{"id":"https://openalex.org/W2044178408","doi":"https://doi.org/10.1137/09075250x","title":"Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations","display_name":"Certified Reduced Basis Methods and Output Bounds for the Harmonic Maxwell's Equations","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2044178408","doi":"https://doi.org/10.1137/09075250x","mag":"2044178408"},"language":"en","primary_location":{"id":"doi:10.1137/09075250x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09075250x","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":true,"oa_status":"green","oa_url":"https://hal.science/hal-00391996","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041162676","display_name":"Yanlai Chen","orcid":"https://orcid.org/0000-0002-7460-8313"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yanlai Chen","raw_affiliation_strings":["Yanlai_Chen@Brown.edu and Jan.Hesthaven@Brown.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yanlai_Chen@Brown.edu and Jan.Hesthaven@Brown.edu#TAB#","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037681511","display_name":"Jan S. Hesthaven","orcid":"https://orcid.org/0000-0001-8074-1586"},"institutions":[{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jan S. Hesthaven","raw_affiliation_strings":["Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912","institution_ids":["https://openalex.org/I27804330"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089357934","display_name":"Yvon Maday","orcid":"https://orcid.org/0000-0002-0443-6544"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yvon Maday","raw_affiliation_strings":["maday@ann.jussieu.fr#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"maday@ann.jussieu.fr#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021872567","display_name":"Jer\u00f3nimo Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-7367-4394"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jer\u00f3nimo Rodr\u00edguez","raw_affiliation_strings":["jeronimo.rodriguez@usc.es#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"jeronimo.rodriguez@usc.es#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":5.0815,"has_fulltext":false,"cited_by_count":111,"citation_normalized_percentile":{"value":0.96165507,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"32","issue":"2","first_page":"970","last_page":"996"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9991000294685364,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9977999925613403,"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":0.7279435396194458},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5951994061470032},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5700202584266663},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5436444282531738},{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.5219101905822754},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5171574950218201},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.45756983757019043},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.41987791657447815},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.41188132762908936},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.41034963726997375},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.295426607131958},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.28751808404922485},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.20359104871749878}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7279435396194458},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5951994061470032},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5700202584266663},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5436444282531738},{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.5219101905822754},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5171574950218201},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.45756983757019043},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.41987791657447815},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.41188132762908936},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.41034963726997375},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.295426607131958},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28751808404922485},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.20359104871749878},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","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/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/09075250x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/09075250x","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"},{"id":"pmh:oai:HAL:hal-00391996v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00391996","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2009","raw_type":"info:eu-repo/semantics/preprint"},{"id":"pmh:oai:infoscience.epfl.ch:190379","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/190379","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-00391996v1","is_oa":true,"landing_page_url":"https://hal.science/hal-00391996","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"2009","raw_type":"info:eu-repo/semantics/preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1496270222","https://openalex.org/W1496814969","https://openalex.org/W1505358753","https://openalex.org/W1507402195","https://openalex.org/W1516298560","https://openalex.org/W1582734821","https://openalex.org/W1583515859","https://openalex.org/W1594690383","https://openalex.org/W1968287676","https://openalex.org/W1973086722","https://openalex.org/W1976653974","https://openalex.org/W1994841670","https://openalex.org/W2008967183","https://openalex.org/W2032768921","https://openalex.org/W2042426282","https://openalex.org/W2043140788","https://openalex.org/W2044498528","https://openalex.org/W2045627558","https://openalex.org/W2047591100","https://openalex.org/W2047638812","https://openalex.org/W2052690618","https://openalex.org/W2056328108","https://openalex.org/W2061515231","https://openalex.org/W2076048859","https://openalex.org/W2089823252","https://openalex.org/W2102753028","https://openalex.org/W2114847573","https://openalex.org/W2130350269","https://openalex.org/W2140970636","https://openalex.org/W2156368851","https://openalex.org/W2161024376","https://openalex.org/W2165187821","https://openalex.org/W2168970443","https://openalex.org/W2170380225","https://openalex.org/W2172191910","https://openalex.org/W2240238749","https://openalex.org/W2242608853"],"related_works":["https://openalex.org/W2006953814","https://openalex.org/W2542637001","https://openalex.org/W1972782945","https://openalex.org/W3212981098","https://openalex.org/W4221090543","https://openalex.org/W2130622405","https://openalex.org/W2109887391","https://openalex.org/W1748978355","https://openalex.org/W1819996744","https://openalex.org/W2886533026"],"abstract_inverted_index":{"We":[0],"propose":[1],"certified":[2],"reduced":[3,38],"basis":[4,39],"methods":[5],"for":[6,66,119],"the":[7,26,34,37,52,60,68,71,78,90,98,101,107,120,138,164],"efficient":[8,133],"and":[9,33,70,122,129,148,152,169],"reliable":[10],"evaluation":[11],"of":[12,36,51,62,80,97,111,141,154,166],"a":[13,21,41,47,115,124,130,160],"general":[14],"output":[15],"that":[16],"is":[17,44,157],"implicitly":[18],"connected":[19],"to":[20,76,85,136],"given":[22],"parameterized":[23],"input":[24],"through":[25,40,159],"harmonic":[27],"Maxwell's":[28],"equations.":[29],"The":[30,57,94,150],"truth":[31,73],"approximation":[32,50,64,74],"development":[35],"greedy":[42],"approach":[43,156],"based":[45],"on":[46,106],"discontinuous":[48],"Galerkin":[49],"linear":[53],"partial":[54],"differential":[55],"equation.":[56],"formulation":[58],"allows":[59],"use":[61],"different":[63],"spaces":[65],"solving":[67],"primal":[69],"dual":[72],"problems":[75,143,170],"respect":[77],"characteristics":[79],"both":[81],"problem":[82],"types,":[83],"leading":[84],"an":[86],"overall":[87],"reduction":[88],"in":[89,145],"off-line":[91,127],"computational":[92],"effort.":[93],"main":[95],"features":[96],"method":[99],"are":[100],"following:":[102],"(i)":[103],"rapid":[104,139],"convergence":[105],"entire":[108],"representative":[109],"set":[110],"parameters,":[112],"(ii)":[113],"rigorous":[114],"posteriori":[116],"error":[117],"estimators":[118],"output,":[121],"(iii)":[123],"parameter":[125],"independent":[126],"phase":[128,135],"computationally":[131],"very":[132],"on-line":[134],"enable":[137],"solution":[140],"many-query":[142],"arising":[144],"control,":[146],"optimization,":[147],"design.":[149],"versatility":[151],"performance":[153],"this":[155],"shown":[158],"numerical":[161],"experiment,":[162],"illustrating":[163],"modeling":[165],"material":[167],"variations":[168],"with":[171],"resonant":[172],"behavior.":[173]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":8},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":13},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":7},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":13},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":5}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
