{"id":"https://openalex.org/W2057235791","doi":"https://doi.org/10.1137/120873558","title":"Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs","display_name":"Automated Derivation of the Adjoint of High-Level Transient Finite Element Programs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2057235791","doi":"https://doi.org/10.1137/120873558","mag":"2057235791"},"language":"en","primary_location":{"id":"doi:10.1137/120873558","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120873558","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/1204.5577","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"P. E. Farrell","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"P. E. Farrell","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"D. A. Ham","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"D. A. Ham","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"S. W. Funke","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"S. W. Funke","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"M. E. Rognes","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. E. Rognes","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":7.0275,"has_fulltext":false,"cited_by_count":237,"citation_normalized_percentile":{"value":0.97371002,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"35","issue":"4","first_page":"C369","last_page":"C393"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.3052000105381012,"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":0.3052000105381012,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.23010000586509705,"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":0.17180000245571136,"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/finite-element-method","display_name":"Finite element method","score":0.6388000249862671},{"id":"https://openalex.org/keywords/automatic-differentiation","display_name":"Automatic differentiation","score":0.6183000206947327},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5184999704360962},{"id":"https://openalex.org/keywords/compiler","display_name":"Compiler","score":0.47369998693466187},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.4544000029563904},{"id":"https://openalex.org/keywords/fortran","display_name":"Fortran","score":0.424699991941452},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.42329999804496765},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.375900000333786},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.3698999881744385}],"concepts":[{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6388000249862671},{"id":"https://openalex.org/C133512626","wikidata":"https://www.wikidata.org/wiki/Q787371","display_name":"Automatic differentiation","level":3,"score":0.6183000206947327},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5975000262260437},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5184999704360962},{"id":"https://openalex.org/C169590947","wikidata":"https://www.wikidata.org/wiki/Q47506","display_name":"Compiler","level":2,"score":0.47369998693466187},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.4544000029563904},{"id":"https://openalex.org/C2778241615","wikidata":"https://www.wikidata.org/wiki/Q83303","display_name":"Fortran","level":2,"score":0.424699991941452},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.42329999804496765},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.375900000333786},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37119999527931213},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3698999881744385},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3650999963283539},{"id":"https://openalex.org/C2777904410","wikidata":"https://www.wikidata.org/wiki/Q7397","display_name":"Software","level":2,"score":0.36489999294281006},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3582000136375427},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35359999537467957},{"id":"https://openalex.org/C37785467","wikidata":"https://www.wikidata.org/wiki/Q385325","display_name":"Modelica","level":2,"score":0.3465999960899353},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.32269999384880066},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3190000057220459},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.31439998745918274},{"id":"https://openalex.org/C165551260","wikidata":"https://www.wikidata.org/wiki/Q4428962","display_name":"Adjoint equation","level":3,"score":0.3077999949455261},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28790000081062317},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C200288055","wikidata":"https://www.wikidata.org/wiki/Q2621792","display_name":"Element (criminal law)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C96147967","wikidata":"https://www.wikidata.org/wiki/Q190686","display_name":"Subroutine","level":2,"score":0.28040000796318054},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.2799000144004822},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C133162039","wikidata":"https://www.wikidata.org/wiki/Q1061077","display_name":"Code generation","level":3,"score":0.2754000127315521},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2597000002861023},{"id":"https://openalex.org/C43126263","wikidata":"https://www.wikidata.org/wiki/Q128751","display_name":"Source code","level":2,"score":0.25600001215934753},{"id":"https://openalex.org/C186644900","wikidata":"https://www.wikidata.org/wiki/Q194152","display_name":"Parsing","level":2,"score":0.251800000667572}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120873558","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120873558","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:1204.5577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5577","pdf_url":"https://arxiv.org/pdf/1204.5577","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1204.5577","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1204.5577","pdf_url":"https://arxiv.org/pdf/1204.5577","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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/G2934007857","display_name":null,"funder_award_id":"NE/I001360/1","funder_id":"https://openalex.org/F4320334631","funder_display_name":"Natural Environment Research Council"},{"id":"https://openalex.org/G2946230651","display_name":null,"funder_award_id":"NE/I001360/1","funder_id":"https://openalex.org/F4320320022","funder_display_name":"Sight Research UK"},{"id":"https://openalex.org/G6225080052","display_name":null,"funder_award_id":"EP/I00405X/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320320022","display_name":"Sight Research UK","ror":"https://ror.org/03z2py885"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334631","display_name":"Natural Environment Research Council","ror":"https://ror.org/02b5d8509"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":33,"referenced_works":["https://openalex.org/W51269470","https://openalex.org/W1946796247","https://openalex.org/W1967134278","https://openalex.org/W1970661577","https://openalex.org/W1975435453","https://openalex.org/W1979836673","https://openalex.org/W1982474448","https://openalex.org/W1988314016","https://openalex.org/W2006700733","https://openalex.org/W2008949920","https://openalex.org/W2017393458","https://openalex.org/W2020527870","https://openalex.org/W2028741947","https://openalex.org/W2039406585","https://openalex.org/W2046528357","https://openalex.org/W2056582033","https://openalex.org/W2060636614","https://openalex.org/W2064636372","https://openalex.org/W2065317334","https://openalex.org/W2065689258","https://openalex.org/W2078031695","https://openalex.org/W2082585997","https://openalex.org/W2084041252","https://openalex.org/W2084820956","https://openalex.org/W2096237543","https://openalex.org/W2099425512","https://openalex.org/W2100418324","https://openalex.org/W2105812569","https://openalex.org/W2128095813","https://openalex.org/W2133147107","https://openalex.org/W2167657634","https://openalex.org/W2569713119","https://openalex.org/W4232726482"],"related_works":[],"abstract_inverted_index":{"In":[0,46],"this":[1],"paper":[2],"we":[3],"demonstrate":[4],"a":[5,17,38,50,78,106,160,231],"new":[6],"technique":[7,22],"for":[8,149,183],"deriving":[9],"discrete":[10],"adjoint":[11,122,172,198],"and":[12,27,97,135,197,221],"tangent":[13,195],"linear":[14,196],"models":[15,199],"of":[16,42,85,128,132,163,223,234],"finite":[18,139],"element":[19,140],"model.":[20],"The":[21,34,99,171,218],"is":[23,88,103],"significantly":[24],"more":[25,92],"efficient":[26],"automatic":[28],"than":[29],"standard":[30],"algorithmic":[31],"differentiation":[32],"techniques.":[33],"approach":[35,119,154,225],"relies":[36,124],"on":[37,114,125],"high-level":[39,57],"symbolic":[40],"representation":[41],"the":[43,60,64,82,86,115,129,133,137,146,150,194,224],"forward":[44,164],"problem.":[45],"contrast":[47],"to":[48,62,67,94,120,143,159,179,207,211,214],"developing":[49],"model":[51,134,173],"directly":[52],"in":[53,70,105,202],"Fortran":[54],"or":[55,190,213],"C++,":[56],"systems":[58,76],"allow":[59],"developer":[61],"express":[63],"variational":[65],"problems":[66],"be":[68],"solved":[69],"near-mathematical":[71],"notation.":[72],"As":[73],"such,":[74],"these":[75],"have":[77],"key":[79],"advantage:":[80],"since":[81],"mathematical":[83],"structure":[84,131],"problem":[87],"preserved,":[89],"they":[90],"are":[91,226],"amenable":[93],"automated":[95,121],"analysis":[96],"manipulation.":[98],"framework":[100],"introduced":[101],"here":[102],"implemented":[104],"freely":[107],"available":[108],"software":[109],"package":[110],"named":[111],"dolfin-adjoint,":[112],"based":[113],"FEniCS":[116,138],"Project.":[117],"Our":[118],"derivation":[123],"run-time":[126],"annotation":[127],"temporal":[130],"employs":[136,175],"form":[141],"compiler":[142],"automatically":[144,174],"generate":[145],"low-level":[147],"code":[148],"derived":[151],"models.":[152,170],"This":[153],"requires":[155],"only":[156],"trivial":[157],"changes":[158],"large":[161],"class":[162],"models,":[165,185],"including":[166],"complicated":[167],"time-dependent":[168],"nonlinear":[169,184],"optimal":[176],"checkpointing":[177],"schemes":[178],"mitigate":[180],"storage":[181],"requirements":[182],"without":[186,204],"any":[187,205],"user":[188],"management":[189],"intervention.":[191],"Furthermore,":[192],"both":[193],"naturally":[200],"work":[201],"parallel,":[203],"need":[206],"differentiate":[208],"through":[209],"calls":[210],"MPI":[212],"parse":[215],"OpenMP":[216],"directives.":[217],"generality,":[219],"applicability,":[220],"efficiency":[222],"demonstrated":[227],"with":[228],"examples":[229],"from":[230],"wide":[232],"range":[233],"scientific":[235],"applications.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":14},{"year":2024,"cited_by_count":24},{"year":2023,"cited_by_count":26},{"year":2022,"cited_by_count":31},{"year":2021,"cited_by_count":28},{"year":2020,"cited_by_count":25},{"year":2019,"cited_by_count":22},{"year":2018,"cited_by_count":24},{"year":2017,"cited_by_count":22},{"year":2016,"cited_by_count":10},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":3}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2016-06-24T00:00:00"}