{"id":"https://openalex.org/W4282979333","doi":"https://doi.org/10.1090/mcom/3767","title":"Finite element/holomorphic operator function method for the transmission eigenvalue problem","display_name":"Finite element/holomorphic operator function method for the transmission eigenvalue problem","publication_year":2022,"publication_date":"2022-06-15","ids":{"openalex":"https://openalex.org/W4282979333","doi":"https://doi.org/10.1090/mcom/3767"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3767","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3767","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","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/A5101888616","display_name":"Bo Gong","orcid":"https://orcid.org/0000-0002-1987-036X"},"institutions":[{"id":"https://openalex.org/I37796252","display_name":"Beijing University of Technology","ror":"https://ror.org/037b1pp87","country_code":"CN","type":"education","lineage":["https://openalex.org/I37796252"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Bo Gong","raw_affiliation_strings":["Beijing University of Technology, Beijing 100124, People\u00e2\u0080\u0099s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Beijing University of Technology, Beijing 100124, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I37796252"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054679759","display_name":"Jiguang Sun","orcid":"https://orcid.org/0000-0003-4105-8463"},"institutions":[{"id":"https://openalex.org/I11957088","display_name":"Michigan Technological University","ror":"https://ror.org/0036rpn28","country_code":"US","type":"education","lineage":["https://openalex.org/I11957088"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jiguang Sun","raw_affiliation_strings":["Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Michigan Technological University, Houghton, Michigan 49931","institution_ids":["https://openalex.org/I11957088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030163673","display_name":"Tiara Turner","orcid":"https://orcid.org/0000-0002-6744-6256"},"institutions":[{"id":"https://openalex.org/I22407884","display_name":"University of Maryland Eastern Shore","ror":"https://ror.org/006cymg18","country_code":"US","type":"education","lineage":["https://openalex.org/I22407884"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Tiara Turner","raw_affiliation_strings":["Department of Mathematics and Computer Science, University of Maryland Eastern Shore, Princess Anne, Maryland 21853"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science, University of Maryland Eastern Shore, Princess Anne, Maryland 21853","institution_ids":["https://openalex.org/I22407884"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5102804383","display_name":"Chunxiong Zheng","orcid":"https://orcid.org/0000-0001-5735-633X"},"institutions":[{"id":"https://openalex.org/I96908189","display_name":"Xinjiang University","ror":"https://ror.org/059gw8r13","country_code":"CN","type":"education","lineage":["https://openalex.org/I96908189"]},{"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":"Chunxiong Zheng","raw_affiliation_strings":["College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People\u00e2\u0080\u0099s Republic of China; and Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u00e2\u0080\u0099s Republic of China","Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u00e2\u0080\u0099s Republic of China","College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People\u00e2\u0080\u0099s Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People\u00e2\u0080\u0099s Republic of China; and Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I96908189"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Tsinghua University, Beijing 100084, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I99065089"]},{"raw_affiliation_string":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I96908189"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5101888616"],"corresponding_institution_ids":["https://openalex.org/I37796252"],"apc_list":null,"apc_paid":null,"fwci":1.9536,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.84372865,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"91","issue":"338","first_page":"2517","last_page":"2537"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":1.0,"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":1.0,"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/T11739","display_name":"Microwave Imaging and Scattering Analysis","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/3107","display_name":"Atomic and Molecular Physics, and Optics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7944601774215698},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6844413876533508},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.6600459218025208},{"id":"https://openalex.org/keywords/holomorphic-function","display_name":"Holomorphic function","score":0.6224268078804016},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.552212655544281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5394599437713623},{"id":"https://openalex.org/keywords/fredholm-integral-equation","display_name":"Fredholm integral equation","score":0.5313530564308167},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5291756987571716},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.49890971183776855},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.4903245270252228},{"id":"https://openalex.org/keywords/inverse-scattering-problem","display_name":"Inverse scattering problem","score":0.4566757380962372},{"id":"https://openalex.org/keywords/differential-operator","display_name":"Differential operator","score":0.42232197523117065},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38352900743484497},{"id":"https://openalex.org/keywords/inverse-problem","display_name":"Inverse problem","score":0.3188698887825012},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.2305993139743805}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7944601774215698},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6844413876533508},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.6600459218025208},{"id":"https://openalex.org/C204575570","wikidata":"https://www.wikidata.org/wiki/Q207476","display_name":"Holomorphic function","level":2,"score":0.6224268078804016},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.552212655544281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5394599437713623},{"id":"https://openalex.org/C89285879","wikidata":"https://www.wikidata.org/wiki/Q2991898","display_name":"Fredholm integral equation","level":3,"score":0.5313530564308167},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5291756987571716},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.49890971183776855},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.4903245270252228},{"id":"https://openalex.org/C174558057","wikidata":"https://www.wikidata.org/wiki/Q11639409","display_name":"Inverse scattering problem","level":3,"score":0.4566757380962372},{"id":"https://openalex.org/C70915906","wikidata":"https://www.wikidata.org/wiki/Q1058681","display_name":"Differential operator","level":2,"score":0.42232197523117065},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38352900743484497},{"id":"https://openalex.org/C135252773","wikidata":"https://www.wikidata.org/wiki/Q1567213","display_name":"Inverse problem","level":2,"score":0.3188698887825012},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.2305993139743805},{"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},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/mcom/3767","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3767","pdf_url":null,"source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:digitalcommons.mtu.edu:michigantech-p-36621","is_oa":false,"landing_page_url":"https://digitalcommons.mtu.edu/michigantech-p/17323","pdf_url":null,"source":{"id":"https://openalex.org/S4377196391","display_name":"Digital Commons - Michigan Tech (Michigan Technological University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I11957088","host_organization_name":"Michigan Technological University","host_organization_lineage":["https://openalex.org/I11957088"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Michigan Tech Publications, Part 1","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8927026918","display_name":null,"funder_award_id":"711922","funder_id":"https://openalex.org/F4320306164","funder_display_name":"Simons Foundation"}],"funders":[{"id":"https://openalex.org/F4320306164","display_name":"Simons Foundation","ror":"https://ror.org/01cmst727"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":52,"referenced_works":["https://openalex.org/W1495084286","https://openalex.org/W1583622322","https://openalex.org/W1602339262","https://openalex.org/W1983311783","https://openalex.org/W1999805625","https://openalex.org/W2047386863","https://openalex.org/W2062347020","https://openalex.org/W2064131862","https://openalex.org/W2071225518","https://openalex.org/W2086226108","https://openalex.org/W2086680732","https://openalex.org/W2087633442","https://openalex.org/W2090910153","https://openalex.org/W2094834088","https://openalex.org/W2104636525","https://openalex.org/W2154913216","https://openalex.org/W2157129549","https://openalex.org/W2175904283","https://openalex.org/W2203700922","https://openalex.org/W2231751449","https://openalex.org/W2345488705","https://openalex.org/W2375307434","https://openalex.org/W2417734176","https://openalex.org/W2421582870","https://openalex.org/W2487284901","https://openalex.org/W2547325909","https://openalex.org/W2557389782","https://openalex.org/W2571804685","https://openalex.org/W2587247504","https://openalex.org/W2607765999","https://openalex.org/W2610305921","https://openalex.org/W2755543468","https://openalex.org/W2783972087","https://openalex.org/W2791967325","https://openalex.org/W2885230488","https://openalex.org/W2886713750","https://openalex.org/W2963029510","https://openalex.org/W2963272389","https://openalex.org/W2964210134","https://openalex.org/W3000315843","https://openalex.org/W3008460147","https://openalex.org/W3045176433","https://openalex.org/W3090009903","https://openalex.org/W3105047119","https://openalex.org/W3133748958","https://openalex.org/W3147899854","https://openalex.org/W3183922141","https://openalex.org/W3190249772","https://openalex.org/W3204708751","https://openalex.org/W4245922824","https://openalex.org/W4250220742","https://openalex.org/W4288652121"],"related_works":["https://openalex.org/W2796073220","https://openalex.org/W2472637427","https://openalex.org/W3188219351","https://openalex.org/W1994155896","https://openalex.org/W1983311783","https://openalex.org/W2130474842","https://openalex.org/W2885654125","https://openalex.org/W4288408952","https://openalex.org/W2383442806","https://openalex.org/W2295656092"],"abstract_inverted_index":{"The":[0,46,91,115],"transmission":[1,26,79],"eigenvalue":[2,80,84],"problem":[3,47,81,85],"arises":[4],"from":[5,31],"the":[6,19,32,39,43,78,83,98,101,106,123,131],"inverse":[7],"scattering":[8,33],"theory":[9,109],"for":[10,97,110],"inhomogeneous":[11,23],"media.":[12,24],"It":[13,65],"plays":[14],"a":[15,51,87],"key":[16],"role":[17],"in":[18],"unique":[20],"determination":[21],"of":[22,42,53,86],"Furthermore,":[25],"eigenvalues":[27],"can":[28],"be":[29],"reconstructed":[30],"data":[34],"and":[35,60,63,100],"used":[36,96],"to":[37,68,121,129],"estimate":[38],"material":[40],"properties":[41],"unknown":[44],"object.":[45],"is":[48,61,66,103,119],"posted":[49],"as":[50,82],"system":[52],"two":[54],"second":[55],"order":[56],"partial":[57],"differential":[58],"equations":[59],"nonlinear":[62],"non-selfadjoint.":[64],"challenging":[67],"develop":[69],"effective":[70],"numerical":[71],"methods.":[72],"In":[73],"this":[74],"paper,":[75],"we":[76],"formulate":[77],"holomorphic":[88,111],"operator":[89,113],"function.":[90],"Lagrange":[92],"finite":[93],"elements":[94],"are":[95,127],"discretization":[99],"convergence":[102],"proved":[104],"using":[105],"abstract":[107],"approximation":[108],"Fredholm":[112],"functions.":[114],"spectral":[116],"indicator":[117],"method":[118],"employed":[120],"compute":[122],"eigenvalues.":[124],"Numerical":[125],"examples":[126],"presented":[128],"validate":[130],"proposed":[132],"method.":[133]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3}],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}