{"id":"https://openalex.org/W2048366414","doi":"https://doi.org/10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","title":"Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems","display_name":"Multilevel Preconditioners for Mixed Methods for Second Order Elliptic Problems","publication_year":1996,"publication_date":"1996-09-01","ids":{"openalex":"https://openalex.org/W2048366414","doi":"https://doi.org/10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","mag":"2048366414"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://conservancy.umn.edu/bitstreams/ec0d3aa0-fd41-4bd8-a7c0-48f7433d1555/download","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5086480330","display_name":"Zhangxin Chen","orcid":"https://orcid.org/0000-0002-9107-1925"},"institutions":[{"id":"https://openalex.org/I178169726","display_name":"Southern Methodist University","ror":"https://ror.org/042tdr378","country_code":"US","type":"education","lineage":["https://openalex.org/I178169726"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Zhangxin Chen","raw_affiliation_strings":["Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156, USA","Department of Mathematics , Southern Methodist University , Dallas , TX , 75275-0156 , USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Southern Methodist University, Dallas, TX 75275-0156, USA","institution_ids":["https://openalex.org/I178169726"]},{"raw_affiliation_string":"Department of Mathematics , Southern Methodist University , Dallas , TX , 75275-0156 , USA","institution_ids":["https://openalex.org/I178169726"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112526925","display_name":"Richard E. Ewing","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard E. Ewing","raw_affiliation_strings":["Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077310702","display_name":"Raytcho Lazarov","orcid":"https://orcid.org/0000-0002-4911-3685"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raytcho D. Lazarov","raw_affiliation_strings":["Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047881113","display_name":"Serguei Maliassov","orcid":null},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Serguei Maliassov","raw_affiliation_strings":["Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA"],"affiliations":[{"raw_affiliation_string":"Institute for Scientific Computation and Department of Mathematics, Texas A&M University, 633 Blocker Bldg., College Station, TX 77843-3404, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007494022","display_name":"Yuri A. Kuznetsov","orcid":"https://orcid.org/0000-0003-2289-0801"},"institutions":[{"id":"https://openalex.org/I4210086928","display_name":"Institute of Numerical Mathematics","ror":"https://ror.org/00520ey40","country_code":"RU","type":"facility","lineage":["https://openalex.org/I1313323035","https://openalex.org/I4210086928","https://openalex.org/I4210124601"]},{"id":"https://openalex.org/I1313323035","display_name":"Russian Academy of Sciences","ror":"https://ror.org/05qrfxd25","country_code":"RU","type":"funder","lineage":["https://openalex.org/I1313323035"]}],"countries":["RU"],"is_corresponding":false,"raw_author_name":"Yuri A. Kuznetsov","raw_affiliation_strings":["Institute of Numerical Mathematics, Russian Academy of Sciences, 32-a Leninski Prospect, 117334 Moscow, Russia"],"affiliations":[{"raw_affiliation_string":"Institute of Numerical Mathematics, Russian Academy of Sciences, 32-a Leninski Prospect, 117334 Moscow, Russia","institution_ids":["https://openalex.org/I4210086928","https://openalex.org/I1313323035"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5086480330"],"corresponding_institution_ids":["https://openalex.org/I178169726"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430},"apc_paid":null,"fwci":5.2343,"has_fulltext":false,"cited_by_count":33,"citation_normalized_percentile":{"value":0.95712856,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"3","issue":"5","first_page":"427","last_page":"453"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.7981995344161987},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7026575803756714},{"id":"https://openalex.org/keywords/tetrahedron","display_name":"Tetrahedron","score":0.5621992945671082},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.558475136756897},{"id":"https://openalex.org/keywords/triangulation","display_name":"Triangulation","score":0.5339615941047668},{"id":"https://openalex.org/keywords/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.5294563174247742},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4993412494659424},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.4941892921924591},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.46145355701446533},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.4132010340690613},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.33242809772491455},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3056054413318634},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2502754032611847},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.23867961764335632},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.19651585817337036}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7981995344161987},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7026575803756714},{"id":"https://openalex.org/C105239961","wikidata":"https://www.wikidata.org/wiki/Q160003","display_name":"Tetrahedron","level":2,"score":0.5621992945671082},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.558475136756897},{"id":"https://openalex.org/C135981907","wikidata":"https://www.wikidata.org/wiki/Q188056","display_name":"Triangulation","level":2,"score":0.5339615941047668},{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.5294563174247742},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4993412494659424},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.4941892921924591},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.46145355701446533},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.4132010340690613},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.33242809772491455},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3056054413318634},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2502754032611847},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.23867961764335632},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.19651585817337036},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1099-1506(199609/10)3:5<427::aid-nla92>3.0.co;2-i","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Linear Algebra with Applications","raw_type":"journal-article"},{"id":"pmh:oai:conservancy.umn.edu:11299/2684","is_oa":true,"landing_page_url":"http://purl.umn.edu/2684","pdf_url":"https://conservancy.umn.edu/bitstreams/ec0d3aa0-fd41-4bd8-a7c0-48f7433d1555/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.17.4989","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.17.4989","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://phase.etl.go.jp/mgnet/mgnet/papers/ChenZ-et-al/mixprc.ps.gz","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.367.4882","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.367.4882","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isc.tamu.edu/publications-reports/tr/9414.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.47.9125","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.47.9125","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://sunset3.math.tamu.edu/~Raytcho.Lazarov/papers/chen_ew_ku_lazma.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.49.4373","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.49.4373","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.isc.tamu.edu/iscpubs/9414.ps","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:conservancy.umn.edu:11299/2684","is_oa":true,"landing_page_url":"http://purl.umn.edu/2684","pdf_url":"https://conservancy.umn.edu/bitstreams/ec0d3aa0-fd41-4bd8-a7c0-48f7433d1555/download","source":{"id":"https://openalex.org/S4306402521","display_name":"University of Minnesota Digital Conservancy (University of Minnesota)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I130238516","host_organization_name":"University of Minnesota","host_organization_lineage":["https://openalex.org/I130238516"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":""},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2048366414.pdf"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W120757762","https://openalex.org/W136185420","https://openalex.org/W1513884443","https://openalex.org/W1972927314","https://openalex.org/W1985340647","https://openalex.org/W1988796619","https://openalex.org/W1993043362","https://openalex.org/W1999331305","https://openalex.org/W2004291775","https://openalex.org/W2009441498","https://openalex.org/W2031182879","https://openalex.org/W2032730144","https://openalex.org/W2033480487","https://openalex.org/W2040933131","https://openalex.org/W2050532615","https://openalex.org/W2051558262","https://openalex.org/W2051682834","https://openalex.org/W2061860499","https://openalex.org/W2061992706","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2066610136","https://openalex.org/W2069697314","https://openalex.org/W2078843646","https://openalex.org/W2464997744","https://openalex.org/W2491027544","https://openalex.org/W2798909945","https://openalex.org/W4213291691","https://openalex.org/W4285719527","https://openalex.org/W6651275371","https://openalex.org/W6750968397"],"related_works":["https://openalex.org/W3118783749","https://openalex.org/W2002583644","https://openalex.org/W3119989344","https://openalex.org/W2025402442","https://openalex.org/W2098990162","https://openalex.org/W1987870972","https://openalex.org/W2993813190","https://openalex.org/W2567351266","https://openalex.org/W1998766989","https://openalex.org/W2323903082"],"abstract_inverted_index":{"A":[0],"new":[1],"approach":[2],"for":[3,8,13,44,63,90,97],"constructing":[4],"algebraic":[5],"multilevel":[6,61],"preconditioners":[7,62],"mixed":[9,32,99],"finite":[10,57,100],"element":[11,58,101],"methods":[12,33,102],"second":[14],"order":[15],"elliptic":[16],"problems":[17],"with":[18],"tensor":[19],"coefficients":[20],"on":[21,70],"general":[22],"geometry":[23],"is":[24,34],"proposed.":[25],"The":[26],"linear":[27,51],"system":[28,43,52,65],"arising":[29],"from":[30],"the":[31,74,91,98,107],"first":[35],"algebraically":[36],"condensed":[37],"to":[38,49,105],"a":[39,50,71],"symmetric,":[40],"positive":[41],"definite":[42],"Lagrange":[45],"multipliers,":[46],"which":[47],"corresponds":[48],"generated":[53],"by":[54],"standard":[55],"nonconforming":[56],"methods.":[59],"Algebraic":[60],"this":[64],"are":[66,88,103],"then":[67],"constructed":[68,92],"based":[69],"triangulation":[72],"of":[73,81],"domain":[75],"into":[76],"tetrahedral":[77],"substructures.":[78],"Explicit":[79],"estimates":[80],"condition":[82],"numbers":[83],"and":[84],"simple":[85],"computational":[86],"schemes":[87],"established":[89],"preconditioners.":[93],"Finally,":[94],"numerical":[95],"results":[96],"presented":[104],"illustrate":[106],"present":[108],"theory.":[109]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2017,"cited_by_count":2},{"year":2016,"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"}
