{"id":"https://openalex.org/W2010852247","doi":"https://doi.org/10.2478/v10006-007-0034-z","title":"A Level Set Method in Shape and Topology Optimization for Variational Inequalities","display_name":"A Level Set Method in Shape and Topology Optimization for Variational Inequalities","publication_year":2007,"publication_date":"2007-10-01","ids":{"openalex":"https://openalex.org/W2010852247","doi":"https://doi.org/10.2478/v10006-007-0034-z","mag":"2010852247"},"language":"en","primary_location":{"id":"doi:10.2478/v10006-007-0034-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0034-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0034-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://sciendo.com/pdf/10.2478/v10006-007-0034-z","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058396980","display_name":"Piotr Fulma\u0144ski","orcid":"https://orcid.org/0000-0003-4939-0882"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["PL"],"is_corresponding":true,"raw_author_name":"Piotr Fulma\u0144ski","raw_affiliation_strings":["Faculty of Mathematics [Lodz] (Narutowicza 65, 90-131 \u0141\u00f3d\u017a, POLAND - Poland)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics [Lodz] (Narutowicza 65, 90-131 \u0141\u00f3d\u017a, POLAND - Poland)","institution_ids":["https://openalex.org/I34250744"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082364655","display_name":"Antoine Laurain","orcid":"https://orcid.org/0000-0002-8733-5190"},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]}],"countries":["FR","PL"],"is_corresponding":false,"raw_author_name":"Antoine Laurain","raw_affiliation_strings":["Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","institution_ids":["https://openalex.org/I34250744"]},{"raw_affiliation_string":"Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442"]},{"raw_affiliation_string":"IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083333458","display_name":"Jean-Fran\u00e7ois Scheid","orcid":"https://orcid.org/0000-0002-2777-3324"},"institutions":[{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]},{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]}],"countries":["FR","PL"],"is_corresponding":false,"raw_author_name":"Jean-Francois Scheid","raw_affiliation_strings":["Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)","CORIDA - Robust control of infinite dimensional systems and applications (France)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","institution_ids":["https://openalex.org/I34250744"]},{"raw_affiliation_string":"Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442"]},{"raw_affiliation_string":"IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]},{"raw_affiliation_string":"CORIDA - Robust control of infinite dimensional systems and applications (France)","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078359464","display_name":"Jan Soko\u0142owski","orcid":"https://orcid.org/0000-0002-3560-7342"},"institutions":[{"id":"https://openalex.org/I34250744","display_name":"University of \u0141\u00f3d\u017a","ror":"https://ror.org/05cq64r17","country_code":"PL","type":"education","lineage":["https://openalex.org/I34250744"]},{"id":"https://openalex.org/I90183372","display_name":"Universit\u00e9 de Lorraine","ror":"https://ror.org/04vfs2w97","country_code":"FR","type":"education","lineage":["https://openalex.org/I90183372"]},{"id":"https://openalex.org/I3017839442","display_name":"Institut \u00c9lie Cartan de Lorraine","ror":"https://ror.org/04rvw8791","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I3017839442","https://openalex.org/I4210141950","https://openalex.org/I90183372"]}],"countries":["FR","PL"],"is_corresponding":false,"raw_author_name":"Jan Soko\u0142owski","raw_affiliation_strings":["Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, University of dz, ul. Banacha 22, 90-232 d, Poland","institution_ids":["https://openalex.org/I34250744"]},{"raw_affiliation_string":"Institut Elie Cartan, Laboratoire de Mathmatiques, Universit Henri Poincar Nancy I, B.P. 239, 54506 Vandoeuvre-ls-Nancy Cedex, France","institution_ids":["https://openalex.org/I3017839442"]},{"raw_affiliation_string":"IECN - Institut \u00c9lie Cartan de Nancy (Universit\u00e9 Henri Poincar\u00e9, Campus Scientifique, boulevard des Aiguillettes, 54000 Vandoeuvre-les-Nancy - France)","institution_ids":["https://openalex.org/I3017839442","https://openalex.org/I90183372"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5058396980"],"corresponding_institution_ids":["https://openalex.org/I34250744"],"apc_list":{"value":4080,"currency":"PLN","value_usd":1100},"apc_paid":{"value":4080,"currency":"PLN","value_usd":1100},"fwci":17.6057,"has_fulltext":true,"cited_by_count":61,"citation_normalized_percentile":{"value":0.99207186,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"17","issue":"3","first_page":"413","last_page":"430"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9861999750137329,"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9851999878883362,"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/shape-optimization","display_name":"Shape optimization","score":0.7952882051467896},{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.7879151105880737},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6992116570472717},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.6386418342590332},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6352003216743469},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.6232590675354004},{"id":"https://openalex.org/keywords/variational-inequality","display_name":"Variational inequality","score":0.6003108024597168},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5848358273506165},{"id":"https://openalex.org/keywords/level-set-method","display_name":"Level set method","score":0.501176118850708},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4630349576473236},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43369007110595703},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4225327968597412},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23882073163986206},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2108212411403656},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.09746623039245605},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.0703476071357727}],"concepts":[{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.7952882051467896},{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.7879151105880737},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6992116570472717},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.6386418342590332},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6352003216743469},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.6232590675354004},{"id":"https://openalex.org/C161999928","wikidata":"https://www.wikidata.org/wiki/Q4556320","display_name":"Variational inequality","level":2,"score":0.6003108024597168},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5848358273506165},{"id":"https://openalex.org/C125269122","wikidata":"https://www.wikidata.org/wiki/Q1751397","display_name":"Level set method","level":4,"score":0.501176118850708},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4630349576473236},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43369007110595703},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4225327968597412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23882073163986206},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2108212411403656},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.09746623039245605},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0703476071357727},{"id":"https://openalex.org/C124504099","wikidata":"https://www.wikidata.org/wiki/Q56933","display_name":"Image segmentation","level":3,"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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","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/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.2478/v10006-007-0034-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0034-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0034-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.390.7802","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.390.7802","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://matwbn.icm.edu.pl/ksiazki/amc/amc17/amc17311.pdf","raw_type":"text"},{"id":"pmh:oai:HAL:hal-00092000v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00092000","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":"International Journal of Applied Mathematics and Computer Science, 2007, 17 (3), pp.413-430. ⟨10.2478/v10006-007-0034-z⟩","raw_type":"Journal articles"},{"id":"pmh:oai:unipub.uni-graz.at:133172","is_oa":false,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubg:3-874","pdf_url":null,"source":{"id":"https://openalex.org/S4306400359","display_name":"Unipub UB Graz (Universit\u00e4t Graz)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I15766117","host_organization_name":"University of Graz","host_organization_lineage":["https://openalex.org/I15766117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:zbc.uz.zgora.pl:78664","is_oa":false,"landing_page_url":"https://zbc.uz.zgora.pl/dlibra/docmetadata?showContent=true&id=78664","pdf_url":null,"source":{"id":"https://openalex.org/S4306400400","display_name":"Digital library of Zielona Gora (University of Zielona G\u00f3ra)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I46305939","host_organization_name":"University of Zielona G\u00f3ra","host_organization_lineage":["https://openalex.org/I46305939"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://www.amcs.uz.zgora.pl/?action=papers&issue=29","raw_type":"artyku\u0142"}],"best_oa_location":{"id":"doi:10.2478/v10006-007-0034-z","is_oa":true,"landing_page_url":"https://doi.org/10.2478/v10006-007-0034-z","pdf_url":"https://sciendo.com/pdf/10.2478/v10006-007-0034-z","source":{"id":"https://openalex.org/S117679522","display_name":"International Journal of Applied Mathematics and Computer Science","issn_l":"1641-876X","issn":["1641-876X","2083-8492"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320322","host_organization_name":"De Gruyter Open","host_organization_lineage":["https://openalex.org/P4310320322","https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter Open","De Gruyter"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Applied Mathematics and Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.8500000238418579,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2010852247.pdf","grobid_xml":"https://content.openalex.org/works/W2010852247.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W21326251","https://openalex.org/W175246081","https://openalex.org/W625077519","https://openalex.org/W1002919431","https://openalex.org/W1516415680","https://openalex.org/W1974303482","https://openalex.org/W1975255402","https://openalex.org/W1979905552","https://openalex.org/W1987709406","https://openalex.org/W1991113069","https://openalex.org/W1994133356","https://openalex.org/W1994875376","https://openalex.org/W1995067704","https://openalex.org/W2006610457","https://openalex.org/W2023915174","https://openalex.org/W2037004190","https://openalex.org/W2060654491","https://openalex.org/W2067860458","https://openalex.org/W2093834886","https://openalex.org/W2101560656","https://openalex.org/W2132363464","https://openalex.org/W2139513792","https://openalex.org/W2286052476","https://openalex.org/W2473691458","https://openalex.org/W2494779131","https://openalex.org/W3142828186","https://openalex.org/W4230684562","https://openalex.org/W4235957410","https://openalex.org/W4244750309","https://openalex.org/W4301440339"],"related_works":["https://openalex.org/W2131668762","https://openalex.org/W2790144624","https://openalex.org/W2626393126","https://openalex.org/W2691297431","https://openalex.org/W2225569501","https://openalex.org/W2658832254","https://openalex.org/W2644691884","https://openalex.org/W2707457586","https://openalex.org/W2323997591","https://openalex.org/W2354244208"],"abstract_inverted_index":{"A":[0],"Level":[1],"Set":[2],"Method":[3],"in":[4,35,88,105],"Shape":[5],"and":[6,107,118],"Topology":[7],"Optimization":[8],"for":[9,18,25,84],"Variational":[10],"Inequalities":[11],"The":[12,29,46,59,74,94],"level":[13],"set":[14],"method":[15,115],"is":[16,33,57,99,116],"used":[17,34],"shape":[19,40,80,126],"optimization":[20,64,127],"of":[21,42,49,70,77,91,96],"the":[22,26,39,43,54,63,78,85,89,102,114,124],"energy":[23,44,79],"functional":[24,81],"Signorini":[27],"problem.":[28],"boundary":[30,55],"variations":[31,56,87],"technique":[32],"order":[36],"to":[37,53],"derive":[38],"gradients":[41],"functional.":[45],"conical":[47],"differentiability":[48],"solutions":[50],"with":[51,123],"respect":[52],"exploited.":[58],"topology":[60,86],"modifications":[61],"during":[62],"process":[65],"are":[66,82],"identified":[67],"by":[68],"means":[69],"an":[71],"asymptotic":[72],"analysis.":[73],"topological":[75,97],"derivatives":[76,98],"employed":[83],"form":[90],"small":[92],"holes.":[93],"derivation":[95],"performed":[100],"within":[101],"framework":[103],"proposed":[104],"(Soko\u0142owski":[106],"\u017bochowski,":[108],"2003).":[109],"Numerical":[110],"results":[111,121],"confirm":[112],"that":[113],"efficient":[117],"gives":[119],"better":[120],"compared":[122],"classical":[125],"techniques.":[128]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":5},{"year":2012,"cited_by_count":4}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}