{"id":"https://openalex.org/W2784834036","doi":"https://doi.org/10.1137/17m1132562","title":"Algebraic Hybridization and Static Condensation with Application to Scalable $H$(div) Preconditioning","display_name":"Algebraic Hybridization and Static Condensation with Application to Scalable $H$(div) Preconditioning","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2784834036","doi":"https://doi.org/10.1137/17m1132562","mag":"2784834036"},"language":"en","primary_location":{"id":"doi:10.1137/17m1132562","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1132562","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1801.08914","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027158038","display_name":"Veselin Dobrev","orcid":"https://orcid.org/0000-0003-1793-5622"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"V. Dobrev","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003911272","display_name":"Tzanio Kolev","orcid":"https://orcid.org/0000-0002-2810-3090"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Kolev","raw_affiliation_strings":[],"raw_orcid":"https://orcid.org/0000-0002-2810-3090","affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5003575107","display_name":"Chak Shing Lee","orcid":"https://orcid.org/0000-0002-9573-3463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. S. Lee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056525853","display_name":"Vladimir Tomov","orcid":"https://orcid.org/0000-0002-1846-6816"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"V. Tomov","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"P. S. Vassilevski","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5027158038"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.00375856,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"41","issue":"3","first_page":"B425","last_page":"B447"},"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":0.9994999766349792,"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":0.9994999766349792,"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":0.9991999864578247,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9934999942779541,"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/solver","display_name":"Solver","score":0.6935027241706848},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6766282320022583},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6670849919319153},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5990561842918396},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.5809135437011719},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4808286428451538},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.44557029008865356},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4073474407196045},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.36730754375457764},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2641477584838867},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.22976145148277283},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.11780223250389099},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11176934838294983},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.08515024185180664}],"concepts":[{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6935027241706848},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6766282320022583},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6670849919319153},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5990561842918396},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.5809135437011719},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4808286428451538},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.44557029008865356},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4073474407196045},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.36730754375457764},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2641477584838867},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.22976145148277283},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.11780223250389099},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11176934838294983},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.08515024185180664},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1132562","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1132562","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:arXiv.org:1801.08914","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.08914","pdf_url":"https://arxiv.org/pdf/1801.08914","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"mag:2784834036","is_oa":true,"landing_page_url":"http://arxiv.org/pdf/1801.08914.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:osti.gov:1515347","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1515347","pdf_url":null,"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":"doi:10.48550/arxiv.1801.08914","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1801.08914","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1801.08914","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.08914","pdf_url":"https://arxiv.org/pdf/1801.08914","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G5522089832","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/G855205906","display_name":null,"funder_award_id":"LLNL-JRNL-732140","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"}],"funders":[{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W73153831","https://openalex.org/W1525132831","https://openalex.org/W1657900019","https://openalex.org/W1997239292","https://openalex.org/W1998894128","https://openalex.org/W2000867371","https://openalex.org/W2001012465","https://openalex.org/W2005047411","https://openalex.org/W2010804587","https://openalex.org/W2023166590","https://openalex.org/W2034955757","https://openalex.org/W2039789965","https://openalex.org/W2051682834","https://openalex.org/W2054019633","https://openalex.org/W2069697314","https://openalex.org/W2075993982","https://openalex.org/W2078367662","https://openalex.org/W2080673722","https://openalex.org/W2082452417","https://openalex.org/W2089558316","https://openalex.org/W2095346333","https://openalex.org/W2097762161","https://openalex.org/W2115411128","https://openalex.org/W2132292023","https://openalex.org/W2132509247","https://openalex.org/W2159575423","https://openalex.org/W2339526232","https://openalex.org/W2480409024","https://openalex.org/W2491027544","https://openalex.org/W2542358525","https://openalex.org/W2560398873","https://openalex.org/W2625919695","https://openalex.org/W3122081001","https://openalex.org/W4239299544"],"related_works":["https://openalex.org/W2339526232","https://openalex.org/W2596931072","https://openalex.org/W2787267874","https://openalex.org/W2949074005","https://openalex.org/W2244397961","https://openalex.org/W2995054741","https://openalex.org/W2008178409","https://openalex.org/W3211185367","https://openalex.org/W1553704505","https://openalex.org/W2970912382","https://openalex.org/W2912245917","https://openalex.org/W335628795","https://openalex.org/W2620146726","https://openalex.org/W2935617892","https://openalex.org/W2026144424","https://openalex.org/W1986589373","https://openalex.org/W2053656257","https://openalex.org/W3032492735","https://openalex.org/W2750342106","https://openalex.org/W1970524585"],"abstract_inverted_index":{"We":[0,24,50],"propose":[1],"a":[2,69],"unified":[3],"algebraic":[4,30],"approach":[5],"for":[6,32,38,118],"the":[7,26,33,55,59,100,103],"practical":[8],"application":[9],"and":[10,15,77,92],"preconditioning":[11],"of":[12,28,35,47,58,102],"static":[13],"condensation":[14],"hybridization,":[16],"two":[17,60],"popular":[18],"techniques":[19,65],"in":[20,66,106],"finite":[21],"element":[22],"discretizations.":[23],"demonstrate":[25],"use":[27,101],"this":[29],"framework":[31],"construction":[34],"scalable":[36],"solvers":[37],"problems":[39],"involving":[40],"$H$(div)-spaces":[41],"discretized":[42],"by":[43],"conforming":[44],"(Raviart--Thomas)":[45],"elements":[46],"arbitrary":[48],"order.":[49],"illustrate":[51],"through":[52],"numerical":[53],"experiments":[54],"relative":[56],"performance":[57,114],"(in":[61],"some":[62],"sense":[63],"dual)":[64],"comparison":[67],"with":[68,115],"state-of-the-art":[70],"parallel":[71],"solver,":[72],"ADS":[73],"[T.":[74],"V.":[75],"Kolev":[76],"P.":[78],"S.":[79],"Vassilevski,":[80],"SIAM":[81],"J.":[82],"Sci.":[83],"Comput.,":[84],"34":[85],"(2012),":[86],"pp.":[87],"A3079--A3098],":[88],"available":[89],"at":[90],"http://www.llnl.gov/casc/hypre":[91],"http://mfem.org.":[93],"Based":[94],"on":[95],"these":[96],"results,":[97],"we":[98],"recommend":[99],"hybridization":[104],"technique":[105],"practice,":[107],"due":[108],"to":[109],"its":[110],"clearly":[111],"demonstrated":[112],"superior":[113],"increased":[116],"benefit":[117],"higher-order":[119],"elements.":[120]},"counts_by_year":[],"updated_date":"2026-05-12T08:28:47.272897","created_date":"2025-10-10T00:00:00"}