{"id":"https://openalex.org/W2076641507","doi":"https://doi.org/10.1137/050624108","title":"Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization","display_name":"Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization","publication_year":2006,"publication_date":"2006-01-01","ids":{"openalex":"https://openalex.org/W2076641507","doi":"https://doi.org/10.1137/050624108","mag":"2076641507"},"language":"en","primary_location":{"id":"doi:10.1137/050624108","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624108","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-01880854","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015910078","display_name":"Fr\u00e9d\u00e9ric de Gournay","orcid":"https://orcid.org/0000-0003-4721-3137"},"institutions":[{"id":"https://openalex.org/I84500057","display_name":"Institut de Math\u00e9matiques de Toulouse","ror":"https://ror.org/014vp6c30","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I196454796","https://openalex.org/I4210092408","https://openalex.org/I4210126056","https://openalex.org/I4210141950","https://openalex.org/I4210152422","https://openalex.org/I4405258862","https://openalex.org/I84500057"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Fr\u00e9d\u00e9ric de Gournay","raw_affiliation_strings":["Institut de Math\u00e9matiques de Toulouse (UMR5219)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut de Math\u00e9matiques de Toulouse (UMR5219)","institution_ids":["https://openalex.org/I84500057"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5015910078"],"corresponding_institution_ids":["https://openalex.org/I84500057"],"apc_list":null,"apc_paid":null,"fwci":14.0344,"has_fulltext":false,"cited_by_count":139,"citation_normalized_percentile":{"value":0.98781765,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"45","issue":"1","first_page":"343","last_page":"367"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9997000098228455,"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":0.9997000098228455,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9970999956130981,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9908999800682068,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8980451822280884},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.7635217905044556},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7114144563674927},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.7018905282020569},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.592978298664093},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.48960572481155396},{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.48870518803596497},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.48297277092933655},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4521222710609436},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44090625643730164},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4391133189201355},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.43785473704338074},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.43111705780029297},{"id":"https://openalex.org/keywords/level-set","display_name":"Level set (data structures)","score":0.42989233136177063},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4283354580402374},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.09234532713890076},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07391494512557983}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8980451822280884},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7635217905044556},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7114144563674927},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.7018905282020569},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.592978298664093},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.48960572481155396},{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.48870518803596497},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.48297277092933655},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4521222710609436},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44090625643730164},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4391133189201355},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.43785473704338074},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.43111705780029297},{"id":"https://openalex.org/C153008295","wikidata":"https://www.wikidata.org/wiki/Q6535093","display_name":"Level set (data structures)","level":2,"score":0.42989233136177063},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4283354580402374},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.09234532713890076},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07391494512557983},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"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/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1137/050624108","is_oa":false,"landing_page_url":"https://doi.org/10.1137/050624108","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"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.218.4149","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.218.4149","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cmap.polytechnique.fr/preprint/repository/591.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.644.3531","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.644.3531","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ann.jussieu.fr/~frey/papers/topological_optimization/De Gournay F.%2C Velocity Extension for the Level-set Method and Multiple Eigenvalues in Shape Optimization.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-01880854v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01880854","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2006, 45 (1), pp.343 - 367. ⟨10.1137/050624108⟩","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01880854v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01880854","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Control and Optimization, 2006, 45 (1), pp.343 - 367. ⟨10.1137/050624108⟩","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W21432690","https://openalex.org/W613838126","https://openalex.org/W1551360398","https://openalex.org/W1575147392","https://openalex.org/W1575923498","https://openalex.org/W1580724525","https://openalex.org/W1584280986","https://openalex.org/W1982739078","https://openalex.org/W1991113069","https://openalex.org/W2000388899","https://openalex.org/W2002428563","https://openalex.org/W2003943233","https://openalex.org/W2010964098","https://openalex.org/W2016413885","https://openalex.org/W2037004190","https://openalex.org/W2060709740","https://openalex.org/W2061502567","https://openalex.org/W2066137585","https://openalex.org/W2068668671","https://openalex.org/W2069697210","https://openalex.org/W2086948940","https://openalex.org/W2094251381","https://openalex.org/W2132034927","https://openalex.org/W2138715797","https://openalex.org/W2139513792","https://openalex.org/W2166783044","https://openalex.org/W2181453853","https://openalex.org/W2503518947","https://openalex.org/W2912346027","https://openalex.org/W2912522929","https://openalex.org/W4214706872","https://openalex.org/W4230378860","https://openalex.org/W4241610645","https://openalex.org/W4249480917","https://openalex.org/W4293183906","https://openalex.org/W4300599381"],"related_works":["https://openalex.org/W2164189677","https://openalex.org/W2950745223","https://openalex.org/W4299978068","https://openalex.org/W4294959669","https://openalex.org/W4301407218","https://openalex.org/W2086948940","https://openalex.org/W2048634512","https://openalex.org/W2100745875","https://openalex.org/W2162606802","https://openalex.org/W2114406852"],"abstract_inverted_index":{"In":[0],"the":[1,7,15,18,33,50,55,62],"context":[2],"of":[3,14,17,49,52,54,64],"structural":[4],"optimization":[5,63],"by":[6],"level-set":[8,56],"method,":[9],"we":[10],"propose":[11],"an":[12],"extension":[13],"velocity":[16],"underlying":[19],"Hamilton-Jacobi":[20],"equation.":[21],"The":[22],"gradient":[23],"method":[24],"is":[25,61],"endowed":[26],"with":[27],"a":[28,46],"Hilbertian":[29],"structure":[30],"based":[31],"on":[32],"H1":[34],"Sobolev":[35],"space.":[36],"Numerical":[37],"results":[38],"for":[39],"compliance":[40],"minimization":[41],"and":[42],"mechanism":[43],"design":[44],"show":[45],"strong":[47],"improvement":[48],"rate":[51],"convergence":[53],"method.":[57],"Another":[58],"important":[59],"application":[60],"multiple":[65],"eigenvalues.":[66]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":11},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":10},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":12},{"year":2014,"cited_by_count":9},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":6}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}