/W2477040106"],"related_works":["https://openalex.org/W2357336958","https://openalex.org/W4281839678","https://openalex.org/W2535797495","https://openalex.org/W152950973","https://openalex.org/W2300963337","https://openalex.org/W2283235658","https://openalex.org/W3162287216","https://openalex.org/W2108077990","https://openalex.org/W2187142289","https://openalex.org/W1638910463"],"abstract_inverted_index":{"We":[0,81],"introduce":[1],"a":[2,37,40,75],"preconditioner":[3],"for":[4],"the":[5,14,19,34,91],"linearized":[6],"Navier--Stokes":[7],"equations":[8],"that":[9,33,47,64,84],"is":[10,49],"effective":[11],"when":[12],"either":[13],"discretization":[15],"mesh":[16,55],"size":[17],"or":[18],"viscosity":[20,53],"approaches":[21],"zero.":[22],"For":[23,57],"constant":[24],"coefficient":[25],"problems":[26],"with":[27,39,107],"periodic":[28],"boundary":[29,59],"conditions,":[30,60],"we":[31,61,73],"show":[32,83],"preconditioning":[35],"yields":[36],"system":[38],"single":[41],"eigenvalue":[42],"equal":[43],"to":[44],"1,":[45],"so":[46],"performance":[48],"independent":[50],"of":[51,78,101,111],"both":[52],"and":[54,72],"size.":[56],"other":[58],"demonstrate":[62],"empirically":[63],"convergence":[65],"depends":[66],"only":[67],"mildly":[68],"on":[69,105],"these":[70,102],"parameters":[71],"give":[74],"partial":[76],"analysis":[77],"this":[79],"phenomenon.":[80],"also":[82],"some":[85],"expensive":[86],"subsidiary":[87],"computations":[88],"required":[89],"by":[90,97],"new":[92],"method":[93],"can":[94],"be":[95],"replaced":[96],"inexpensive":[98],"approximate":[99],"versions":[100],"tasks":[103],"based":[104],"iteration,":[106],"virtually":[108],"no":[109],"degradation":[110],"performance.":[112]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":11},{"year":2019,"cited_by_count":8},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":11},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":12},{"year":2014,"cited_by_count":33},{"year":2013,"cited_by_count":10},{"year":2012,"cited_by_count":5}],"updated_date":"2026-05-16T08:24:45.110214","created_date":"2025-10-10T00:00:00"}
