{"id":"https://openalex.org/W1966937669","doi":"https://doi.org/10.1090/s0025-5718-00-01244-8","title":"An iterative substructuring method for Maxwell's equations in two dimensions","display_name":"An iterative substructuring method for Maxwell's equations in two dimensions","publication_year":2000,"publication_date":"2000-03-01","ids":{"openalex":"https://openalex.org/W1966937669","doi":"https://doi.org/10.1090/s0025-5718-00-01244-8","mag":"1966937669"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-00-01244-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01244-8","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01244-8/S0025-5718-00-01244-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01244-8/S0025-5718-00-01244-8.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012810207","display_name":"Andrea Toselli","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Andrea Toselli","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113456504","display_name":"Olof B. Widlund","orcid":null},"institutions":[{"id":"https://openalex.org/I36672615","display_name":"Courant Institute of Mathematical Sciences","ror":"https://ror.org/037tm7f56","country_code":"US","type":"education","lineage":["https://openalex.org/I36672615","https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Olof B. Widlund","raw_affiliation_strings":["Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012"],"affiliations":[{"raw_affiliation_string":"Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012","institution_ids":["https://openalex.org/I36672615"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018841476","display_name":"Barbara Wohlmuth","orcid":"https://orcid.org/0000-0001-6908-6015"},"institutions":[{"id":"https://openalex.org/I119916105","display_name":"Augsburg University","ror":"https://ror.org/057ewhh68","country_code":"US","type":"education","lineage":["https://openalex.org/I119916105"]},{"id":"https://openalex.org/I179225836","display_name":"University of Augsburg","ror":"https://ror.org/03p14d497","country_code":"DE","type":"education","lineage":["https://openalex.org/I179225836"]}],"countries":["DE","US"],"is_corresponding":false,"raw_author_name":"Barbara I. Wohlmuth","raw_affiliation_strings":["Math. Institut, Universit\u00c3\u00a4t Augsburg, Universit\u00c3\u00a4tsstr. 14, D-86 159 Augsburg, Germany","Math. Institut, Universit\u00e4t Augsburg, Universit\u00e4tsstr. 14, D-86 159 Augsburg, Germany"],"affiliations":[{"raw_affiliation_string":"Math. Institut, Universit\u00c3\u00a4t Augsburg, Universit\u00c3\u00a4tsstr. 14, D-86 159 Augsburg, Germany","institution_ids":["https://openalex.org/I179225836"]},{"raw_affiliation_string":"Math. Institut, Universit\u00e4t Augsburg, Universit\u00e4tsstr. 14, D-86 159 Augsburg, Germany","institution_ids":["https://openalex.org/I119916105"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5012810207"],"corresponding_institution_ids":["https://openalex.org/I36672615"],"apc_list":null,"apc_paid":null,"fwci":6.4315,"has_fulltext":true,"cited_by_count":36,"citation_normalized_percentile":{"value":0.96410393,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"70","issue":"235","first_page":"935","last_page":"950"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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"}},"topics":[{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9998999834060669,"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/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/T10739","display_name":"Electromagnetic Scattering and Analysis","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8429900407791138},{"id":"https://openalex.org/keywords/maxwells-equations","display_name":"Maxwell's equations","score":0.7777490615844727},{"id":"https://openalex.org/keywords/iterative-method","display_name":"Iterative method","score":0.5949649810791016},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5538352131843567},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.41337472200393677},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.35386747121810913},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2809877097606659}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8429900407791138},{"id":"https://openalex.org/C59282198","wikidata":"https://www.wikidata.org/wiki/Q51501","display_name":"Maxwell's equations","level":2,"score":0.7777490615844727},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.5949649810791016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5538352131843567},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.41337472200393677},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.35386747121810913},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2809877097606659},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1090/s0025-5718-00-01244-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01244-8","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01244-8/S0025-5718-00-01244-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:mediatum.ub.tum.de:node/1684526","is_oa":false,"landing_page_url":"https://mediatum.ub.tum.de/1684526","pdf_url":null,"source":{"id":"https://openalex.org/S4377196330","display_name":"mediaTUM  (Technical University of Munich)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I62916508","host_organization_name":"Technical University of Munich","host_organization_lineage":["https://openalex.org/I62916508"],"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"},{"id":"pmh:oai:uni-augsburg.opus-bayern.de:26519","is_oa":false,"landing_page_url":"https://opus.bibliothek.uni-augsburg.de/opus4/frontdoor/index/index/docId/26519","pdf_url":null,"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":"doi:10.1090/s0025-5718-00-01244-8","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-00-01244-8","pdf_url":"https://www.ams.org/mcom/2001-70-235/S0025-5718-00-01244-8/S0025-5718-00-01244-8.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4459550895","display_name":"Iterative Substructuring Methods for Elliptic Problems","funder_award_id":"9732208","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5219260752","display_name":null,"funder_award_id":"DE-FG","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7186324567","display_name":null,"funder_award_id":"DE-FG02-","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7679498328","display_name":"MDC: A Numerical Laboratory for Multi-Model Multi-Domain    Computational Methods in Aerodynamics and Acoustics","funder_award_id":"9527169","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G848032724","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8684078510","display_name":null,"funder_award_id":"DE-FG02","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"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/W1966937669.pdf","grobid_xml":"https://content.openalex.org/works/W1966937669.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W5800307","https://openalex.org/W93214714","https://openalex.org/W206714260","https://openalex.org/W619458845","https://openalex.org/W1520203544","https://openalex.org/W1542243431","https://openalex.org/W1584365460","https://openalex.org/W1674659126","https://openalex.org/W1967011851","https://openalex.org/W1978324465","https://openalex.org/W1994934002","https://openalex.org/W2001104413","https://openalex.org/W2006895912","https://openalex.org/W2033986961","https://openalex.org/W2049374408","https://openalex.org/W2062618977","https://openalex.org/W2068876583","https://openalex.org/W2075896209","https://openalex.org/W2078783107","https://openalex.org/W2140280828","https://openalex.org/W2235234346","https://openalex.org/W2597153873","https://openalex.org/W2750235028","https://openalex.org/W3042562017","https://openalex.org/W3149667697","https://openalex.org/W4243054974","https://openalex.org/W4252104256","https://openalex.org/W4292079189","https://openalex.org/W4297789110","https://openalex.org/W6611088299"],"related_works":["https://openalex.org/W1973641256","https://openalex.org/W1544640938","https://openalex.org/W2859358578","https://openalex.org/W2044446392","https://openalex.org/W2057289358","https://openalex.org/W2412311587","https://openalex.org/W2040941802","https://openalex.org/W2084415399","https://openalex.org/W4238207569","https://openalex.org/W2339251345"],"abstract_inverted_index":{"Iterative":[0],"substructuring":[1],"methods,":[2,8],"also":[3,125],"known":[4,50],"as":[5,80],"Schur":[6],"complement":[7],"form":[9],"an":[10,92],"important":[11],"family":[12],"of":[13,46,54,70,73,83,86,121],"domain":[14],"decomposition":[15],"algorithms.":[16],"They":[17],"are":[18,35,124],"preconditioned":[19],"conjugate":[20,55],"gradient":[21,56],"methods":[22,106],"where":[23],"solvers":[24],"on":[25,31],"local":[26,88],"subregions":[27],"and":[28,75],"a":[29,32,65],"solver":[30],"coarse":[33],"mesh":[34],"used":[36],"to":[37,59],"construct":[38],"the":[39,52,61,71,81,84,87,98],"preconditioner.":[40],"For":[41],"conforming":[42],"finite":[43,110],"element":[44],"approximations":[45],"$H^1$,":[47],"it":[48,77],"is":[49,68,101],"that":[51,76],"number":[53,72],"steps":[57],"required":[58],"reduce":[60],"residual":[62],"norm":[63],"by":[64],"fixed":[66],"factor":[67],"independent":[69],"substructures,":[74],"grows":[78],"only":[79],"logarithm":[82],"dimension":[85],"problem":[89],"associated":[90],"with":[91],"individual":[93],"substructure.":[94],"In":[95],"this":[96],"paper,":[97],"same":[99],"result":[100],"established":[102],"for":[103,107],"similar":[104],"iterative":[105],"low-order":[108],"N\u00c3\u00a9d\u00c3\u00a9lec":[109],"elements,":[111],"which":[112],"approximate":[113],"$H(\\mathrm":[114],"{curl};\\Omega":[115],")$":[116],"in":[117],"two":[118],"dimensions.":[119],"Results":[120],"numerical":[122],"experiments":[123],"provided.":[126]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2019,"cited_by_count":3},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}