{"id":"https://openalex.org/W7167902120","doi":"https://doi.org/10.48550/arxiv.2607.08172","title":"Algorithm XXXX: Computation of finite element degree-of-freedom transformation matrices","display_name":"Algorithm XXXX: Computation of finite element degree-of-freedom transformation matrices","publication_year":2026,"publication_date":"2026-07-09","ids":{"openalex":"https://openalex.org/W7167902120","doi":"https://doi.org/10.48550/arxiv.2607.08172"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.08172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08172","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.08172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029535233","display_name":"Matthew W. Scroggs","orcid":"https://orcid.org/0000-0002-4658-2443"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Scroggs, Matthew W.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5030408094","display_name":"Garth N. Wells","orcid":"https://orcid.org/0000-0001-5291-7951"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wells, Garth N.","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":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.19120000302791595,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.19120000302791595,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.16359999775886536,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T11697","display_name":"Numerical Methods and Algorithms","score":0.12489999830722809,"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/computation","display_name":"Computation","score":0.6036999821662903},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5855000019073486},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.5625},{"id":"https://openalex.org/keywords/fraction","display_name":"Fraction (chemistry)","score":0.5091000199317932},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4106999933719635},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.40610000491142273},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.39959999918937683},{"id":"https://openalex.org/keywords/construct","display_name":"Construct (python library)","score":0.36980000138282776}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6270999908447266},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6036999821662903},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5855000019073486},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.5625},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5464000105857849},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5091000199317932},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4106999933719635},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.40610000491142273},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.36980000138282776},{"id":"https://openalex.org/C84211073","wikidata":"https://www.wikidata.org/wiki/Q117879","display_name":"Floating point","level":2,"score":0.36809998750686646},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.3361999988555908},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3237000107765198},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.31700000166893005},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.31679999828338623},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.31310001015663147},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.3027999997138977},{"id":"https://openalex.org/C25878781","wikidata":"https://www.wikidata.org/wiki/Q1473607","display_name":"Degree of a polynomial","level":3,"score":0.29899999499320984},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.29820001125335693},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.2849000096321106},{"id":"https://openalex.org/C17349429","wikidata":"https://www.wikidata.org/wiki/Q1049914","display_name":"Matrix multiplication","level":3,"score":0.2840000092983246},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.2824999988079071},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2808000147342682},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C188045654","wikidata":"https://www.wikidata.org/wiki/Q17148339","display_name":"Memory bandwidth","level":2,"score":0.2632000148296356},{"id":"https://openalex.org/C106516650","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm design","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.08172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08172","pdf_url":null,"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.08172","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.08172","pdf_url":null,"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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Peace, Justice and strong institutions","score":0.8402993679046631,"id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"arithmetic":[1],"intensity":[2],"of":[3,51,56,70,75,101,137,160,170,172],"algorithms":[4],"for":[5,82,97,105,124,147,178],"computing":[6,83,121],"finite":[7,85,128],"element":[8,86,129],"operators":[9],"increases":[10],"with":[11,112,184],"increasing":[12],"polynomial":[13],"degree.":[14],"This":[15,150],"has":[16,187],"made":[17],"high":[18],"degree":[19,36,62,107],"methods":[20,63,81],"particularly":[21],"attractive":[22],"on":[23,30],"modern":[24,76],"CPU":[25],"and":[26,45,94,135,141,186],"GPU":[27],"architectures,":[28],"since":[29],"these":[31],"architectures":[32],"performance":[33],"at":[34,200],"low":[35],"is":[37,59,91,152],"limited":[38],"(severely)":[39],"by":[40],"the":[41,52,57,71,98,102,132,138,155,161,175,204],"available":[42,72],"memory":[43],"bandwidth":[44],"only":[46,131],"a":[47,66,113,144,158,173,196,215],"very":[48],"small":[49],"fraction":[50,69],"floating":[53],"point":[54],"capacity":[55],"processor":[58],"used.":[60],"Higher":[61],"can":[64,117,198],"exploit":[65],"significantly":[67],"greater":[68],"compute":[73],"power":[74],"architectures.":[77],"However,":[78],"whilst":[79],"stable":[80],"high-degree":[84],"bases":[87],"are":[88],"well-established,":[89],"there":[90],"no":[92],"universal":[93],"automated":[95],"algorithm":[96,115,176],"efficient":[99],"construction":[100],"degree-of-freedom":[103,122,216],"map":[104],"arbitrary":[106,126],"elements.":[108],"We":[109],"address":[110],"this":[111],"new":[114,179],"that":[116,195],"be":[118,182],"used":[119],"in":[120,154],"maps":[123],"an":[125],"Ciarlet-type":[127],"using":[130],"element's":[133],"definition":[134],"properties":[136],"reference":[139],"cell,":[140],"without":[142,202],"requiring":[143,203],"specific":[145],"implementation":[146],"each":[148],"element.":[149],"method":[151],"implemented":[153,183],"library":[156],"Basix,":[157],"component":[159],"FEniCSx":[162],"libraries.":[163],"As":[164],"well":[165],"as":[166],"allowing":[167],"vast":[168],"simplifications":[169],"parts":[171],"codebase,":[174],"allows":[177],"elements":[180,194],"to":[181,190,206,213],"ease":[185],"allowed":[188],"us":[189],"support":[191],"user-defined":[192],"custom":[193],"user":[197,205],"create":[199],"runtime":[201],"input":[207],"any":[208],"information":[209],"about":[210],"transformations":[211],"required":[212],"construct":[214],"map.":[217]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-11T00:00:00"}
