{"id":"https://openalex.org/W1900062463","doi":"https://doi.org/10.2312/pe/vriphys/vriphys08/011-019","title":"Corotated Finite Elements Made Fast and Stable","display_name":"Corotated Finite Elements Made Fast and Stable","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W1900062463","doi":"https://doi.org/10.2312/pe/vriphys/vriphys08/011-019","mag":"1900062463"},"language":"en","primary_location":{"id":"pmh:oai:CiteSeerX.psu:10.1.1.219.5754","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.5754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwcg.in.tum.de/Research/data/Publications/vriphys08.pdf","raw_type":"text"},"type":"article","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.2312/pe/vriphys/vriphys08/011-019","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054001020","display_name":"Joachim Georgii","orcid":"https://orcid.org/0009-0000-3874-461X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Georgii, Joachim","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029621326","display_name":"R\u00fcdiger Westermann","orcid":"https://orcid.org/0000-0002-3394-0731"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Westermann, R\u00fcdiger","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054001020"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":42,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9869999885559082,"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":0.9869999885559082,"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/T10481","display_name":"Computer Graphics and Visualization Techniques","score":0.984000027179718,"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"}},{"id":"https://openalex.org/T11366","display_name":"Elasticity and Material Modeling","score":0.982699990272522,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"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/finite-element-method","display_name":"Finite element method","score":0.807023286819458},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.790191650390625},{"id":"https://openalex.org/keywords/rigid-body","display_name":"Rigid body","score":0.5569903254508972},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5020520687103271},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4470616281032562},{"id":"https://openalex.org/keywords/linear-elasticity","display_name":"Linear elasticity","score":0.42852017283439636},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4031907021999359},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.37159594893455505},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.3476337790489197},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.32659584283828735},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20625320076942444},{"id":"https://openalex.org/keywords/structural-engineering","display_name":"Structural engineering","score":0.14890724420547485},{"id":"https://openalex.org/keywords/engineering","display_name":"Engineering","score":0.12889528274536133},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1270766258239746},{"id":"https://openalex.org/keywords/classical-mechanics","display_name":"Classical mechanics","score":0.1244594156742096},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.09910851716995239}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.807023286819458},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.790191650390625},{"id":"https://openalex.org/C145980571","wikidata":"https://www.wikidata.org/wiki/Q192788","display_name":"Rigid body","level":2,"score":0.5569903254508972},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5020520687103271},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4470616281032562},{"id":"https://openalex.org/C3161131","wikidata":"https://www.wikidata.org/wiki/Q14097093","display_name":"Linear elasticity","level":3,"score":0.42852017283439636},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4031907021999359},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37159594893455505},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.3476337790489197},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.32659584283828735},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20625320076942444},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.14890724420547485},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.12889528274536133},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1270766258239746},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.1244594156742096},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.09910851716995239}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:CiteSeerX.psu:10.1.1.219.5754","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.5754","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://wwwcg.in.tum.de/Research/data/Publications/vriphys08.pdf","raw_type":"text"},{"id":"doi:10.2312/pe/vriphys/vriphys08/011-019","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vriphys/vriphys08/011-019","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"doi:10.2312/pe/vriphys/vriphys08/011-019","is_oa":true,"landing_page_url":"https://doi.org/10.2312/pe/vriphys/vriphys08/011-019","pdf_url":null,"source":{"id":"https://openalex.org/S7407052899","display_name":"Eurographics","issn_l":null,"issn":[],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"article"},"sustainable_development_goals":[{"score":0.800000011920929,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1483559473","https://openalex.org/W1492940985","https://openalex.org/W1494671974","https://openalex.org/W1530872699","https://openalex.org/W1561021726","https://openalex.org/W1573186872","https://openalex.org/W1596475617","https://openalex.org/W1874409481","https://openalex.org/W1969783366","https://openalex.org/W1971609847","https://openalex.org/W1976783998","https://openalex.org/W1980757084","https://openalex.org/W1981673074","https://openalex.org/W1985787666","https://openalex.org/W1989871863","https://openalex.org/W1991202364","https://openalex.org/W1997542937","https://openalex.org/W2026121678","https://openalex.org/W2063189491","https://openalex.org/W2064459118","https://openalex.org/W2067497591","https://openalex.org/W2095842012","https://openalex.org/W2120673203","https://openalex.org/W2125537373","https://openalex.org/W2126264167","https://openalex.org/W2133281300","https://openalex.org/W2135521054","https://openalex.org/W2140188262","https://openalex.org/W2141654056","https://openalex.org/W2144909146","https://openalex.org/W2145804351","https://openalex.org/W2147774191","https://openalex.org/W2164888711","https://openalex.org/W2171186721","https://openalex.org/W2235036220","https://openalex.org/W2236592196","https://openalex.org/W2249925049","https://openalex.org/W2296166276"],"related_works":["https://openalex.org/W1980757084","https://openalex.org/W2141731969","https://openalex.org/W2169055648","https://openalex.org/W3138143451","https://openalex.org/W2116287770","https://openalex.org/W1985787666","https://openalex.org/W2171186721","https://openalex.org/W2156086757","https://openalex.org/W2126264167","https://openalex.org/W2074433215","https://openalex.org/W2074363080","https://openalex.org/W1561021726","https://openalex.org/W2071661704","https://openalex.org/W2055174129","https://openalex.org/W2111237478","https://openalex.org/W2107288692","https://openalex.org/W2054620740","https://openalex.org/W2004167999","https://openalex.org/W1585138277","https://openalex.org/W1551542124"],"abstract_inverted_index":{"Multigrid":[0],"finite-element":[1],"solvers":[2],"using":[3,35,229],"the":[4,15,31,43,57,60,87,99,106,116,141,146,159,170,175,178,196,203,221,230],"corotational":[5,61,135,231],"formulation":[6,62,136,232],"of":[7,17,26,42,59,89,92,158,181,210,238],"finite":[8,93,101,122,224],"elements":[9,94],"provide":[10],"an":[11],"attractive":[12],"means":[13],"for":[14,50,154,241],"simulation":[16,206],"deformable":[18,226],"bodies":[19],"exhibiting":[20],"linear":[21],"elastic":[22],"response.":[23],"The":[24,79],"separation":[25],"rigid":[27,117],"body":[28,118,227],"motions":[29,34],"from":[30,120],"total":[32,121],"element":[33,52,102,123,225],"purely":[36],"geometric":[37],"methods":[38],"or":[39],"polar":[40],"decomposition":[41],"deformation":[44],"gradient,":[45],"however,":[46],"can":[47,233],"introduce":[48],"instabilities":[49],"large":[51,90],"rotations":[53],"and":[54,185],"deformations.":[55],"Furthermore,":[56],"integration":[58],"into":[63,177],"dynamic":[64],"multigrid":[65,171,204,217],"elasticity":[66],"simulations":[67,228],"requires":[68],"to":[69,98,114,165,168,212,215,220,243],"continually":[70],"rebuild":[71],"consistent":[72],"system":[73],"matrices":[74],"at":[75,95,236],"different":[76],"resolution":[77],"levels.":[78],"computational":[80,142],"load":[81],"imposed":[82],"by":[83,149,207],"these":[84],"updates":[85],"prohibits":[86],"use":[88],"numbers":[91],"rates":[96,237],"comparable":[97],"small-strain":[100],"formulation.":[103],"To":[104],"overcome":[105],"first":[107],"problem,":[108],"we":[109],"present":[110],"a":[111,132,151,182,208],"new":[112],"method":[113],"extract":[115],"motion":[119],"displacements":[124],"based":[125],"on":[126],"energy":[127],"minimization.":[128],"This":[129],"results":[130],"in":[131],"very":[133],"stable":[134],"that":[137],"only":[138],"slightly":[139],"increases":[140,198],"overhead.":[143],"We":[144],"address":[145],"second":[147],"problem":[148,176],"introducing":[150],"novel":[152],"algorithm":[153,197],"computing":[155],"sparse":[156],"products":[157],"form":[160],"RKRT,":[161],"as":[162],"they":[163],"have":[164],"be":[166,234],"evaluated":[167],"update":[169],"hierarchy.":[172],"By":[173],"reformulating":[174],"simultaneous":[179],"processing":[180],"sequential":[183],"data":[184],"control":[186],"stream,":[187],"cache":[188],"miss":[189],"penalties":[190],"are":[191],"significantly":[192],"reduced.":[193],"Even":[194],"though":[195],"memory":[199],"requirements,":[200],"it":[201],"accelerates":[202],"FE":[205],"factor":[209],"up":[211,242],"4":[213],"compared":[214],"previous":[216],"approaches.":[218],"Due":[219],"proposed":[222],"improvements,":[223],"performed":[235],"17":[239],"tps":[240],"12k":[244],"elements.":[245]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":6},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
