{"id":"https://openalex.org/W2558661249","doi":"https://doi.org/10.1137/15m1039225","title":"A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations","display_name":"A New Heterogeneous Multiscale Method for Time-Harmonic Maxwell's Equations","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2558661249","doi":"https://doi.org/10.1137/15m1039225","mag":"2558661249"},"language":"en","primary_location":{"id":"doi:10.1137/15m1039225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039225","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":true,"oa_status":"green","oa_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/65104/15m1039225.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061248986","display_name":"Patrick Henning","orcid":"https://orcid.org/0000-0002-6432-5504"},"institutions":[{"id":"https://openalex.org/I86987016","display_name":"KTH Royal Institute of Technology","ror":"https://ror.org/026vcq606","country_code":"SE","type":"education","lineage":["https://openalex.org/I86987016"]}],"countries":["SE"],"is_corresponding":true,"raw_author_name":"Patrick Henning","raw_affiliation_strings":["Division of Numerical Analysis, Mathematics, Kungliga Tekniska H\u00f6geskolan, 10044 Stockholm, Sweden"],"affiliations":[{"raw_affiliation_string":"Division of Numerical Analysis, Mathematics, Kungliga Tekniska H\u00f6geskolan, 10044 Stockholm, Sweden","institution_ids":["https://openalex.org/I86987016"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039193717","display_name":"Mario Ohlberger","orcid":"https://orcid.org/0000-0002-6260-3574"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Mario Ohlberger","raw_affiliation_strings":["Institut f\u00fcr Numerische und Angewandte Mathematik, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, D-48149 M\u00fcnster, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Numerische und Angewandte Mathematik, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, D-48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5045393330","display_name":"Barbara Verf\u00fcrth","orcid":"https://orcid.org/0000-0002-8286-4501"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Barbara Verf\u00fcrth","raw_affiliation_strings":["Institut f\u00fcr Numerische und Angewandte Mathematik, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, D-48149 M\u00fcnster, Germany"],"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Numerische und Angewandte Mathematik, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, D-48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5061248986"],"corresponding_institution_ids":["https://openalex.org/I86987016"],"apc_list":null,"apc_paid":null,"fwci":4.3127,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.94655951,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"54","issue":"6","first_page":"3493","last_page":"3522"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"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":0.9997000098228455,"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/T11558","display_name":"Composite Material Mechanics","score":0.9991999864578247,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.8062798976898193},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7339372634887695},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7235761880874634},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.6096187829971313},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.6089692711830139},{"id":"https://openalex.org/keywords/scattering-matrix-method","display_name":"Scattering-matrix method","score":0.5279753804206848},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5251076817512512},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5052233338356018},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4609087109565735},{"id":"https://openalex.org/keywords/residual","display_name":"Residual","score":0.45750004053115845},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.44546663761138916},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4020520746707916},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3476608395576477},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2076176404953003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.17893630266189575},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09218040108680725}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.8062798976898193},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7339372634887695},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7235761880874634},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.6096187829971313},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.6089692711830139},{"id":"https://openalex.org/C22480482","wikidata":"https://www.wikidata.org/wiki/Q7430620","display_name":"Scattering-matrix method","level":3,"score":0.5279753804206848},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5251076817512512},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5052233338356018},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4609087109565735},{"id":"https://openalex.org/C155512373","wikidata":"https://www.wikidata.org/wiki/Q287450","display_name":"Residual","level":2,"score":0.45750004053115845},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.44546663761138916},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4020520746707916},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3476608395576477},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2076176404953003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.17893630266189575},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09218040108680725},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/15m1039225","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1039225","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"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:65104","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-651049","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/65104/15m1039225.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"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":{"id":"pmh:oai:uni-augsburg.opus-bayern.de:65104","is_oa":true,"landing_page_url":"https://nbn-resolving.org/urn:nbn:de:bvb:384-opus4-651049","pdf_url":"https://opus.bibliothek.uni-augsburg.de/opus4/files/65104/15m1039225.pdf","source":{"id":"https://openalex.org/S4306400930","display_name":"OPUS (Augsburg University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I119916105","host_organization_name":"Augsburg University","host_organization_lineage":["https://openalex.org/I119916105"],"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"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G317474130","display_name":null,"funder_award_id":"OH 98/6-1","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G5106512922","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6024419964","display_name":null,"funder_award_id":"Deutsche Forschungsgemeinschaft (DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6052429835","display_name":null,"funder_award_id":"(DFG)","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2558661249.pdf","grobid_xml":"https://content.openalex.org/works/W2558661249.grobid-xml"},"referenced_works_count":37,"referenced_works":["https://openalex.org/W1531212795","https://openalex.org/W1730415915","https://openalex.org/W1966194794","https://openalex.org/W1973604357","https://openalex.org/W1983515720","https://openalex.org/W1983989325","https://openalex.org/W1990157709","https://openalex.org/W1999034403","https://openalex.org/W2000554621","https://openalex.org/W2002791333","https://openalex.org/W2006509721","https://openalex.org/W2015148405","https://openalex.org/W2027239222","https://openalex.org/W2028434980","https://openalex.org/W2029450279","https://openalex.org/W2031485972","https://openalex.org/W2035358778","https://openalex.org/W2037707132","https://openalex.org/W2050578943","https://openalex.org/W2056087726","https://openalex.org/W2065700840","https://openalex.org/W2070161878","https://openalex.org/W2075594705","https://openalex.org/W2079298002","https://openalex.org/W2083281683","https://openalex.org/W2088568870","https://openalex.org/W2092751877","https://openalex.org/W2102635728","https://openalex.org/W2108845300","https://openalex.org/W2109690658","https://openalex.org/W2118551467","https://openalex.org/W2142252293","https://openalex.org/W2149810455","https://openalex.org/W2169501376","https://openalex.org/W2295743790","https://openalex.org/W2537350039","https://openalex.org/W3214098784"],"related_works":["https://openalex.org/W2118277127","https://openalex.org/W2134757969","https://openalex.org/W2110491180","https://openalex.org/W2084533666","https://openalex.org/W2084867621","https://openalex.org/W2117998300","https://openalex.org/W1760405442","https://openalex.org/W1531212795","https://openalex.org/W2003080029","https://openalex.org/W1963572177"],"abstract_inverted_index":{"In":[0,102],"this":[1,100,127],"paper,":[2],"we":[3,61,129,146],"suggest":[4],"a":[5,26,46,73,97,108,119,135,153,164],"new":[6,74],"heterogeneous":[7],"multiscale":[8],"method":[9,21],"(HMM)":[10],"for":[11,67,118],"the":[12,31,59,81,84,92,114,124,140,143,163],"time-harmonic":[13,68],"Maxwell":[14,69],"equations":[15,70],"in":[16,28,83,107,139],"locally":[17],"periodic":[18],"media.":[19],"The":[20],"is":[22,94,113],"constructed":[23],"by":[24],"using":[25],"divergence-regularization":[27,82],"one":[29],"of":[30,80,99,123],"cell":[32],"problems.":[33],"This":[34],"allows":[35],"us":[36],"to":[37,45,96,132,161],"introduce":[38],"fine-scale":[39],"correctors":[40],"that":[41,77,91],"are":[42,130,159],"not":[43],"subject":[44],"cumbersome":[47],"divergence-free":[48],"constraint":[49],"and":[50,71,142,145,149],"which":[51],"can":[52],"hence":[53],"easily":[54],"be":[55],"implemented.":[56],"To":[57],"analyze":[58],"method,":[60],"first":[62],"revisit":[63],"classical":[64],"homogenization":[65,75],"theory":[66],"derive":[72,147],"result":[76],"makes":[78],"use":[79],"two-scale":[85,111],"homogenized":[86],"equation.":[87,101],"We":[88],"then":[89],"show":[90],"HMM":[93],"equivalent":[95],"discretization":[98],"particular,":[103],"writing":[104],"both":[105],"problems":[106],"fully":[109],"coupled":[110],"formulation":[112],"crucial":[115],"starting":[116],"point":[117],"corresponding":[120],"numerical":[121],"analysis":[122],"method.":[125],"With":[126],"approach":[128],"able":[131],"prove":[133],"rigorous":[134],"priori":[136,165],"error":[137,155],"estimates":[138],"$\\mathbf{H}({curl})$-":[141],"$H^{-1}$-norm,":[144],"reliable":[148],"efficient":[150],"localized":[151],"residual-based":[152],"posteriori":[154],"estimates.":[156],"Numerical":[157],"experiments":[158],"presented":[160],"verify":[162],"convergence":[166],"results.":[167]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}