{"id":"https://openalex.org/W2002132376","doi":"https://doi.org/10.1137/050635547","title":"Topological Optimization of the Evaluation of Finite Element Matrices","display_name":"Topological Optimization of the Evaluation of Finite Element Matrices","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2002132376","doi":"https://doi.org/10.1137/050635547","mag":"2002132376"},"language":"en","primary_location":{"id":"doi:10.1137/050635547","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635547","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1205.3001","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Robert C. Kirby","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Robert C. Kirby","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Anders Logg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Anders Logg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"L. Ridgway Scott","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"L. Ridgway Scott","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Andy R. Terrel","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andy R. Terrel","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.0233,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.98237337,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"28","issue":"1","first_page":"224","last_page":"240"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.8598999977111816,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.8598999977111816,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.028599999845027924,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"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":0.01119999960064888,"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/multilinear-map","display_name":"Multilinear map","score":0.7824000120162964},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.6906999945640564},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6272000074386597},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.5485000014305115},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5049999952316284},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.503600001335144},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.46059998869895935},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.45190000534057617}],"concepts":[{"id":"https://openalex.org/C84392682","wikidata":"https://www.wikidata.org/wiki/Q1952404","display_name":"Multilinear map","level":2,"score":0.7824000120162964},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7322999835014343},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.6906999945640564},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6272000074386597},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.5485000014305115},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5049999952316284},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.503600001335144},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.46059998869895935},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.45190000534057617},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4129999876022339},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.38999998569488525},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.35899999737739563},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.35760000348091125},{"id":"https://openalex.org/C60321788","wikidata":"https://www.wikidata.org/wiki/Q1197190","display_name":"Multilinear algebra","level":5,"score":0.3490000069141388},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.3377000093460083},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32749998569488525},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28870001435279846},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.27559998631477356},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.257999986410141},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2578999996185303},{"id":"https://openalex.org/C146380142","wikidata":"https://www.wikidata.org/wiki/Q1137726","display_name":"Directed graph","level":2,"score":0.2535000145435333}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/050635547","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050635547","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:1205.3001","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1205.3001","pdf_url":"https://arxiv.org/pdf/1205.3001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"pmh:oai:research.chalmers.se:191161","is_oa":false,"landing_page_url":"https://research.chalmers.se/en/publication/191161","pdf_url":null,"source":{"id":"https://openalex.org/S4306402469","display_name":"Chalmers Research (Chalmers University of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I66862912","host_organization_name":"Chalmers University of Technology","host_organization_lineage":["https://openalex.org/I66862912"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1205.3001","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1205.3001","pdf_url":"https://arxiv.org/pdf/1205.3001","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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/G222768804","display_name":null,"funder_award_id":"DE\u2010FG02\u2010","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3670372212","display_name":"AUTOMATIC PARALLEL FINITE ELEMENT COMPUTATION: GENERAL VARIATIONAL FORMS WITH ARBITRARY FINITE ELEMENT SPACES","funder_award_id":"FG02-04ER25650","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2002132376.pdf","grobid_xml":"https://content.openalex.org/works/W2002132376.grobid-xml"},"referenced_works_count":6,"referenced_works":["https://openalex.org/W1978064247","https://openalex.org/W1983655899","https://openalex.org/W1994484297","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W4292166829"],"related_works":[],"abstract_inverted_index":{"We":[0,52,92],"present":[1,54,93],"a":[2,55,75,88],"topological":[3],"framework":[4,28],"for":[5,9,18,96,113,119],"finding":[6],"low-flop":[7],"algorithms":[8,112],"evaluating":[10],"element":[11,20,36,45,69],"stiffness":[12],"matrices":[13],"associated":[14],"with":[15,47],"multilinear":[16,99],"forms":[17,100],"finite":[19],"methods":[21],"posed":[22],"over":[23],"straight-sided":[24],"affine":[25],"domains.":[26],"This":[27,71],"relies":[29],"on":[30,34],"phrasing":[31],"the":[32,38,115,120],"computation":[33],"each":[35,41],"as":[37,63],"contraction":[39],"of":[40,43,58],"collection":[42],"reference":[44,68],"tensors":[46],"an":[48,83],"element-specific":[49],"geometric":[50],"tensor.":[51],"then":[53],"new":[56],"concept":[57],"complexity-reducing":[59],"relations":[60,65],"that":[61],"serve":[62],"distance":[64],"between":[66],"these":[67],"tensors.":[70],"notion":[72],"sets":[73],"up":[74],"graph-theoretic":[76],"context":[77],"in":[78,104],"which":[79],"we":[80,117],"may":[81],"find":[82],"optimized":[84],"algorithm":[85],"by":[86],"computing":[87],"minimum":[89],"spanning":[90],"tree.":[91],"experimental":[94],"results":[95],"some":[97,110],"common":[98],"showing":[101],"significant":[102],"reductions":[103],"operation":[105],"count":[106],"and":[107],"also":[108],"discuss":[109],"efficient":[111],"building":[114],"graph":[116],"use":[118],"optimization.":[121]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2017,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2016-06-24T00:00:00"}