{"id":"https://openalex.org/W2027061181","doi":"https://doi.org/10.1080/10556780500130459","title":"Second-order shape optimization using wavelet BEM","display_name":"Second-order shape optimization using wavelet BEM","publication_year":2006,"publication_date":"2006-02-01","ids":{"openalex":"https://openalex.org/W2027061181","doi":"https://doi.org/10.1080/10556780500130459","mag":"2027061181"},"language":"en","primary_location":{"id":"doi:10.1080/10556780500130459","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500130459","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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/A5048643878","display_name":"Karsten Eppler","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092021","display_name":"Weierstrass Institute for Applied Analysis and Stochastics","ror":"https://ror.org/00h1x4t21","country_code":"DE","type":"facility","lineage":["https://openalex.org/I315704651","https://openalex.org/I4210092021"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"K. Eppler","raw_affiliation_strings":["Weierstrass Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstr 39, 10117, Berlin, Germany","Weierstrass Institut f\u00fcr Angewandte Analysis und Stochastik , Mohrenstr 39, 10117, Berlin, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Weierstrass Institut f\u00fcr Angewandte Analysis und Stochastik, Mohrenstr 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]},{"raw_affiliation_string":"Weierstrass Institut f\u00fcr Angewandte Analysis und Stochastik , Mohrenstr 39, 10117, Berlin, Germany","institution_ids":["https://openalex.org/I4210092021"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005562022","display_name":"Helmut Harbrecht","orcid":"https://orcid.org/0000-0003-0093-5706"},"institutions":[{"id":"https://openalex.org/I32021983","display_name":"Christian-Albrechts-Universit\u00e4t zu Kiel","ror":"https://ror.org/04v76ef78","country_code":"DE","type":"education","lineage":["https://openalex.org/I32021983"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"H. Harbrecht","raw_affiliation_strings":["Institut f\u00fcr Informatik und Praktische Mathematik, Christian-Albrechts-Universit\u00e4t zu Kiel, Olshausenstr 40, 24098, Kiel, Germany","Institut f\u00fcr Informatik und Praktische Mathematik, Christian-Albrechts-Universit\u00e4t zu Kiel, Olshausenstr. 40, 24098 Kiel, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Informatik und Praktische Mathematik, Christian-Albrechts-Universit\u00e4t zu Kiel, Olshausenstr 40, 24098, Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]},{"raw_affiliation_string":"Institut f\u00fcr Informatik und Praktische Mathematik, Christian-Albrechts-Universit\u00e4t zu Kiel, Olshausenstr. 40, 24098 Kiel, Germany","institution_ids":["https://openalex.org/I32021983"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5048643878"],"corresponding_institution_ids":["https://openalex.org/I4210092021"],"apc_list":null,"apc_paid":null,"fwci":4.4477,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.94563331,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"1","first_page":"135","last_page":"153"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9966999888420105,"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"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9966999888420105,"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/T10638","display_name":"Optical measurement and interference techniques","score":0.9940999746322632,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10688","display_name":"Image and Signal Denoising Methods","score":0.9908000230789185,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.6702388525009155},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.5077472925186157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.48417168855667114},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3486325740814209},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23330047726631165},{"id":"https://openalex.org/keywords/economics","display_name":"Economics","score":0.06026628613471985}],"concepts":[{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.6702388525009155},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.5077472925186157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.48417168855667114},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3486325740814209},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23330047726631165},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.06026628613471985},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/10556780500130459","is_oa":false,"landing_page_url":"https://doi.org/10.1080/10556780500130459","pdf_url":null,"source":{"id":"https://openalex.org/S103047102","display_name":"Optimization methods & software","issn_l":"1026-7670","issn":["1026-7670","1029-4937","1055-6788"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Optimization Methods and Software","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":38,"referenced_works":["https://openalex.org/W131892725","https://openalex.org/W271667515","https://openalex.org/W904189111","https://openalex.org/W1516415680","https://openalex.org/W1566949704","https://openalex.org/W1588974174","https://openalex.org/W1595449796","https://openalex.org/W1989056711","https://openalex.org/W1992268304","https://openalex.org/W1994575568","https://openalex.org/W2008036799","https://openalex.org/W2014746566","https://openalex.org/W2034550061","https://openalex.org/W2036499678","https://openalex.org/W2075900396","https://openalex.org/W2083206954","https://openalex.org/W2083684146","https://openalex.org/W2089276552","https://openalex.org/W2094585768","https://openalex.org/W2115566547","https://openalex.org/W2118851059","https://openalex.org/W2289808822","https://openalex.org/W2326806701","https://openalex.org/W2328288328","https://openalex.org/W2339602297","https://openalex.org/W2481432830","https://openalex.org/W2484931134","https://openalex.org/W2491010324","https://openalex.org/W2911695249","https://openalex.org/W3005363104","https://openalex.org/W3021722416","https://openalex.org/W3196290810","https://openalex.org/W4231154391","https://openalex.org/W4251819670","https://openalex.org/W4252239758","https://openalex.org/W4285719527","https://openalex.org/W4293183906","https://openalex.org/W4293515312"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793","https://openalex.org/W4238204885"],"abstract_inverted_index":{"This":[0],"present":[1],"paper":[2],"is":[3],"concerned":[4],"with":[5],"second-order":[6,30],"methods":[7],"for":[8],"a":[9,17,52,69],"class":[10],"of":[11,22,32,45,80,84],"shape":[12,24,48],"optimization":[13],"problems.":[14],"We":[15,50],"employ":[16],"complete":[18],"boundary":[19,53,62],"integral":[20,54,63],"representation":[21],"the":[23,33,36,81,85],"Hessian":[25],"which":[26],"involves":[27],"first-":[28],"and":[29,35],"derivatives":[31,44],"state":[34,38],"adjoint":[37],"function,":[39],"as":[40,42],"well":[41],"normal":[43],"its":[46],"local":[47],"derivatives.":[49],"introduce":[51],"formulation":[55],"to":[56,89],"compute":[57],"these":[58],"quantities.":[59],"The":[60],"derived":[61],"equations":[64],"are":[65],"solved":[66],"efficiently":[67],"by":[68],"wavelet":[70],"Galerkin":[71],"scheme.":[72],"A":[73],"numerical":[74],"example":[75],"validates":[76],"that,":[77],"in":[78,97],"spite":[79],"higher":[82],"effort":[83],"Newton":[86],"method":[87],"compared":[88],"first-order":[90],"algorithms,":[91],"we":[92],"obtain":[93],"more":[94],"accurate":[95],"solutions":[96],"less":[98],"computational":[99],"time.":[100]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}
