{"id":"https://openalex.org/W4361205232","doi":"https://doi.org/10.1137/21m1392012","title":"A Two-Level Preconditioned Helmholtz Subspace Iterative Method for Maxwell Eigenvalue Problems","display_name":"A Two-Level Preconditioned Helmholtz Subspace Iterative Method for Maxwell Eigenvalue Problems","publication_year":2023,"publication_date":"2023-03-28","ids":{"openalex":"https://openalex.org/W4361205232","doi":"https://doi.org/10.1137/21m1392012"},"language":"en","primary_location":{"id":"doi:10.1137/21m1392012","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/21m1392012","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/A5023412512","display_name":"Qigang Liang","orcid":"https://orcid.org/0000-0001-8955-4920"},"institutions":[{"id":"https://openalex.org/I116953780","display_name":"Tongji University","ror":"https://ror.org/03rc6as71","country_code":"CN","type":"education","lineage":["https://openalex.org/I116953780"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Qigang Liang","raw_affiliation_strings":["School of Mathematical Science, Tongji University, Shanghai 200092, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Tongji University, Shanghai 200092, China","institution_ids":["https://openalex.org/I116953780"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100742189","display_name":"Xuejun Xu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xuejun Xu","raw_affiliation_strings":["School of Mathematical Science, Tongji University, Shanghai 200092, China, and Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematical Science, Tongji University, Shanghai 200092, China, and Institute of Computational Mathematics, AMSS, Chinese Academy of Sciences, Beijing 100190, China","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5023412512"],"corresponding_institution_ids":["https://openalex.org/I116953780"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.03468141,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"61","issue":"2","first_page":"642","last_page":"674"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"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"}},"topics":[{"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/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9997000098228455,"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/mathematics","display_name":"Mathematics","score":0.8311264514923096},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.7616530656814575},{"id":"https://openalex.org/keywords/helmholtz-equation","display_name":"Helmholtz equation","score":0.647854745388031},{"id":"https://openalex.org/keywords/helmholtz-free-energy","display_name":"Helmholtz free energy","score":0.5577676892280579},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.46871963143348694},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.4545251131057739},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.45225927233695984},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4407600164413452},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.42790326476097107},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.41171687841415405},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.2007690966129303},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.17260628938674927},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07355493307113647}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8311264514923096},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.7616530656814575},{"id":"https://openalex.org/C18591234","wikidata":"https://www.wikidata.org/wiki/Q860615","display_name":"Helmholtz equation","level":3,"score":0.647854745388031},{"id":"https://openalex.org/C27592594","wikidata":"https://www.wikidata.org/wiki/Q865821","display_name":"Helmholtz free energy","level":2,"score":0.5577676892280579},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.46871963143348694},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.4545251131057739},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.45225927233695984},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4407600164413452},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.42790326476097107},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.41171687841415405},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.2007690966129303},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.17260628938674927},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07355493307113647},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/21m1392012","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1137/21m1392012","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":[{"display_name":"Peace, Justice and strong institutions","score":0.8199999928474426,"id":"https://metadata.un.org/sdg/16"}],"awards":[{"id":"https://openalex.org/G2626887494","display_name":null,"funder_award_id":"11871272","funder_id":"https://openalex.org/F4320336807","funder_display_name":"National Natural Science Foundation of China-China Academy of General Technology Joint Fund for Basic Research"},{"id":"https://openalex.org/G4722677053","display_name":null,"funder_award_id":"12071350","funder_id":"https://openalex.org/F4320336807","funder_display_name":"National Natural Science Foundation of China-China Academy of General Technology Joint Fund for Basic Research"}],"funders":[{"id":"https://openalex.org/F4320321885","display_name":"Science and Technology Commission of Shanghai Municipality","ror":"https://ror.org/03kt66j61"},{"id":"https://openalex.org/F4320336807","display_name":"National Natural Science Foundation of China-China Academy of General Technology Joint Fund for Basic Research","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":41,"referenced_works":["https://openalex.org/W1524573041","https://openalex.org/W1542736314","https://openalex.org/W1548589512","https://openalex.org/W1575147392","https://openalex.org/W1969732357","https://openalex.org/W1986038455","https://openalex.org/W1989748191","https://openalex.org/W1992857919","https://openalex.org/W2001104413","https://openalex.org/W2023576489","https://openalex.org/W2027009705","https://openalex.org/W2039904556","https://openalex.org/W2041568728","https://openalex.org/W2051389949","https://openalex.org/W2062618977","https://openalex.org/W2064909895","https://openalex.org/W2071704402","https://openalex.org/W2072267808","https://openalex.org/W2076242982","https://openalex.org/W2078467537","https://openalex.org/W2106311058","https://openalex.org/W2118536081","https://openalex.org/W2143783905","https://openalex.org/W2146553400","https://openalex.org/W2151052797","https://openalex.org/W2157129549","https://openalex.org/W2172969761","https://openalex.org/W2244139635","https://openalex.org/W2327471624","https://openalex.org/W2527451000","https://openalex.org/W2592267541","https://openalex.org/W2785206729","https://openalex.org/W2884902418","https://openalex.org/W2889612743","https://openalex.org/W2894083638","https://openalex.org/W2962711883","https://openalex.org/W2963444718","https://openalex.org/W3021975867","https://openalex.org/W3046457476","https://openalex.org/W3084370023","https://openalex.org/W3213239670"],"related_works":["https://openalex.org/W2132719248","https://openalex.org/W1997716701","https://openalex.org/W4255634477","https://openalex.org/W2765426120","https://openalex.org/W2012246388","https://openalex.org/W2071128778","https://openalex.org/W2099169296","https://openalex.org/W2046520066","https://openalex.org/W3101053097","https://openalex.org/W2167434321"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"based":[3],"on":[4],"a":[5,12,68,82,88,108],"domain":[6],"decomposition":[7],"method,":[8],"we":[9,91],"shall":[10],"propose":[11],"two-level":[13,35],"preconditioned":[14,74],"Helmholtz":[15,77],"subspace":[16],"iterative":[17],"(PHSI)":[18],"method":[19,37,60,143],"for":[20,53],"solving":[21,54,81],"algebraic":[22],"eigenvalue":[23,32,56,65,85],"problems":[24,57,66],"resulting":[25],"from":[26],"edge":[27],"element":[28],"approximation":[29],"of":[30,63,70,72,98,121,128,150,179],"Maxwell":[31,55,139],"problems.":[33],"The":[34,123,155,164],"PHSI":[36],"may":[38],"compute":[39],"simple":[40],"eigenpairs,":[41,43],"multiple":[42],"and":[44,51,76,117,132,152,160],"clustered":[45],"eigenpairs.":[46],"It":[47],"is":[48,107,111,118,126,144],"very":[49],"efficient":[50],"robust":[52],"since":[58],"the":[59,94,99,112,119,129,136,142,148,175,177,181,183],"reduces":[61],"solutions":[62,71],"fine":[64],"to":[67,147,169],"series":[69],"parallel":[73],"systems":[75],"projected":[78],"systems.":[79],"After":[80],"small":[83],"dimensional":[84],"problem":[86],"in":[87],"trial":[89],"subspace,":[90],"finally":[92],"get":[93],"total":[95],"error":[96],"reduction":[97],"first":[100,137],"several":[101,138],"discrete":[102],"eigenvalues":[103],"as":[104,171],",":[105,172],"where":[106],"positive":[109,124],"parameter,":[110],"overlapping":[113],"size":[114,131],"among":[115,135],"subdomains,":[116,180],"diameter":[120],"subdomains.":[122],"number":[125,156,178],"independent":[127],"mesh":[130],"internal":[133],"gaps":[134],"eigenvalues,":[140],"i.e.,":[141],"optimal":[145],"corresponding":[146],"degrees":[149],"freedom":[151],"cluster":[153],"robust.":[154],"increases":[157],"with":[158,162],"increasing,":[159],"decreases":[161,167],"increasing.":[163],"-dependent":[165],"constant":[166],"monotonically":[168],"1":[170],"which":[173],"means":[174],"more":[176],"better":[182],"convergence":[184],"rate.":[185],"Numerical":[186],"results":[187],"supporting":[188],"our":[189],"theory":[190],"are":[191],"given.":[192]},"counts_by_year":[],"updated_date":"2025-12-19T19:40:27.379048","created_date":"2025-10-10T00:00:00"}