{"id":"https://openalex.org/W2075482377","doi":"https://doi.org/10.1137/060652208","title":"Methods for Reliable Topology Changes for Perimeter-Regularized Geometric Inverse Problems","display_name":"Methods for Reliable Topology Changes for Perimeter-Regularized Geometric Inverse Problems","publication_year":2007,"publication_date":"2007-01-01","ids":{"openalex":"https://openalex.org/W2075482377","doi":"https://doi.org/10.1137/060652208","mag":"2075482377"},"language":"en","primary_location":{"id":"doi:10.1137/060652208","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060652208","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","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/A5070635955","display_name":"Benjamin Hackl","orcid":"https://orcid.org/0000-0003-2998-9599"},"institutions":[{"id":"https://openalex.org/I138211613","display_name":"Austrian Academy of Sciences","ror":"https://ror.org/03anc3s24","country_code":"AT","type":"funder","lineage":["https://openalex.org/I138211613"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Benjamin Hackl","raw_affiliation_strings":["Austrian Academy of Sciences"],"affiliations":[{"raw_affiliation_string":"Austrian Academy of Sciences","institution_ids":["https://openalex.org/I138211613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5070635955"],"corresponding_institution_ids":["https://openalex.org/I138211613"],"apc_list":null,"apc_paid":null,"fwci":1.3425,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.78163745,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"45","issue":"5","first_page":"2201","last_page":"2227"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9979000091552734,"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":0.9312999844551086,"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":0.7983509302139282},{"id":"https://openalex.org/keywords/perimeter","display_name":"Perimeter","score":0.7920801639556885},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5785118937492371},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.5176661610603333},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4537340998649597},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4524562954902649},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.4396655857563019},{"id":"https://openalex.org/keywords/lebesgue-measure","display_name":"Lebesgue measure","score":0.4198918342590332},{"id":"https://openalex.org/keywords/descent","display_name":"Descent (aeronautics)","score":0.4151616394519806},{"id":"https://openalex.org/keywords/lebesgue-integration","display_name":"Lebesgue integration","score":0.40996870398521423},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34619325399398804},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29898107051849365},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17508983612060547},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14315402507781982},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.12853437662124634}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7983509302139282},{"id":"https://openalex.org/C98503990","wikidata":"https://www.wikidata.org/wiki/Q28474","display_name":"Perimeter","level":2,"score":0.7920801639556885},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5785118937492371},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.5176661610603333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4537340998649597},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4524562954902649},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.4396655857563019},{"id":"https://openalex.org/C2777105136","wikidata":"https://www.wikidata.org/wiki/Q827230","display_name":"Lebesgue measure","level":3,"score":0.4198918342590332},{"id":"https://openalex.org/C2776637919","wikidata":"https://www.wikidata.org/wiki/Q624380","display_name":"Descent (aeronautics)","level":2,"score":0.4151616394519806},{"id":"https://openalex.org/C14158598","wikidata":"https://www.wikidata.org/wiki/Q853831","display_name":"Lebesgue integration","level":2,"score":0.40996870398521423},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34619325399398804},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29898107051849365},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17508983612060547},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14315402507781982},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.12853437662124634},{"id":"https://openalex.org/C146978453","wikidata":"https://www.wikidata.org/wiki/Q3798668","display_name":"Aerospace engineering","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/060652208","is_oa":false,"landing_page_url":"https://doi.org/10.1137/060652208","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7099999785423279,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":43,"referenced_works":["https://openalex.org/W178344362","https://openalex.org/W649818166","https://openalex.org/W1480714962","https://openalex.org/W1496364532","https://openalex.org/W1523113578","https://openalex.org/W1575923498","https://openalex.org/W1582916216","https://openalex.org/W1929011921","https://openalex.org/W1970206100","https://openalex.org/W1973628819","https://openalex.org/W1975659605","https://openalex.org/W1979646278","https://openalex.org/W1979905552","https://openalex.org/W1983053523","https://openalex.org/W1994133356","https://openalex.org/W1995067704","https://openalex.org/W2000141640","https://openalex.org/W2000388899","https://openalex.org/W2002428563","https://openalex.org/W2004162158","https://openalex.org/W2008064893","https://openalex.org/W2011181254","https://openalex.org/W2016413885","https://openalex.org/W2020577281","https://openalex.org/W2025155468","https://openalex.org/W2026500470","https://openalex.org/W2037677143","https://openalex.org/W2041494914","https://openalex.org/W2046489591","https://openalex.org/W2061502567","https://openalex.org/W2063736654","https://openalex.org/W2079578802","https://openalex.org/W2085115947","https://openalex.org/W2088880127","https://openalex.org/W2093834886","https://openalex.org/W2124686419","https://openalex.org/W2139513792","https://openalex.org/W2159451621","https://openalex.org/W2163106901","https://openalex.org/W2177493694","https://openalex.org/W2181453853","https://openalex.org/W2201224646","https://openalex.org/W2323496416"],"related_works":["https://openalex.org/W4245795910","https://openalex.org/W2074721578","https://openalex.org/W928772053","https://openalex.org/W3008743878","https://openalex.org/W2032212755","https://openalex.org/W2917668491","https://openalex.org/W4287864225","https://openalex.org/W3184958942","https://openalex.org/W4244471727","https://openalex.org/W1567236373"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4,25,31,59],"the":[5,26,32,36,46,51,64,75,79,83],"incorporation":[6],"of":[7,35,53,82],"topological":[8],"derivativelike":[9],"expansions":[10,21],"into":[11],"level":[12,65],"set":[13,66],"methods":[14],"for":[15],"perimeter-regularized":[16],"geometric":[17],"inverse":[18],"problems.":[19],"The":[20],"are":[22,71],"done":[23],"up":[24],"second":[27],"order":[28],"with":[29],"respect":[30],"Lebesgue":[33],"measure":[34],"symmetric":[37],"difference.":[38],"They":[39],"provide":[40],"simpler":[41],"shape":[42],"functionals,":[43],"still":[44],"including":[45],"perimeter,":[47],"and":[48,56,77],"therefore":[49],"allow":[50],"construction":[52],"steepest":[54],"descent-":[55],"Newton-type":[57],"algorithms":[58],"force":[60],"topology":[61],"changes":[62],"during":[63],"evolution.":[67],"Numerous":[68],"numerical":[69],"examples":[70],"provided":[72],"that":[73],"show":[74],"strong":[76],"also":[78],"weak":[80],"points":[81],"newly":[84],"developed":[85],"algorithms.":[86]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}