{"id":"https://openalex.org/W3034558515","doi":"https://doi.org/10.1137/19m1282866","title":"Mathematical and Numerical Study of a Three-Dimensional Inverse Eddy Current Problem","display_name":"Mathematical and Numerical Study of a Three-Dimensional Inverse Eddy Current Problem","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3034558515","doi":"https://doi.org/10.1137/19m1282866","mag":"3034558515"},"language":"en","primary_location":{"id":"doi:10.1137/19m1282866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1282866","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","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/A5101962646","display_name":"Junqing Chen","orcid":"https://orcid.org/0000-0002-8262-1526"},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Junqing Chen","raw_affiliation_strings":["Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, China","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100414176","display_name":"Ying Liang","orcid":"https://orcid.org/0000-0002-2594-3318"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Ying Liang","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5054388151","display_name":"Jun Zou","orcid":"https://orcid.org/0000-0002-2976-8713"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"HK","type":"education","lineage":["https://openalex.org/I177725633"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Jun Zou","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong","institution_ids":["https://openalex.org/I177725633"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7642,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.66111851,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"80","issue":"3","first_page":"1467","last_page":"1492"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.9998999834060669,"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"}},"topics":[{"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"}},{"id":"https://openalex.org/T12169","display_name":"Non-Destructive Testing Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical 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/T10514","display_name":"Numerical methods in engineering","score":0.9966999888420105,"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/inverse-problem","display_name":"Inverse problem","score":0.6986744403839111},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6875371932983398},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.6737141013145447},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.6717536449432373},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5875791311264038},{"id":"https://openalex.org/keywords/nonlinear-conjugate-gradient-method","display_name":"Nonlinear conjugate gradient method","score":0.5800830721855164},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5711867213249207},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5234705209732056},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.4767414331436157},{"id":"https://openalex.org/keywords/inverse","display_name":"Inverse","score":0.4676639139652252},{"id":"https://openalex.org/keywords/gradient-method","display_name":"Gradient method","score":0.44727379083633423},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42317166924476624},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4231463074684143},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.41384124755859375},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3645351827144623},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.20992153882980347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18368226289749146},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.07730841636657715}],"concepts":[{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.6986744403839111},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6875371932983398},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.6737141013145447},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6717536449432373},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5875791311264038},{"id":"https://openalex.org/C26362088","wikidata":"https://www.wikidata.org/wiki/Q17086453","display_name":"Nonlinear conjugate gradient method","level":4,"score":0.5800830721855164},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5711867213249207},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5234705209732056},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.4767414331436157},{"id":"https://openalex.org/C207467116","wikidata":"https://www.wikidata.org/wiki/Q4385666","display_name":"Inverse","level":2,"score":0.4676639139652252},{"id":"https://openalex.org/C115680565","wikidata":"https://www.wikidata.org/wiki/Q5977448","display_name":"Gradient method","level":2,"score":0.44727379083633423},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42317166924476624},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4231463074684143},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.41384124755859375},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3645351827144623},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.20992153882980347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18368226289749146},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.07730841636657715},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/19m1282866","is_oa":false,"landing_page_url":"https://doi.org/10.1137/19m1282866","pdf_url":null,"source":{"id":"https://openalex.org/S77200987","display_name":"SIAM Journal on Applied Mathematics","issn_l":"0036-1399","issn":["0036-1399","1095-712X"],"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 Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G151420641","display_name":null,"funder_award_id":"N_CUHK437/16","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1526853822","display_name":"Adaptive Finite Element Methods and Convergence Analyses for Solving Ill-posed Inverse Problems by Non-smooth Regularizations","funder_award_id":"14304517","funder_id":"https://openalex.org/F4320321592","funder_display_name":"Research Grants Council, University Grants Committee"},{"id":"https://openalex.org/G2101694825","display_name":"\u5927\u5730\u7535\u78c1\u6d4b\u6df1\u4e09\u7ef4\u6b63\u53cd\u6f14\u5e76\u884c\u81ea\u9002\u5e94\u7b97\u6cd5\u53ca\u5176\u5b9e\u73b0\u6280\u672f\u7814\u7a76","funder_award_id":"11771440","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3912101811","display_name":null,"funder_award_id":"91630205","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6085333457","display_name":"\u7535\u78c1\u611f\u5e94\u63a2\u6d4b\u65b9\u6cd5\u7684\u7406\u8bba\u4e0e\u7b97\u6cd5\u7814\u7a76","funder_award_id":"11871300","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321592","display_name":"Research Grants Council, University Grants Committee","ror":"https://ror.org/00djwmt25"},{"id":"https://openalex.org/F4320322942","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":16,"referenced_works":["https://openalex.org/W1735387029","https://openalex.org/W1968395891","https://openalex.org/W1970198065","https://openalex.org/W1976173851","https://openalex.org/W1978148400","https://openalex.org/W1993491255","https://openalex.org/W2005047411","https://openalex.org/W2010947252","https://openalex.org/W2053630948","https://openalex.org/W2071704402","https://openalex.org/W2072507162","https://openalex.org/W2076792665","https://openalex.org/W2085576744","https://openalex.org/W2087849682","https://openalex.org/W2123252306","https://openalex.org/W2128162818"],"related_works":["https://openalex.org/W2356977358","https://openalex.org/W4291138102","https://openalex.org/W4319027779","https://openalex.org/W2183734858","https://openalex.org/W2005717169","https://openalex.org/W3131790919","https://openalex.org/W2375129592","https://openalex.org/W2382015157","https://openalex.org/W2941778027","https://openalex.org/W2098528027"],"abstract_inverted_index":{"We":[0,11],"study":[1],"an":[2,7,85],"inverse":[3,18,77],"problem":[4,19,78,83],"associated":[5],"with":[6,28,84],"eddy":[8],"current":[9],"model.":[10],"first":[12],"address":[13],"the":[14,17,22,25,31,34,37,53,57,61,76,90,95,100,104,119,122,128,134,145,156,165,168],"ill-posedness":[15],"of":[16,24,36,43,56,94,103,121,133,167],"by":[20,41],"proving":[21],"compactness":[23],"forward":[26],"map":[27],"respect":[29],"to":[30,66,154,163],"conductivity":[32],"and":[33,88,92,114,148],"nonuniqueness":[35],"recovery":[38],"process.":[39,158],"Then":[40,118],"virtue":[42],"nonradiating":[44],"source":[45],"conceptions,":[46],"we":[47,74,109],"establish":[48],"a":[49,80,111,136,149],"regularity":[50],"result":[51],"for":[52,143],"tangential":[54],"trace":[55],"true":[58],"solution":[59,102],"on":[60],"boundary,":[62],"which":[63],"is":[64,125,141,152],"necessary":[65],"justify":[67],"our":[68],"subsequent":[69],"mathematical":[70],"formulation.":[71],"After":[72],"that,":[73],"formulate":[75],"as":[79],"constrained":[81,107],"optimization":[82,146],"appropriate":[86],"regularization":[87],"prove":[89],"existence":[91],"stability":[93],"regularized":[96],"minimizers.":[97],"To":[98],"facilitate":[99],"numerical":[101],"nonlinear":[105,137],"nonconvex":[106],"optimization,":[108],"introduce":[110],"feasible":[112],"Lagrangian":[113],"its":[115],"discrete":[116],"variant.":[117],"gradient":[120,139,151],"objective":[123],"functional":[124],"derived":[126],"using":[127],"adjoint":[129],"technique.":[130],"By":[131],"means":[132],"gradient,":[135],"conjugate":[138],"method":[140],"formulated":[142],"solving":[144],"system,":[147],"Sobolev":[150],"incorporated":[153],"accelerate":[155],"iterative":[157],"Numerical":[159],"examples":[160],"are":[161],"provided":[162],"demonstrate":[164],"feasibility":[166],"proposed":[169],"algorithm.":[170]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
