{"id":"https://openalex.org/W2002308788","doi":"https://doi.org/10.1137/140959602","title":"Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics","display_name":"Preserving Lagrangian Structure in Nonlinear Model Reduction with Application to Structural Dynamics","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2002308788","doi":"https://doi.org/10.1137/140959602","mag":"2002308788"},"language":"en","primary_location":{"id":"doi:10.1137/140959602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140959602","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/1401.8044","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Kevin Carlberg","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Kevin Carlberg","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Ray Tuminaro","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ray Tuminaro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Paul Boggs","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paul Boggs","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":5.1534,"has_fulltext":true,"cited_by_count":90,"citation_normalized_percentile":{"value":0.95816449,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"37","issue":"2","first_page":"B153","last_page":"B184"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9485999941825867,"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"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9485999941825867,"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/T12435","display_name":"Bladed Disk Vibration Dynamics","score":0.017500000074505806,"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/T11416","display_name":"Numerical methods for differential equations","score":0.008999999612569809,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.7710999846458435},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6383000016212463},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.5354999899864197},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5203999876976013},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.48080000281333923},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.4259999990463257},{"id":"https://openalex.org/keywords/model-order-reduction","display_name":"Model order reduction","score":0.40230000019073486},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.39800000190734863},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.3799000084400177}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.7710999846458435},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7652000188827515},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6383000016212463},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.5354999899864197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5263000130653381},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5203999876976013},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.4259999990463257},{"id":"https://openalex.org/C2779277453","wikidata":"https://www.wikidata.org/wiki/Q12202921","display_name":"Model order reduction","level":3,"score":0.40230000019073486},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.39800000190734863},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.3799000084400177},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3686000108718872},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3361999988555908},{"id":"https://openalex.org/C14037181","wikidata":"https://www.wikidata.org/wiki/Q215007","display_name":"Equations of motion","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29089999198913574},{"id":"https://openalex.org/C2779886137","wikidata":"https://www.wikidata.org/wiki/Q21030012","display_name":"Symmetry (geometry)","level":2,"score":0.28630000352859497},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C2984998066","wikidata":"https://www.wikidata.org/wiki/Q105037988","display_name":"Proper orthogonal decomposition","level":3,"score":0.2696000039577484},{"id":"https://openalex.org/C2731191","wikidata":"https://www.wikidata.org/wiki/Q1778169","display_name":"Schur complement","level":3,"score":0.2678999900817871},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C42355184","wikidata":"https://www.wikidata.org/wiki/Q1361088","display_name":"Matrix decomposition","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C499771625","wikidata":"https://www.wikidata.org/wiki/Q324669","display_name":"Lagrangian mechanics","level":5,"score":0.26159998774528503},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.2563999891281128},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.2502000033855438}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/140959602","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140959602","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:1401.8044","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1401.8044","pdf_url":"https://arxiv.org/pdf/1401.8044","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:osti.gov:1140523","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1140523","pdf_url":"https://www.osti.gov/servlets/purl/1140523","source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1401.8044","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1401.8044","pdf_url":"https://arxiv.org/pdf/1401.8044","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/G1867850364","display_name":null,"funder_award_id":"DE-AC04-94AL85000","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G194215011","display_name":null,"funder_award_id":"DE\u2013AC04\u201394AL85000","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G351415096","display_name":null,"funder_award_id":"DEAC04-94AL85000","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G7318852158","display_name":null,"funder_award_id":"AC04-94AL85000","funder_id":"https://openalex.org/F4320338291","funder_display_name":"Sandia National Laboratories"},{"id":"https://openalex.org/G8456466421","display_name":null,"funder_award_id":"AC04-94AL85000","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"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320338291","display_name":"Sandia National Laboratories","ror":"https://ror.org/01apwpt12"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1544956813","https://openalex.org/W2034840616","https://openalex.org/W2047591100","https://openalex.org/W2049753327","https://openalex.org/W2058078260","https://openalex.org/W2068991306","https://openalex.org/W2091461904","https://openalex.org/W2102753028","https://openalex.org/W2104225554","https://openalex.org/W2120101088","https://openalex.org/W2124500362","https://openalex.org/W2161155740","https://openalex.org/W2161797061","https://openalex.org/W2168386575","https://openalex.org/W2170039048","https://openalex.org/W3037995832"],"related_works":[],"abstract_inverted_index":{"This":[0],"work":[1],"proposes":[2],"a":[3,132],"model-reduction":[4,165],"methodology":[5],"that":[6,167],"preserves":[7],"Lagrangian":[8,142],"structure":[9,143],"and":[10,20,37,52,55,82,119,127,144,158],"achieves":[11],"computational":[12],"efficiency":[13],"in":[14,160],"the":[15,26,66,70,76,79,83,94,102,137,146],"presence":[16],"of":[17,90,140],"high-order":[18],"nonlinearities":[19],"arbitrary":[21],"parameter":[22],"dependence.":[23],"As":[24],"such,":[25],"resulting":[27],"reduced-order":[28,88],"model":[29],"retains":[30],"key":[31,105],"properties":[32],"such":[33],"as":[34],"energy":[35],"conservation":[36],"symplectic":[38],"time-evolution":[39],"maps.":[40],"We":[41],"focus":[42],"on":[43],"parameterized":[44,113,133],"simple":[45],"mechanical":[46],"systems":[47],"subjected":[48],"to":[49,59,162],"Rayleigh":[50],"damping":[51],"external":[53,84],"forces,":[54],"consider":[56],"an":[57],"application":[58],"nonlinear":[60,164],"structural":[61],"dynamics.":[62],"To":[63],"preserve":[64,170],"structure,":[65],"method":[67],"first":[68],"approximates":[69],"system's":[71],"\u201cLagrangian":[72],"ingredients''---the":[73],"Riemannian":[74],"metric,":[75],"potential-energy":[77],"function,":[78,81],"dissipation":[80],"force---and":[85],"subsequently":[86],"derives":[87],"equations":[89],"motion":[91],"by":[92],"applying":[93],"(forced)":[95],"Euler--Lagrange":[96],"equation":[97],"with":[98],"these":[99],"quantities.":[100],"From":[101],"algebraic":[103],"perspective,":[104],"contributions":[106],"include":[107],"two":[108],"efficient":[109],"techniques":[110,166],"for":[111,131],"approximating":[112],"reduced":[114],"matrices":[115],"while":[116,154],"preserving":[117,141],"symmetry":[118],"positive":[120],"definiteness:":[121],"matrix":[122],"gappy":[123],"proper":[124],"orthogonal":[125],"decomposition":[126],"reduced-basis":[128],"sparsification.":[129],"Results":[130],"truss-structure":[134],"problem":[135],"demonstrate":[136],"practical":[138],"importance":[139],"illustrate":[145],"proposed":[147],"method's":[148],"merits:":[149],"it":[150],"reduces":[151],"computation":[152],"time":[153],"maintaining":[155],"high":[156],"accuracy":[157],"stability,":[159],"contrast":[161],"existing":[163],"do":[168],"not":[169],"structure.":[171]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":9},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":10},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":5},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-01T09:00:35.917206","created_date":"2016-06-24T00:00:00"}
