{"id":"https://openalex.org/W2015492419","doi":"https://doi.org/10.1137/130914048","title":"Pyramid Algorithms for Bernstein--B\u00e9zier Finite Elements of High, Nonuniform Order in Any Dimension","display_name":"Pyramid Algorithms for Bernstein--B\u00e9zier Finite Elements of High, Nonuniform Order in Any Dimension","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2015492419","doi":"https://doi.org/10.1137/130914048","mag":"2015492419"},"language":"en","primary_location":{"id":"doi:10.1137/130914048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130914048","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":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091196582","display_name":"Mark Ainsworth","orcid":"https://orcid.org/0000-0002-4899-1048"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Mark Ainsworth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5091196582"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8713,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83756055,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"36","issue":"2","first_page":"A543","last_page":"A569"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9998999834060669,"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/T10531","display_name":"Advanced Vision and Imaging","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/algorithm","display_name":"Algorithm","score":0.7434365749359131},{"id":"https://openalex.org/keywords/pyramid","display_name":"Pyramid (geometry)","score":0.6648865342140198},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6208793520927429},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5957615375518799},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5686677694320679},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5346547365188599},{"id":"https://openalex.org/keywords/b\u00e9zier-curve","display_name":"B\u00e9zier curve","score":0.530933141708374},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.518928050994873},{"id":"https://openalex.org/keywords/affine-transformation","display_name":"Affine transformation","score":0.46980103850364685},{"id":"https://openalex.org/keywords/element","display_name":"Element (criminal law)","score":0.44323819875717163},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4315708577632904},{"id":"https://openalex.org/keywords/time-complexity","display_name":"Time complexity","score":0.4126732349395752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.32561415433883667},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.20702320337295532},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.12923100590705872},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10502010583877563}],"concepts":[{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.7434365749359131},{"id":"https://openalex.org/C142575187","wikidata":"https://www.wikidata.org/wiki/Q3358290","display_name":"Pyramid (geometry)","level":2,"score":0.6648865342140198},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6208793520927429},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5957615375518799},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5686677694320679},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5346547365188599},{"id":"https://openalex.org/C206423108","wikidata":"https://www.wikidata.org/wiki/Q214728","display_name":"B\u00e9zier curve","level":2,"score":0.530933141708374},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.518928050994873},{"id":"https://openalex.org/C92757383","wikidata":"https://www.wikidata.org/wiki/Q382497","display_name":"Affine transformation","level":2,"score":0.46980103850364685},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.44323819875717163},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4315708577632904},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.4126732349395752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.32561415433883667},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.20702320337295532},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.12923100590705872},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10502010583877563},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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":1,"locations":[{"id":"doi:10.1137/130914048","is_oa":false,"landing_page_url":"https://doi.org/10.1137/130914048","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"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.47999998927116394,"id":"https://metadata.un.org/sdg/11","display_name":"Sustainable cities and communities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W321261355","https://openalex.org/W396760590","https://openalex.org/W629836974","https://openalex.org/W837422817","https://openalex.org/W1490482062","https://openalex.org/W1492326914","https://openalex.org/W1516988755","https://openalex.org/W1540740892","https://openalex.org/W1964673636","https://openalex.org/W1975977317","https://openalex.org/W1982739053","https://openalex.org/W1985144286","https://openalex.org/W2004993896","https://openalex.org/W2009674606","https://openalex.org/W2011212378","https://openalex.org/W2015255083","https://openalex.org/W2041523977","https://openalex.org/W2048113184","https://openalex.org/W2053149981","https://openalex.org/W2064514791","https://openalex.org/W2066450870","https://openalex.org/W2071289502","https://openalex.org/W2087828859","https://openalex.org/W2102076631","https://openalex.org/W2118341834","https://openalex.org/W2135723931","https://openalex.org/W2138517065","https://openalex.org/W2140835714","https://openalex.org/W2151579113","https://openalex.org/W2167690872","https://openalex.org/W2169266183","https://openalex.org/W3023870838","https://openalex.org/W3130571686"],"related_works":["https://openalex.org/W2873344491","https://openalex.org/W2313232378","https://openalex.org/W2389575128","https://openalex.org/W1903555144","https://openalex.org/W2357871848","https://openalex.org/W2165642858","https://openalex.org/W2372035321","https://openalex.org/W2956876562","https://openalex.org/W388904218","https://openalex.org/W2790198549"],"abstract_inverted_index":{"The":[0,104,148],"archetypal":[1],"pyramid":[2,77],"algorithm":[3,108,126],"is":[4,10,115,127,130],"the":[5,15,65,80,86,93,96,107,111,123,133,145,151,155],"de":[6,124],"Casteljau":[7,125],"algorithm,":[8],"which":[9],"a":[11,28,34,159],"standard":[12],"tool":[13],"for":[14,49,79,109],"evaluation":[16],"of":[17,37,83,85,95,106,122,158,163,177],"B\u00e9zier":[18],"curves":[19,54],"and":[20,41,55,75,100],"surfaces.":[21,56],"Pyramid":[22,57],"algorithms":[23,58,78],"replace":[24],"an":[25],"operation":[26],"on":[27],"single":[29],"high":[30,52,66],"order":[31,53,69,136],"polynomial":[32,135,164],"by":[33],"recursive":[35],"sequence":[36],"self-similar":[38],"affine":[39],"combinations,":[40],"are":[42],"ubiquitous":[43],"in":[44,169,174],"computer":[45],"aided":[46],"geometric":[47],"design":[48],"computations":[50],"involving":[51],"have":[59],"received":[60],"no":[61,140],"attention":[62],"whatsoever":[63],"from":[64],"(or":[67],"low)":[68],"finite":[70,88],"element":[71,89,97,101,112],"community.":[72],"We":[73],"develop":[74],"analyze":[76],"efficient":[81,156],"handling":[82],"all":[84],"basic":[87],"building":[90],"blocks,":[91],"including":[92],"assembly":[94],"load":[98],"vectors":[99],"stiffness":[102,113],"matrices.":[103],"complexity":[105,142],"generating":[110],"matrix":[114],"optimal.":[116],"A":[117],"new,":[118],"nonuniform":[119],"order,":[120],"variant":[121],"developed":[128],"that":[129,153],"applicable":[131],"to":[132],"variable":[134],"case":[137],"but":[138],"incurs":[139],"additional":[141],"compared":[143],"with":[144],"original":[146],"algorithm.":[147],"work":[149],"provides":[150],"methodology":[152],"enables":[154],"use":[157],"completely":[160],"general":[161],"distribution":[162],"degrees":[165],"without":[166],"any":[167,175],"restriction":[168],"changes":[170],"between":[171],"adjacent":[172],"cells,":[173],"number":[176],"spatial":[178],"dimensions.":[179]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}