{"id":"https://openalex.org/W2008595332","doi":"https://doi.org/10.1137/s0363012901384193","title":"The Topological Asymptotic Expansion for the Dirichlet Problem","display_name":"The Topological Asymptotic Expansion for the Dirichlet Problem","publication_year":2002,"publication_date":"2002-01-01","ids":{"openalex":"https://openalex.org/W2008595332","doi":"https://doi.org/10.1137/s0363012901384193","mag":"2008595332"},"language":"en","primary_location":{"id":"doi:10.1137/s0363012901384193","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901384193","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","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/A5045173039","display_name":"Ph. Guillaume","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ph. Guillaume","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5029653363","display_name":"K. Sid Idris","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"K. Sid Idris","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":14.1295,"has_fulltext":false,"cited_by_count":91,"citation_normalized_percentile":{"value":0.98814947,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"41","issue":"4","first_page":"1042","last_page":"1072"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998000264167786,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9994999766349792,"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/T11558","display_name":"Composite Material Mechanics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/mathematics","display_name":"Mathematics","score":0.8289823532104492},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.8253962993621826},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5541003346443176},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.49633294343948364},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.48816853761672974},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4712931215763092},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.46544158458709717},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.4615632891654968},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45691758394241333},{"id":"https://openalex.org/keywords/dirichlet-problem","display_name":"Dirichlet problem","score":0.44335824251174927},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.41431140899658203},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32827451825141907},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.32755047082901},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.12440037727355957},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.10357528924942017}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8289823532104492},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.8253962993621826},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5541003346443176},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.49633294343948364},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.48816853761672974},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4712931215763092},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.46544158458709717},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.4615632891654968},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45691758394241333},{"id":"https://openalex.org/C2779560616","wikidata":"https://www.wikidata.org/wiki/Q1192869","display_name":"Dirichlet problem","level":3,"score":0.44335824251174927},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.41431140899658203},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32827451825141907},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.32755047082901},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.12440037727355957},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.10357528924942017},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"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/s0363012901384193","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0363012901384193","pdf_url":null,"source":{"id":"https://openalex.org/S897311980","display_name":"SIAM Journal on Control and Optimization","issn_l":"0363-0129","issn":["0363-0129","1095-7138"],"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 Control and Optimization","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W52531309","https://openalex.org/W147304697","https://openalex.org/W762291902","https://openalex.org/W1589236075","https://openalex.org/W1995067704","https://openalex.org/W2003305312","https://openalex.org/W2008633227","https://openalex.org/W2013269090","https://openalex.org/W2017091038","https://openalex.org/W2020577281","https://openalex.org/W2035629106","https://openalex.org/W2041523977","https://openalex.org/W2062618977","https://openalex.org/W2062893182","https://openalex.org/W2094251381","https://openalex.org/W2473059737","https://openalex.org/W2491155384","https://openalex.org/W2529767787"],"related_works":["https://openalex.org/W1985820779","https://openalex.org/W2131027811","https://openalex.org/W1595431397","https://openalex.org/W1972896192","https://openalex.org/W2888270039","https://openalex.org/W3144491958","https://openalex.org/W1566960010","https://openalex.org/W2019314278","https://openalex.org/W2380855050","https://openalex.org/W4237337559"],"abstract_inverted_index":{"The":[0],"topological":[1],"sensitivity":[2],"analysis":[3],"provides":[4],"an":[5,49],"asymptotic":[6,121,140],"expansion":[7,21,50,73,122],"of":[8,61,78,125,138,147],"a":[9,14,18,23,38,58,144,151],"shape":[10,31,77,127],"function":[11,89,112],"when":[12],"creating":[13],"small":[15],"hole":[16,80],"inside":[17],"domain.":[19],"This":[20],"yields":[22,143],"descent":[24],"direction":[25],"which":[26,142],"can":[27],"be":[28],"used":[29],"for":[30,53,57],"optimization":[32,43],"if":[33,86,109],"one":[34],"wishes":[35],"to":[36,95],"keep":[37],"classical":[39,148,155],"domain":[40],"throughout":[41],"the":[42,54,69,76,79,87,92,96,110,114,120,126,129,136,139],"process.":[44],"In":[45,68,118],"this":[46,72],"paper,":[47],"such":[48],"is":[51,123],"obtained":[52],"Poisson":[55],"equation":[56],"large":[59],"class":[60],"cost":[62,88,111],"functions":[63],"and":[64],"arbitrarily":[65],"shaped":[66],"holes.":[67],"three-dimensional":[70],"case,":[71],"depends":[74],"on":[75,83,106],"but":[81],"not":[82],"its":[84,107],"orientation":[85,108],"involves":[90,113],"only":[91],"solution":[93,156],"u":[94],"underlying":[97],"partial":[98],"differential":[99],"equation,":[100],"whereas":[101],"it":[102],"may":[103],"also":[104],"depend":[105],"gradient":[115],"$\\nabla":[116],"u$.":[117],"contrast,":[119],"independent":[124],"in":[128,150],"two-dimensional":[130],"case.":[131],"A":[132],"numerical":[133],"example":[134],"illustrates":[135],"use":[137],"expansion,":[141],"minimizing":[145],"sequence":[146],"domains":[149],"case":[152],"where":[153],"no":[154],"exists.":[157]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":6},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":4},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":6},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":7}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
