{"id":"https://openalex.org/W2022705049","doi":"https://doi.org/10.1137/120872486","title":"Eigendecomposition of the Discrete Double-Curl Operator with Application to Fast Eigensolver for Three-Dimensional Photonic Crystals","display_name":"Eigendecomposition of the Discrete Double-Curl Operator with Application to Fast Eigensolver for Three-Dimensional Photonic Crystals","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2022705049","doi":"https://doi.org/10.1137/120872486","mag":"2022705049"},"language":"en","primary_location":{"id":"doi:10.1137/120872486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872486","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","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/A5110707252","display_name":"Tsung-Ming Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I134161618","display_name":"National Taiwan Normal University","ror":"https://ror.org/059dkdx38","country_code":"TW","type":"education","lineage":["https://openalex.org/I134161618"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Tsung-Ming Huang","raw_affiliation_strings":["National Taiwan Normal University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan Normal University","institution_ids":["https://openalex.org/I134161618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108435965","display_name":"Han-En Hsieh","orcid":null},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Han-En Hsieh","raw_affiliation_strings":["National Taiwan University > > > >  >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University > > > >  >  >","institution_ids":["https://openalex.org/I16733864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109995085","display_name":"Wen-Wei Lin","orcid":null},"institutions":[{"id":"https://openalex.org/I148366613","display_name":"National Yang Ming Chiao Tung University","ror":"https://ror.org/00se2k293","country_code":"TW","type":"education","lineage":["https://openalex.org/I148366613"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Wen-Wei Lin","raw_affiliation_strings":["National Yang Ming Chiao Tung University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Yang Ming Chiao Tung University","institution_ids":["https://openalex.org/I148366613"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5005786936","display_name":"Weichung Wang","orcid":"https://orcid.org/0000-0002-6154-7750"},"institutions":[{"id":"https://openalex.org/I16733864","display_name":"National Taiwan University","ror":"https://ror.org/05bqach95","country_code":"TW","type":"education","lineage":["https://openalex.org/I16733864"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Weichung Wang","raw_affiliation_strings":["National Taiwan University > > > >  >  >"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Taiwan University > > > >  >  >","institution_ids":["https://openalex.org/I16733864"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.7684,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.84305543,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"34","issue":"2","first_page":"369","last_page":"391"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10666","display_name":"Photonic Crystals and Applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10666","display_name":"Photonic Crystals and Applications","score":0.9998000264167786,"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/T10299","display_name":"Photonic and Optical Devices","score":0.9957000017166138,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9883000254631042,"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":0.6681022644042969},{"id":"https://openalex.org/keywords/lanczos-resampling","display_name":"Lanczos resampling","score":0.662136435508728},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6593953371047974},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.5100963711738586},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46959415078163147},{"id":"https://openalex.org/keywords/conjugate-gradient-method","display_name":"Conjugate gradient method","score":0.44503462314605713},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.43149763345718384},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.4266057014465332},{"id":"https://openalex.org/keywords/eigendecomposition-of-a-matrix","display_name":"Eigendecomposition of a matrix","score":0.4217727780342102},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.35445231199264526},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.289497435092926},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17995893955230713},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17529141902923584},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11152958869934082},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.10608354210853577}],"concepts":[{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6681022644042969},{"id":"https://openalex.org/C119256216","wikidata":"https://www.wikidata.org/wiki/Q913012","display_name":"Lanczos resampling","level":3,"score":0.662136435508728},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6593953371047974},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.5100963711738586},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46959415078163147},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.44503462314605713},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.43149763345718384},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.4266057014465332},{"id":"https://openalex.org/C169756996","wikidata":"https://www.wikidata.org/wiki/Q194919","display_name":"Eigendecomposition of a matrix","level":3,"score":0.4217727780342102},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.35445231199264526},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.289497435092926},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17995893955230713},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17529141902923584},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11152958869934082},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.10608354210853577},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120872486","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120872486","pdf_url":null,"source":{"id":"https://openalex.org/S16958353","display_name":"SIAM Journal on Matrix Analysis and Applications","issn_l":"0895-4798","issn":["0895-4798","1095-7162"],"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 Matrix Analysis and Applications","raw_type":"journal-article"},{"id":"pmh:oai:140.112.114.62:246246/271291","is_oa":false,"landing_page_url":"http://ntur.lib.ntu.edu.tw/bitstream/246246/271291/1/index.html","pdf_url":null,"source":{"id":"https://openalex.org/S4306402491","display_name":"NTUR (\u81fa\u7063\u6a5f\u69cb\u5178\u85cf)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I16733864","host_organization_name":"National Taiwan University","host_organization_lineage":["https://openalex.org/I16733864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":31,"referenced_works":["https://openalex.org/W1506342804","https://openalex.org/W1507437630","https://openalex.org/W1522382323","https://openalex.org/W1592958377","https://openalex.org/W1605773447","https://openalex.org/W1622427319","https://openalex.org/W1963738920","https://openalex.org/W2001538993","https://openalex.org/W2013029478","https://openalex.org/W2017287201","https://openalex.org/W2022322490","https://openalex.org/W2039904556","https://openalex.org/W2047861338","https://openalex.org/W2055307648","https://openalex.org/W2056051089","https://openalex.org/W2056536494","https://openalex.org/W2056722718","https://openalex.org/W2057749604","https://openalex.org/W2058685142","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2091221772","https://openalex.org/W2117032748","https://openalex.org/W2142063750","https://openalex.org/W2160313937","https://openalex.org/W2169269621","https://openalex.org/W2282382546","https://openalex.org/W2312606703","https://openalex.org/W2328491652","https://openalex.org/W2798909945","https://openalex.org/W3139543928"],"related_works":["https://openalex.org/W2034683969","https://openalex.org/W2045370380","https://openalex.org/W2949942660","https://openalex.org/W4301754683","https://openalex.org/W157842926","https://openalex.org/W2033180095","https://openalex.org/W2062695168","https://openalex.org/W2804140902","https://openalex.org/W1990972291","https://openalex.org/W2119404459"],"abstract_inverted_index":{"This":[0,114],"article":[1],"focuses":[2],"on":[3,225],"the":[4,10,27,32,39,47,60,70,79,90,94,98,102,111,122,130,142,161,166,179,184],"discrete":[5,23],"double-curl":[6,24],"operator":[7,25],"arising":[8],"in":[9],"Maxwell":[11,40],"equation":[12],"that":[13],"models":[14],"three-dimensional":[15],"photonic":[16],"crystals":[17],"with":[18,93,228],"face-centered":[19],"cubic":[20],"lattice.":[21],"The":[22,126,200],"is":[26],"degenerate":[28,48],"coefficient":[29,49],"matrix":[30,50],"of":[31,46,56,65,97,156,165,189,211,214],"generalized":[33],"eigenvalue":[34,84,198,218],"problems":[35,219],"(GEVP)":[36],"due":[37,177],"to":[38,77,81,178,181,222],"equation.":[41],"We":[42,150],"derive":[43],"an":[44,53],"eigendecomposition":[45,180],"and":[51,62,100,107,136,192,207],"explore":[52],"explicit":[54],"form":[55],"orthogonal":[57],"basis":[58],"for":[59],"range":[61],"null":[63],"spaces":[64],"this":[66],"matrix.":[67],"To":[68],"solve":[69],"GEVP,":[71,99],"we":[72,194],"apply":[73],"these":[74,190],"theoretical":[75],"results":[76],"project":[78],"GEVP":[80],"a":[82,148,196,212,226],"standard":[83],"problem":[85],"(SEVP),":[86],"which":[87,159],"involves":[88],"only":[89],"eigenspace":[91],"associated":[92],"nonzero":[95],"eigenvalues":[96,104],"therefore":[101],"zero":[103],"are":[105,134,160],"excluded":[106],"will":[108],"not":[109],"degrade":[110],"computational":[112],"efficiency.":[113],"projected":[115],"SEVP":[116],"can":[117,137,170],"be":[118,138,171],"solved":[119,139],"efficiently":[120,140],"by":[121,141,173,205],"inverse":[123,131,167],"Lanczos":[124,132,168],"method.":[125],"linear":[127],"systems":[128],"within":[129,220],"method":[133,145],"well-conditioned":[135],"conjugate":[143],"gradient":[144],"without":[146],"using":[147],"preconditioner.":[149],"also":[151],"demonstrate":[152],"how":[153],"two":[154,229],"forms":[155],"matrix-vector":[157],"multiplications,":[158],"most":[162],"costly":[163],"part":[164],"method,":[169],"computed":[172],"fast":[174,197],"Fourier":[175],"transformation":[176],"significantly":[182],"reduce":[183],"computation":[185],"cost.":[186],"Integrating":[187],"all":[188],"findings":[191],"techniques,":[193],"obtain":[195],"solver.":[199],"solver":[201],"has":[202],"been":[203],"implemented":[204],"MATLAB":[206],"successfully":[208],"solves":[209],"each":[210],"set":[213],"5.184":[215],"million":[216],"dimension":[217],"50":[221],"104":[223],"minutes":[224],"workstation":[227],"Intel":[230],"Quad-Core":[231],"Xeon":[232],"X5687":[233],"3.6":[234],"GHz":[235],"CPUs.":[236]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
