{"id":"https://openalex.org/W2028506927","doi":"https://doi.org/10.1137/100810800","title":"Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems","display_name":"Material and Shape Derivative Method for Quasi-Linear Elliptic Systems with Applications in Inverse Electromagnetic Interface Problems","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W2028506927","doi":"https://doi.org/10.1137/100810800","mag":"2028506927"},"language":"en","primary_location":{"id":"doi:10.1137/100810800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100810800","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/A5068000944","display_name":"Ivan Cimr\u00e1k","orcid":"https://orcid.org/0000-0002-0389-7891"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Ivan Cimr\u00e1k","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5068000944"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6848,"has_fulltext":false,"cited_by_count":12,"citation_normalized_percentile":{"value":0.83843931,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"3","first_page":"1086","last_page":"1110"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/shape-optimization","display_name":"Shape optimization","score":0.7569184303283691},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5848323106765747},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.554472804069519},{"id":"https://openalex.org/keywords/interface","display_name":"Interface (matter)","score":0.5313138365745544},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5278480052947998},{"id":"https://openalex.org/keywords/material-derivative","display_name":"Material derivative","score":0.5240707397460938},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5217143893241882},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.5085614919662476},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4972136318683624},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.48552918434143066},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.44328126311302185},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4214783310890198},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.30362939834594727},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.26916688680648804},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.247150719165802},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.17281299829483032},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.138107568025589}],"concepts":[{"id":"https://openalex.org/C29513896","wikidata":"https://www.wikidata.org/wiki/Q7489239","display_name":"Shape optimization","level":3,"score":0.7569184303283691},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5848323106765747},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.554472804069519},{"id":"https://openalex.org/C113843644","wikidata":"https://www.wikidata.org/wiki/Q901882","display_name":"Interface (matter)","level":4,"score":0.5313138365745544},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5278480052947998},{"id":"https://openalex.org/C111915175","wikidata":"https://www.wikidata.org/wiki/Q1801562","display_name":"Material derivative","level":2,"score":0.5240707397460938},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5217143893241882},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.5085614919662476},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4972136318683624},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.48552918434143066},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.44328126311302185},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4214783310890198},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.30362939834594727},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.26916688680648804},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.247150719165802},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.17281299829483032},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.138107568025589},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","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/C129307140","wikidata":"https://www.wikidata.org/wiki/Q6795880","display_name":"Maximum bubble pressure method","level":3,"score":0.0},{"id":"https://openalex.org/C157915830","wikidata":"https://www.wikidata.org/wiki/Q2928001","display_name":"Bubble","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/100810800","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100810800","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W597907832","https://openalex.org/W1575849776","https://openalex.org/W1584280986","https://openalex.org/W1866311589","https://openalex.org/W1983053523","https://openalex.org/W1984408604","https://openalex.org/W1984815757","https://openalex.org/W1988044952","https://openalex.org/W1989974635","https://openalex.org/W2001303543","https://openalex.org/W2001515817","https://openalex.org/W2001906790","https://openalex.org/W2002310015","https://openalex.org/W2002996216","https://openalex.org/W2006226342","https://openalex.org/W2013592534","https://openalex.org/W2027296153","https://openalex.org/W2036887935","https://openalex.org/W2042669113","https://openalex.org/W2052454954","https://openalex.org/W2054510035","https://openalex.org/W2068412155","https://openalex.org/W2093834886","https://openalex.org/W2094250119","https://openalex.org/W2115389016","https://openalex.org/W2159451621","https://openalex.org/W2160945572","https://openalex.org/W2489863506","https://openalex.org/W2491155384","https://openalex.org/W2740398758","https://openalex.org/W4297747974"],"related_works":["https://openalex.org/W2329606267","https://openalex.org/W2165098046","https://openalex.org/W2095031547","https://openalex.org/W2153959387","https://openalex.org/W1965784592","https://openalex.org/W2941749146","https://openalex.org/W2331917905","https://openalex.org/W2143790181","https://openalex.org/W2082834779","https://openalex.org/W2056856723"],"abstract_inverted_index":{"We":[0,91,166],"study":[1],"a":[2,78],"shape":[3,45,60,64,72,87,104,137],"optimization":[4],"problem":[5,16],"for":[6,132,144,160],"quasi-linear":[7],"elliptic":[8,94],"systems.":[9],"The":[10,36],"state":[11],"equations":[12],"describe":[13],"an":[14,129],"interface":[15,28,37,95],"and":[17,56,70,102],"the":[18,27,41,44,47,51,54,57,63,68,71,85,89,93,100,103,110,123,133,136,145,149,156,161,164,168,172,176,181],"ultimate":[19],"goal":[20],"of":[21,43,62,112,135,148,163,184],"our":[22],"research":[23],"is":[24,38,81,141],"to":[25,127],"determine":[26],"between":[29,53],"two":[30],"materials":[31],"with":[32],"different":[33],"physical":[34],"properties.":[35],"identified":[39],"by":[40],"minimization":[42,150],"(or":[46],"cost)":[48],"functional":[49,65],"representing":[50],"misfit":[52],"data":[55],"simulations.":[58],"For":[59],"sensitivity":[61],"we":[66,108,121,154],"elaborate":[67],"material":[69,101,118,179],"derivative":[73],"method.":[74],"In":[75,106,152],"this":[76],"concept":[77],"vector":[79],"field":[80],"introduced":[82],"that":[83],"deforms":[84],"unknown":[86],"toward":[88],"optimum.":[90],"characterize":[92],"problems":[96],"whose":[97],"solutions":[98],"give":[99],"derivatives.":[105,119],"particular,":[107],"show":[109],"existence":[111],"weak":[113],"as":[114,116],"well":[115],"strong":[117],"Further,":[120],"employ":[122],"adjoint":[124],"variable":[125],"method":[126,159],"obtain":[128],"explicit":[130],"expression":[131],"gradient":[134,140],"functional.":[138],"This":[139],"then":[142],"used":[143],"actual":[146],"implementation":[147],"algorithm.":[151],"simulations":[153],"use":[155],"level":[157],"set":[158],"representation":[162],"interface.":[165],"present":[167],"simulation":[169],"results":[170],"showing":[171],"reconstructed":[173],"voids":[174],"in":[175],"nonlinear":[177],"ferromagnetic":[178],"from":[180],"near-boundary":[182],"measurements":[183],"magnetic":[185],"induction.":[186]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":4},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}