{"id":"https://openalex.org/W2082312113","doi":"https://doi.org/10.1515/cmam-2014-0004","title":"The Construction of the Coarse de Rham Complexes with Improved Approximation Properties","display_name":"The Construction of the Coarse de Rham Complexes with Improved Approximation Properties","publication_year":2014,"publication_date":"2014-03-13","ids":{"openalex":"https://openalex.org/W2082312113","doi":"https://doi.org/10.1515/cmam-2014-0004","mag":"2082312113"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2014-0004","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2014-0004","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2014-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2014-0004/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5011362871","display_name":"Ilya Lashuk","orcid":null},"institutions":[{"id":"https://openalex.org/I130769515","display_name":"Pennsylvania State University","ror":"https://ror.org/04p491231","country_code":"US","type":"education","lineage":["https://openalex.org/I130769515"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ilya V. Lashuk","raw_affiliation_strings":["Department of Mathematics, Pennsylvania State University, 212 McAllister Building, University Park, PA 16802, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Pennsylvania State University, 212 McAllister Building, University Park, PA 16802, USA","institution_ids":["https://openalex.org/I130769515"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027636165","display_name":"Panayot S. Vassilevski","orcid":"https://orcid.org/0000-0002-5294-7242"},"institutions":[{"id":"https://openalex.org/I1282311441","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53","country_code":"US","type":"facility","lineage":["https://openalex.org/I1282311441","https://openalex.org/I1330989302","https://openalex.org/I198811213","https://openalex.org/I4210138311"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Panayot S. Vassilevski","raw_affiliation_strings":["Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94550, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, P.O. Box 808, L-560, Livermore, CA 94550, USA","institution_ids":["https://openalex.org/I1282311441"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011362871"],"corresponding_institution_ids":["https://openalex.org/I130769515"],"apc_list":null,"apc_paid":null,"fwci":4.8207,"has_fulltext":true,"cited_by_count":30,"citation_normalized_percentile":{"value":0.95193563,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"14","issue":"2","first_page":"257","last_page":"303"},"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":0.9994000196456909,"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":0.9994000196456909,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9969000220298767,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/curl","display_name":"Curl (programming language)","score":0.7477056980133057},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.5243176221847534},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.46951979398727417}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.7477056980133057},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5243176221847534},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.46951979398727417},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","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":1,"locations":[{"id":"doi:10.1515/cmam-2014-0004","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2014-0004","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2014-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/cmam-2014-0004","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2014-0004","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2014-0004/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1356433355","display_name":null,"funder_award_id":"DE\u2010AC5207NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G14554683","display_name":null,"funder_award_id":"DEAC5207NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2145270357","display_name":null,"funder_award_id":"AC52\u201007NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4343739756","display_name":null,"funder_award_id":"Contract DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320338286","funder_display_name":"Lawrence Livermore National Laboratory"},{"id":"https://openalex.org/G69709960","display_name":null,"funder_award_id":"Contract DE-AC52-07NA27344","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"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/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320338286","display_name":"Lawrence Livermore National Laboratory","ror":"https://ror.org/041nk4h53"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2082312113.pdf","grobid_xml":"https://content.openalex.org/works/W2082312113.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W625602010","https://openalex.org/W1519509134","https://openalex.org/W1994810579","https://openalex.org/W1997596109","https://openalex.org/W2070232376","https://openalex.org/W2089139137","https://openalex.org/W2090740209","https://openalex.org/W2107576752","https://openalex.org/W2112280313","https://openalex.org/W2142762932","https://openalex.org/W2168914934","https://openalex.org/W3046457476","https://openalex.org/W3103476862"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2382844561","https://openalex.org/W2083529992","https://openalex.org/W816511862","https://openalex.org/W2238883956","https://openalex.org/W2948362504","https://openalex.org/W2643941443","https://openalex.org/W2047855059","https://openalex.org/W1593612916","https://openalex.org/W3012106957"],"abstract_inverted_index":{"Abstract.":[0],"We":[1],"present":[2],"two":[3],"novel":[4],"coarse":[5,36,63,82,104,146,172,192],"spaces":[6,132,147,167,173,184],"(":[7],"H":[8,33,79],"1":[9,34,80],"-":[10,127],"and":[11,41,128,177,222],"<m:math":[12,51,92,116,209,216,223],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[13,52,93,117,210,217,224],"<m:mrow>":[14,53,94,118],"<m:mi>H</m:mi>":[15,54,95,119],"<m:mo>(</m:mo>":[16,55,96,120],"<m:mo":[17,56,97,121,211,218,225],"form=\"prefix\">curl</m:mo>":[18,57,98,212],"<m:mo>)</m:mo>":[19,58,99,123],"</m:mrow>":[20,59,100,124],"</m:math>":[21,60,101,125,213,220,227],"$H(\\operatorname{curl})$":[22,61,102],"-conforming)":[23],"based":[24],"on":[25,28,88,110],"element":[26],"agglomeration":[27],"unstructured":[29],"tetrahedral":[30,48],"meshes.":[31],"Each":[32],"-conforming":[35,62,81,103,131],"basis":[37],"function":[38],"is":[39,65,157,168],"continuous":[40],"piecewise-linear":[42],"with":[43,114],"respect":[44,152],"to":[45,153,196],"an":[46],"original":[47],"mesh.":[49],"The":[50,78,91,170,190],"space":[64,73,83,105],"a":[66,149],"subspace":[67],"of":[68,74,165,180,203,206],"the":[69,75,115,143,162,175,181],"lowest":[70],"order":[71],"N\u00e9d\u00e9lec":[72],"first":[76],"type.":[77],"exactly":[84,106],"interpolates":[85,107],"affine":[86],"functions":[87],"each":[89,111],"agglomerate.":[90,112],"vector":[108],"constants":[109],"Combined":[113],"form=\"prefix\">div</m:mo>":[122,219],"$H(\\operatorname{div})$":[126],"L":[129],"2":[130],"developed":[133],"previously":[134],"in":[135,194],"[Numer.":[136],"Linear":[137],"Algebra":[138],"Appl.":[139],"19":[140],"(2012),":[141],"414\u2013426],":[142],"newly":[144],"constructed":[145,171],"form":[148],"sequence":[150,164],"(with":[151],"exterior":[154],"derivatives)":[155],"which":[156],"exact":[158],"as":[159,161],"long":[160],"underlying":[163,182],"fine-grid":[166,183],"exact.":[169],"inherit":[174],"approximation":[176],"stability":[178],"properties":[179],"supported":[185],"by":[186],"our":[187],"numerical":[188],"experiments.":[189],"new":[191],"spaces,":[193],"addition":[195],"multigrid,":[197],"can":[198],"be":[199],"used":[200],"for":[201],"upscaling":[202],"broad":[204],"range":[205],"PDEs":[207],"involving":[208],"$\\operatorname{curl}$":[214],",":[215],"$\\operatorname{div}$":[221],"form=\"prefix\">grad</m:mo>":[226],"$\\operatorname{grad}$":[228],"differential":[229],"operators.":[230]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":6}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2025-10-10T00:00:00"}