{"id":"https://openalex.org/W2766740076","doi":"https://doi.org/10.1137/17m1153376","title":"The Auxiliary Space Preconditioner for the de Rham Complex","display_name":"The Auxiliary Space Preconditioner for the de Rham Complex","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2766740076","doi":"https://doi.org/10.1137/17m1153376","mag":"2766740076"},"language":"en","primary_location":{"id":"doi:10.1137/17m1153376","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153376","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":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1710.07840","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022236310","display_name":"Jay Gopalakrishnan","orcid":"https://orcid.org/0000-0001-7508-3232"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"J. Gopalakrishnan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5114259151","display_name":"Martin Neum\u00fcller","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Neum\u00fcller","raw_affiliation_strings":[],"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":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022236310"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1974,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.44805928,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"56","issue":"6","first_page":"3196","last_page":"3218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9883000254631042,"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"}},"topics":[{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9883000254631042,"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/T11809","display_name":"Advanced NMR Techniques and Applications","score":0.9872999787330627,"subfield":{"id":"https://openalex.org/subfields/1607","display_name":"Spectroscopy"},"field":{"id":"https://openalex.org/fields/16","display_name":"Chemistry"},"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":0.9804999828338623,"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":0.895922064781189},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.6410456895828247},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5546904802322388},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.5217448472976685},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5117318630218506},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.49156197905540466},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.48189789056777954},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4809664785861969},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4696356952190399},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4523910880088806},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.4151785373687744},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.4120723605155945},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3795766830444336},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3661571741104126},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3586748242378235},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.33889710903167725},{"id":"https://openalex.org/keywords/linear-system","display_name":"Linear system","score":0.21880170702934265},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2088916301727295},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16870176792144775}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.895922064781189},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.6410456895828247},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5546904802322388},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.5217448472976685},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5117318630218506},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.49156197905540466},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.48189789056777954},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4809664785861969},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4696356952190399},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4523910880088806},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.4151785373687744},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4120723605155945},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3795766830444336},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3661571741104126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3586748242378235},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.33889710903167725},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.21880170702934265},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2088916301727295},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16870176792144775},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/17m1153376","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1153376","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:arXiv.org:1710.07840","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.07840","pdf_url":"https://arxiv.org/pdf/1710.07840","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":"","raw_type":"text"},{"id":"pmh:oai:osti.gov:1669220","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1669220","pdf_url":"https://www.osti.gov/servlets/purl/1669220","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":"mag:2766740076","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1710.07840.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:pdxscholar.library.pdx.edu:pics_pub-1006","is_oa":false,"landing_page_url":"https://pdxscholar.library.pdx.edu/pics_pub/7","pdf_url":null,"source":{"id":"https://openalex.org/S4377196300","display_name":"PDXScholar  (Portland State University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I126345244","host_organization_name":"Portland State University","host_organization_lineage":["https://openalex.org/I126345244"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Portland Institute for Computational Science Publications","raw_type":"text"},{"id":"doi:10.48550/arxiv.1710.07840","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1710.07840","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:1710.07840","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1710.07840","pdf_url":"https://arxiv.org/pdf/1710.07840","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":"","raw_type":"text"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.46000000834465027}],"awards":[{"id":"https://openalex.org/G1072749480","display_name":null,"funder_award_id":"FA9550-17","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1157725702","display_name":null,"funder_award_id":"W911NF-15-1-0590","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G1450846816","display_name":null,"funder_award_id":"W911NF-16-1-0307","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G1494814522","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/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1660320720","display_name":null,"funder_award_id":"W911NF-15-1-0590","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G2011246711","display_name":null,"funder_award_id":"FA9550-17-1-009","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G260750634","display_name":null,"funder_award_id":"FA9550-17-1","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G2917824471","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G327963861","display_name":null,"funder_award_id":"162477","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3366966419","display_name":null,"funder_award_id":"W911NF-16-1","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G3391580208","display_name":null,"funder_award_id":"DE-AC52-07NA2","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G3392305090","display_name":null,"funder_award_id":"-16-1-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G3456752399","display_name":null,"funder_award_id":"DMS-1624776","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3689167596","display_name":null,"funder_award_id":"DMS-1624776","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G370164196","display_name":null,"funder_award_id":"FA9550-17-1-0090","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G4711444667","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G4851082355","display_name":null,"funder_award_id":"W911NF-15-1-0590","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5809100787","display_name":null,"funder_award_id":"FA9550","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5816449448","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G5964142490","display_name":null,"funder_award_id":"E-AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G6020043373","display_name":null,"funder_award_id":"DE-AC52-07NA2734","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G61608120","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6206182552","display_name":null,"funder_award_id":"W911NF-16-1-0307","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G6438076168","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G657448715","display_name":null,"funder_award_id":"W911NF-16-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G6711037067","display_name":null,"funder_award_id":"W911NF-15-1-0590","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7762609957","display_name":null,"funder_award_id":"W911NF-16-1-0307","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G7806955302","display_name":null,"funder_award_id":"DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8374966015","display_name":null,"funder_award_id":"AC52-07NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8450301714","display_name":null,"funder_award_id":"DMS-1624776","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8469877248","display_name":null,"funder_award_id":"W911NF-16-1-0307","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8480945789","display_name":null,"funder_award_id":"DMS-1624776","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G8658770765","display_name":null,"funder_award_id":"DE-AC52-07NA27","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8998121839","display_name":null,"funder_award_id":"911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G991281326","display_name":null,"funder_award_id":"AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"},{"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":36,"referenced_works":["https://openalex.org/W1548892666","https://openalex.org/W1963994965","https://openalex.org/W1967820494","https://openalex.org/W1985861577","https://openalex.org/W1986513041","https://openalex.org/W1987628609","https://openalex.org/W1993077381","https://openalex.org/W1994242271","https://openalex.org/W2001691885","https://openalex.org/W2005047411","https://openalex.org/W2006697861","https://openalex.org/W2010804587","https://openalex.org/W2012071009","https://openalex.org/W2012630580","https://openalex.org/W2017976561","https://openalex.org/W2018828557","https://openalex.org/W2027926924","https://openalex.org/W2034797962","https://openalex.org/W2039789965","https://openalex.org/W2047133076","https://openalex.org/W2047391773","https://openalex.org/W2049353172","https://openalex.org/W2075993982","https://openalex.org/W2079386274","https://openalex.org/W2113700277","https://openalex.org/W2118551467","https://openalex.org/W2138486270","https://openalex.org/W2164402335","https://openalex.org/W2169266183","https://openalex.org/W2227629823","https://openalex.org/W2295830377","https://openalex.org/W2325955172","https://openalex.org/W2345779166","https://openalex.org/W2402468387","https://openalex.org/W2532232939","https://openalex.org/W4238437064"],"related_works":["https://openalex.org/W3129158656","https://openalex.org/W3119649728","https://openalex.org/W3119601134","https://openalex.org/W3096278902","https://openalex.org/W162238331","https://openalex.org/W2986372024","https://openalex.org/W2052121881","https://openalex.org/W169961368","https://openalex.org/W2135626959","https://openalex.org/W2460046084","https://openalex.org/W3115094673","https://openalex.org/W2950967068","https://openalex.org/W3141988484","https://openalex.org/W2738632406","https://openalex.org/W2778574121","https://openalex.org/W2021153515","https://openalex.org/W655466607","https://openalex.org/W2767522232","https://openalex.org/W2066439789","https://openalex.org/W3099687355"],"abstract_inverted_index":{"We":[0,56],"generalize":[1],"the":[2,11,17,49,59,93,99,119],"construction":[3],"and":[4,39,89,112],"analysis":[5],"of":[6,16,28,31,51,82,98],"auxiliary":[7],"space":[8,33],"preconditioners":[9,22,100],"to":[10],"$n$-dimensional":[12],"finite":[13,52],"element":[14,53],"subcomplex":[15],"de":[18,61],"Rham":[19,62],"complex.":[20],"These":[21],"are":[23,77],"based":[24],"on":[25,86],"a":[26,29,36,40],"generalization":[27],"decomposition":[30],"Sobolev":[32],"functions":[34],"into":[35],"regular":[37],"part":[38],"potential.":[41],"A":[42],"discrete":[43],"version":[44],"is":[45],"easily":[46],"established":[47],"using":[48],"tools":[50],"exterior":[54],"calculus.":[55],"then":[57],"discuss":[58],"four-dimensional":[60],"complex":[63],"in":[64,69,80,101,116],"detail.":[65],"By":[66],"identifying":[67],"forms":[68],"four":[70,102],"dimensions":[71],"with":[72,118],"simple":[73],"proxies,":[74],"form":[75],"operations":[76,85],"written":[78],"out":[79],"terms":[81],"familiar":[83],"algebraic":[84],"matrices,":[87],"vectors,":[88],"scalars.":[90],"This":[91],"provides":[92],"basis":[94],"for":[95],"our":[96],"implementation":[97],"dimensions.":[103],"Extensive":[104],"numerical":[105],"experiments":[106],"illustrate":[107],"their":[108],"performance,":[109],"practical":[110],"scalability,":[111],"parameter":[113],"robustness,":[114],"all":[115],"accordance":[117],"theory.":[120]},"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}