{"id":"https://openalex.org/W2123551903","doi":"https://doi.org/10.1137/15m1020848","title":"Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional","display_name":"Second-Order Edge-Penalization in the Ambrosio--Tortorelli functional","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W2123551903","doi":"https://doi.org/10.1137/15m1020848","mag":"2123551903"},"language":"en","primary_location":{"id":"doi:10.1137/15m1020848","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1020848","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","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/A5069220813","display_name":"Martin Burger","orcid":"https://orcid.org/0000-0003-2619-2912"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"M. Burger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043123914","display_name":"Teresa Esposito","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"T. Esposito","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5089058307","display_name":"Caterina Ida Zeppieri","orcid":"https://orcid.org/0000-0002-8701-7045"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"C. I. Zeppieri","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":1.9992,"has_fulltext":false,"cited_by_count":18,"citation_normalized_percentile":{"value":0.8417244,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"13","issue":"4","first_page":"1354","last_page":"1389"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9993000030517578,"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":0.9993000030517578,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9979000091552734,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9745000004768372,"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/hessian-matrix","display_name":"Hessian matrix","score":0.8866315484046936},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6715885400772095},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5990971922874451},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5690141916275024},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.4974046051502228},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.4872931241989136},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.48273295164108276},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34324562549591064},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2550331950187683},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2309248447418213},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.06379678845405579}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.8866315484046936},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6715885400772095},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5990971922874451},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5690141916275024},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.4974046051502228},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.4872931241989136},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.48273295164108276},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34324562549591064},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2550331950187683},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2309248447418213},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.06379678845405579},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1020848","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1020848","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.7200000286102295,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":34,"referenced_works":["https://openalex.org/W198116995","https://openalex.org/W622845271","https://openalex.org/W649818166","https://openalex.org/W1480714962","https://openalex.org/W1490926540","https://openalex.org/W1502992081","https://openalex.org/W1515685921","https://openalex.org/W1586623601","https://openalex.org/W1599416169","https://openalex.org/W1974966195","https://openalex.org/W1990541396","https://openalex.org/W1990620164","https://openalex.org/W1991789140","https://openalex.org/W1993822606","https://openalex.org/W2003878476","https://openalex.org/W2012949880","https://openalex.org/W2025092517","https://openalex.org/W2026269844","https://openalex.org/W2030582267","https://openalex.org/W2048811768","https://openalex.org/W2063439636","https://openalex.org/W2068826680","https://openalex.org/W2088186886","https://openalex.org/W2095195575","https://openalex.org/W2114487471","https://openalex.org/W2116040950","https://openalex.org/W2148395215","https://openalex.org/W2155280009","https://openalex.org/W2353767680","https://openalex.org/W2564520718","https://openalex.org/W2595348797","https://openalex.org/W2944437997","https://openalex.org/W3021722416","https://openalex.org/W4256051666"],"related_works":["https://openalex.org/W3004956525","https://openalex.org/W2053308537","https://openalex.org/W2083066101","https://openalex.org/W4297883503","https://openalex.org/W2321464670","https://openalex.org/W1972453316","https://openalex.org/W2059340512","https://openalex.org/W1972403003","https://openalex.org/W2025314782","https://openalex.org/W1996317575"],"abstract_inverted_index":{"We":[0,36,118],"propose":[1],"and":[2,96],"study":[3],"two":[4],"variants":[5,41],"of":[6,14,33,47,54,85,90,101,108],"the":[7,11,15,27,31,40,48,52,58,61,73,87,91,99,102,106,115,121],"Ambrosio--Tortorelli":[8,75],"functional":[9,50],"where":[10],"first-order":[12],"penalization":[13,63],"edge":[16,92],"variable":[17],"$v$":[18],"is":[19],"replaced":[20],"by":[21],"a":[22],"second-order":[23,103],"term":[24],"depending":[25],"on":[26,30],"Hessian":[28],"or":[29],"Laplacian":[32,62],"$v$,":[34],"respectively.":[35],"show":[37],"that":[38],"both":[39],"above":[42],"provide":[43],"an":[44],"elliptic":[45],"approximation":[46,89],"Mumford--Shah":[49],"in":[51],"sense":[53],"$\\Gamma$-convergence.":[55],"In":[56],"particular":[57],"variant":[59],"with":[60,123],"can":[64],"be":[65],"implemented":[66],"numerically":[67],"without":[68],"any":[69],"difficulties":[70],"compared":[71],"to":[72],"standard":[74],"functional.":[76,104,117],"The":[77],"computational":[78,125],"results":[79],"indicate":[80],"several":[81,124],"additional":[82],"advantages.":[83],"First":[84],"all,":[86],"diffuse":[88],"contours":[93],"appears":[94],"smoother":[95],"clearer":[97],"for":[98,114],"minimizers":[100],"Moreover,":[105],"convergence":[107],"alternating":[109],"minimization":[110],"algorithms":[111],"seems":[112],"improved":[113],"new":[116],"also":[119],"illustrate":[120],"findings":[122],"results.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
