{"id":"https://openalex.org/W1973695816","doi":"https://doi.org/10.1137/110839990","title":"Finite Element Methods for Maxwell's Transmission Eigenvalues","display_name":"Finite Element Methods for Maxwell's Transmission Eigenvalues","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1973695816","doi":"https://doi.org/10.1137/110839990","mag":"1973695816"},"language":"en","primary_location":{"id":"doi:10.1137/110839990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110839990","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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/A5028510993","display_name":"Peter Monk","orcid":"https://orcid.org/0000-0002-6539-5897"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Peter Monk","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5054679759","display_name":"Jiguang Sun","orcid":"https://orcid.org/0000-0003-4105-8463"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiguang Sun","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5028510993"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.2566,"has_fulltext":false,"cited_by_count":94,"citation_normalized_percentile":{"value":0.95823357,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"34","issue":"3","first_page":"B247","last_page":"B264"},"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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9997000098228455,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9991000294685364,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7983951568603516},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7623048424720764},{"id":"https://openalex.org/keywords/hermitian-matrix","display_name":"Hermitian matrix","score":0.6343712210655212},{"id":"https://openalex.org/keywords/inverse-iteration","display_name":"Inverse iteration","score":0.6108182668685913},{"id":"https://openalex.org/keywords/divide-and-conquer-eigenvalue-algorithm","display_name":"Divide-and-conquer eigenvalue algorithm","score":0.5987995862960815},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5805081129074097},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5286726951599121},{"id":"https://openalex.org/keywords/transmission","display_name":"Transmission (telecommunications)","score":0.479884535074234},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4489622712135315},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4214808940887451},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14213868975639343},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.13574689626693726},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07909789681434631}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7983951568603516},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7623048424720764},{"id":"https://openalex.org/C94940","wikidata":"https://www.wikidata.org/wiki/Q652941","display_name":"Hermitian matrix","level":2,"score":0.6343712210655212},{"id":"https://openalex.org/C2505209","wikidata":"https://www.wikidata.org/wiki/Q1671724","display_name":"Inverse iteration","level":3,"score":0.6108182668685913},{"id":"https://openalex.org/C192702615","wikidata":"https://www.wikidata.org/wiki/Q5283998","display_name":"Divide-and-conquer eigenvalue algorithm","level":3,"score":0.5987995862960815},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5805081129074097},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5286726951599121},{"id":"https://openalex.org/C761482","wikidata":"https://www.wikidata.org/wiki/Q118093","display_name":"Transmission (telecommunications)","level":2,"score":0.479884535074234},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4489622712135315},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4214808940887451},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14213868975639343},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.13574689626693726},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07909789681434631},{"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C76155785","wikidata":"https://www.wikidata.org/wiki/Q418","display_name":"Telecommunications","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/110839990","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110839990","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","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":27,"referenced_works":["https://openalex.org/W1522382323","https://openalex.org/W1523113578","https://openalex.org/W1582734821","https://openalex.org/W1964288382","https://openalex.org/W1970252823","https://openalex.org/W1970402902","https://openalex.org/W1971870342","https://openalex.org/W1983890677","https://openalex.org/W1994915741","https://openalex.org/W1996838123","https://openalex.org/W2007334673","https://openalex.org/W2009247212","https://openalex.org/W2017916357","https://openalex.org/W2020192814","https://openalex.org/W2033969794","https://openalex.org/W2041502917","https://openalex.org/W2048659456","https://openalex.org/W2062347020","https://openalex.org/W2062618977","https://openalex.org/W2080867142","https://openalex.org/W2085752304","https://openalex.org/W2090910153","https://openalex.org/W2104636525","https://openalex.org/W2316115057","https://openalex.org/W2798909945","https://openalex.org/W2951629574","https://openalex.org/W4237085618"],"related_works":["https://openalex.org/W2350895707","https://openalex.org/W46293795","https://openalex.org/W2963566796","https://openalex.org/W2383221329","https://openalex.org/W2470850800","https://openalex.org/W4285722889","https://openalex.org/W2364889976","https://openalex.org/W1982840214","https://openalex.org/W2074605103","https://openalex.org/W2231174965"],"abstract_inverted_index":{"The":[0],"transmission":[1,25,61,107,110,143],"eigenvalue":[2,73],"problem":[3,74,88],"plays":[4],"a":[5,57,119],"critical":[6],"role":[7],"in":[8,17,67,79],"the":[9,70,84,87,101,127,130,136],"theory":[10],"of":[11,39,65,106,129,138],"qualitative":[12],"methods":[13,54,132],"for":[14,24,42,112,142],"inhomogeneous":[15],"media":[16],"inverse":[18,40],"scattering":[19],"theory.":[20],"Efficient":[21],"computational":[22],"tools":[23],"eigenvalues":[26,62,111],"are":[27,37,64,114,123],"needed":[28],"to":[29,32,55,83,125,134],"motivate":[30],"improvements":[31],"theory,":[33],"and,":[34,78],"more":[35],"importantly,":[36],"parts":[38],"algorithms":[41],"estimating":[43],"material":[44],"properties.":[45],"In":[46],"this":[47],"paper,":[48],"we":[49,94],"propose":[50],"two":[51],"finite":[52],"element":[53],"compute":[56],"few":[58],"lowest":[59],"Maxwell's":[60],"which":[63,99],"interest":[66],"applications.":[68],"Since":[69],"discrete":[71],"matrix":[72],"is":[75,89],"large,":[76],"sparse,":[77],"particular,":[80],"non-Hermitian":[81],"due":[82],"fact":[85],"that":[86],"neither":[90],"elliptic":[91],"nor":[92],"self-adjoint,":[93],"devise":[95],"an":[96],"adaptive":[97],"method":[98],"combines":[100],"Arnoldi":[102],"iteration":[103],"and":[104,116,133],"estimation":[105],"eigenvalues.":[108,144],"Exact":[109],"balls":[113],"derived":[115,140],"used":[117],"as":[118],"benchmark.":[120],"Numerical":[121],"examples":[122],"provided":[124],"show":[126],"viability":[128],"proposed":[131],"test":[135],"accuracy":[137],"recently":[139],"inequalities":[141]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":10},{"year":2017,"cited_by_count":10},{"year":2016,"cited_by_count":7},{"year":2015,"cited_by_count":4},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":5}],"updated_date":"2026-03-04T09:10:02.777135","created_date":"2025-10-10T00:00:00"}
