{"id":"https://openalex.org/W2767169025","doi":"https://doi.org/10.1109/tvcg.2017.2768532","title":"Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation","display_name":"Exponential Rosenbrock-Euler Integrators for Elastodynamic Simulation","publication_year":2017,"publication_date":"2017-11-01","ids":{"openalex":"https://openalex.org/W2767169025","doi":"https://doi.org/10.1109/tvcg.2017.2768532","mag":"2767169025","pmid":"https://pubmed.ncbi.nlm.nih.gov/29990083"},"language":"en","primary_location":{"id":"doi:10.1109/tvcg.2017.2768532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2017.2768532","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5005410211","display_name":"Yu Ju Chen","orcid":"https://orcid.org/0000-0002-7540-6246"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Yu Ju Chen","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0002-7540-6246","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030026541","display_name":"Uri M. Ascher","orcid":"https://orcid.org/0000-0002-5177-7181"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Uri M. Ascher","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0002-5177-7181","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057504177","display_name":"Dinesh K. Pai","orcid":"https://orcid.org/0000-0002-5115-7230"},"institutions":[{"id":"https://openalex.org/I141945490","display_name":"University of British Columbia","ror":"https://ror.org/03rmrcq20","country_code":"CA","type":"education","lineage":["https://openalex.org/I141945490"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Dinesh K. Pai","raw_affiliation_strings":["Department of Computer Science, University of British Columbia, Vancouver, BC, Canada"],"raw_orcid":"https://orcid.org/0000-0002-5115-7230","affiliations":[{"raw_affiliation_string":"Department of Computer Science, University of British Columbia, Vancouver, BC, Canada","institution_ids":["https://openalex.org/I141945490"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4812,"has_fulltext":false,"cited_by_count":22,"citation_normalized_percentile":{"value":0.89768662,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"24","issue":"10","first_page":"2702","last_page":"2713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9889000058174133,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"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":0.9847999811172485,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9825999736785889,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7431701421737671},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.7357410192489624},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6761447787284851},{"id":"https://openalex.org/keywords/eulers-formula","display_name":"Euler's formula","score":0.6027812957763672},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.5592531561851501},{"id":"https://openalex.org/keywords/stiffness","display_name":"Stiffness","score":0.5202471017837524},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5189273357391357},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.49578461050987244},{"id":"https://openalex.org/keywords/euler-method","display_name":"Euler method","score":0.4930519759654999},{"id":"https://openalex.org/keywords/backward-euler-method","display_name":"Backward Euler method","score":0.4661012887954712},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.46523088216781616},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4314066171646118},{"id":"https://openalex.org/keywords/control-theory","display_name":"Control theory (sociology)","score":0.4189058542251587},{"id":"https://openalex.org/keywords/stiffness-matrix","display_name":"Stiffness matrix","score":0.41108202934265137},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37147414684295654},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23276063799858093},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17299330234527588},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14079627394676208},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.09253016114234924}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7431701421737671},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.7357410192489624},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6761447787284851},{"id":"https://openalex.org/C62884695","wikidata":"https://www.wikidata.org/wiki/Q184871","display_name":"Euler's formula","level":2,"score":0.6027812957763672},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.5592531561851501},{"id":"https://openalex.org/C2779372316","wikidata":"https://www.wikidata.org/wiki/Q569057","display_name":"Stiffness","level":2,"score":0.5202471017837524},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5189273357391357},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.49578461050987244},{"id":"https://openalex.org/C75380026","wikidata":"https://www.wikidata.org/wiki/Q868454","display_name":"Euler method","level":3,"score":0.4930519759654999},{"id":"https://openalex.org/C768646","wikidata":"https://www.wikidata.org/wiki/Q2736820","display_name":"Backward Euler method","level":3,"score":0.4661012887954712},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.46523088216781616},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4314066171646118},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.4189058542251587},{"id":"https://openalex.org/C14198674","wikidata":"https://www.wikidata.org/wiki/Q3851930","display_name":"Stiffness matrix","level":3,"score":0.41108202934265137},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37147414684295654},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23276063799858093},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17299330234527588},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14079627394676208},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.09253016114234924},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C2775924081","wikidata":"https://www.wikidata.org/wiki/Q55608371","display_name":"Control (management)","level":2,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"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/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C66938386","wikidata":"https://www.wikidata.org/wiki/Q633538","display_name":"Structural engineering","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tvcg.2017.2768532","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tvcg.2017.2768532","pdf_url":null,"source":{"id":"https://openalex.org/S84775595","display_name":"IEEE Transactions on Visualization and Computer Graphics","issn_l":"1077-2626","issn":["1077-2626","1941-0506","2160-9306"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Visualization and Computer Graphics","raw_type":"journal-article"},{"id":"pmid:29990083","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/29990083","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on visualization and computer graphics","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320994","display_name":"Canada Research Chairs","ror":"https://ror.org/0517h6h17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":51,"referenced_works":["https://openalex.org/W592368443","https://openalex.org/W636856703","https://openalex.org/W1524015806","https://openalex.org/W1553886054","https://openalex.org/W1568806545","https://openalex.org/W1963635807","https://openalex.org/W1976206179","https://openalex.org/W1989262384","https://openalex.org/W1989947528","https://openalex.org/W1990853264","https://openalex.org/W2005092540","https://openalex.org/W2010652522","https://openalex.org/W2013967026","https://openalex.org/W2018931076","https://openalex.org/W2024243735","https://openalex.org/W2027319740","https://openalex.org/W2028212620","https://openalex.org/W2032617361","https://openalex.org/W2036772120","https://openalex.org/W2037283333","https://openalex.org/W2039598846","https://openalex.org/W2053128021","https://openalex.org/W2055035360","https://openalex.org/W2057602562","https://openalex.org/W2077852010","https://openalex.org/W2081958397","https://openalex.org/W2082043116","https://openalex.org/W2082232304","https://openalex.org/W2096932164","https://openalex.org/W2100193742","https://openalex.org/W2106565812","https://openalex.org/W2124969394","https://openalex.org/W2130727150","https://openalex.org/W2133147905","https://openalex.org/W2142123552","https://openalex.org/W2156410578","https://openalex.org/W2171303908","https://openalex.org/W2192608380","https://openalex.org/W2235036220","https://openalex.org/W2256799124","https://openalex.org/W2510393759","https://openalex.org/W2611752399","https://openalex.org/W2737753202","https://openalex.org/W2762162753","https://openalex.org/W3003409178","https://openalex.org/W3137300270","https://openalex.org/W4210897277","https://openalex.org/W4211077197","https://openalex.org/W6674793146","https://openalex.org/W6687733348","https://openalex.org/W6964164060"],"related_works":["https://openalex.org/W2089955609","https://openalex.org/W2189596786","https://openalex.org/W2039299714","https://openalex.org/W2466040413","https://openalex.org/W4382053489","https://openalex.org/W3111435437","https://openalex.org/W2378504881","https://openalex.org/W2375749791","https://openalex.org/W4383710307","https://openalex.org/W2084833136"],"abstract_inverted_index":{"High":[0],"quality":[1],"simulations":[2],"of":[3,6,17,48,124,142],"the":[4,15,46,68,100,104],"dynamics":[5],"soft":[7,143],"flexible":[8],"objects":[9],"can":[10],"be":[11],"rather":[12],"costly,":[13],"because":[14],"assembly":[16],"internal":[18],"forces":[19],"through":[20],"an":[21,49],"often":[22],"nonlinear":[23],"stiffness":[24,106],"at":[25,112],"each":[26],"time":[27,70],"step":[28],"is":[29,61,91,108],"expensive.":[30],"Many":[31],"standard":[32],"implicit":[33],"integrators":[34],"introduce":[35],"significant,":[36],"time-step":[37],"dependent":[38],"artificial":[39,57],"damping.":[40,58],"Here":[41],"we":[42,116],"propose":[43],"and":[44,64,95],"demonstrate":[45],"effectiveness":[47],"exponential":[50],"Rosenbrock-Euler":[51],"(ERE)":[52],"method":[53,60],"which":[54],"avoids":[55],"discretization-dependent":[56],"The":[59],"relatively":[62],"inexpensive":[63],"works":[65],"well":[66,97],"with":[67],"large":[69],"steps":[71],"used":[72],"in":[73,82,99],"computer":[74],"graphics.":[75],"It":[76],"retains":[77],"correct":[78],"qualitative":[79],"behaviour":[80],"even":[81,98],"challenging":[83],"circumstances":[84],"involving":[85],"non-convex":[86],"elastic":[87],"energies.":[88],"Our":[89],"integrator":[90],"designed":[92],"to":[93,119],"handle":[94],"perform":[96],"important":[101],"cases":[102],"where":[103],"symmetric":[105],"matrix":[107],"not":[109],"positive":[110],"definite":[111],"all":[113],"times.":[114],"Thus":[115],"are":[117],"able":[118],"address":[120],"a":[121,139],"wider":[122],"range":[123,141],"practical":[125],"situations":[126],"than":[127],"other":[128],"related":[129],"solvers.":[130],"We":[131],"show":[132],"that":[133],"our":[134],"system":[135],"performs":[136],"efficiently":[137],"for":[138],"wide":[140],"materials.":[144]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":6},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":3}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}