{"id":"https://openalex.org/W2508170771","doi":"https://doi.org/10.1090/mcom/3366","title":"Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions","display_name":"Spectral analysis and spectral symbol for the 2D curl-curl (stabilized) operator with applications to the related iterative solutions","publication_year":2018,"publication_date":"2018-03-21","ids":{"openalex":"https://openalex.org/W2508170771","doi":"https://doi.org/10.1090/mcom/3366","mag":"2508170771"},"language":"en","primary_location":{"id":"doi:10.1090/mcom/3366","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3366","pdf_url":null,"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":"green","oa_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-321246","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5022749162","display_name":"Mariarosa Mazza","orcid":"https://orcid.org/0000-0002-8505-6788"},"institutions":[{"id":"https://openalex.org/I4210139716","display_name":"Max Planck Institute for Plasma Physics","ror":"https://ror.org/03taest98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210139716"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Mariarosa Mazza","raw_affiliation_strings":["Max-Planck Institut f\u00c3\u00bcr Plasmaphysik, Boltzmannstra\u00c3\u009fe 2, 87548 Garching bei, M\u00c3\u00bcnchen, Germany","Max Planck Institute for Plasma Physics"],"affiliations":[{"raw_affiliation_string":"Max-Planck Institut f\u00c3\u00bcr Plasmaphysik, Boltzmannstra\u00c3\u009fe 2, 87548 Garching bei, M\u00c3\u00bcnchen, Germany","institution_ids":["https://openalex.org/I4210139716"]},{"raw_affiliation_string":"Max Planck Institute for Plasma Physics","institution_ids":["https://openalex.org/I4210139716"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Ahmed Ratnani","orcid":null},"institutions":[{"id":"https://openalex.org/I4210139716","display_name":"Max Planck Institute for Plasma Physics","ror":"https://ror.org/03taest98","country_code":"DE","type":"facility","lineage":["https://openalex.org/I149899117","https://openalex.org/I4210139716"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Ahmed Ratnani","raw_affiliation_strings":["Max-Planck Institut f\u00c3\u00bcr Plasmaphysik, Boltzmannstra\u00c3\u009fe 2, 87548 Garching bei, M\u00c3\u00bcnchen, Germany; and Technische Universit\u00c3\u00a4t M\u00c3\u00bcnchen, Boltzmannstra\u00c3\u009fe 3, 87548 Garching bei M\u00c3\u00bcnchen, Germany"],"affiliations":[{"raw_affiliation_string":"Max-Planck Institut f\u00c3\u00bcr Plasmaphysik, Boltzmannstra\u00c3\u009fe 2, 87548 Garching bei, M\u00c3\u00bcnchen, Germany; and Technische Universit\u00c3\u00a4t M\u00c3\u00bcnchen, Boltzmannstra\u00c3\u009fe 3, 87548 Garching bei M\u00c3\u00bcnchen, Germany","institution_ids":["https://openalex.org/I4210139716"]}]},{"author_position":"last","author":{"id":null,"display_name":"Stefano Serra-Capizzano","orcid":null},"institutions":[{"id":"https://openalex.org/I123387679","display_name":"Uppsala University","ror":"https://ror.org/048a87296","country_code":"SE","type":"education","lineage":["https://openalex.org/I123387679"]},{"id":"https://openalex.org/I115752224","display_name":"University of Insubria","ror":"https://ror.org/00s409261","country_code":"IT","type":"education","lineage":["https://openalex.org/I115752224"]}],"countries":["IT","SE"],"is_corresponding":false,"raw_author_name":"Stefano Serra-Capizzano","raw_affiliation_strings":["Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy; and Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden"],"affiliations":[{"raw_affiliation_string":"Department of Science and High Technology, University of Insubria, Via Valleggio 11, 22100 Como, Italy; and Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden","institution_ids":["https://openalex.org/I115752224","https://openalex.org/I123387679"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5022749162"],"corresponding_institution_ids":["https://openalex.org/I4210139716"],"apc_list":null,"apc_paid":null,"fwci":0.2137,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.51077844,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"88","issue":"317","first_page":"1155","last_page":"1188"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.30390000343322754,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.30390000343322754,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.288100004196167,"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":0.16329999268054962,"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/mathematics","display_name":"Mathematics","score":0.7844691872596741},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.6107318997383118},{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.5023870468139648},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.46605098247528076},{"id":"https://openalex.org/keywords/toeplitz-matrix","display_name":"Toeplitz matrix","score":0.4102022051811218},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3905525803565979},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.33046045899391174}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7844691872596741},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.6107318997383118},{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.5023870468139648},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.46605098247528076},{"id":"https://openalex.org/C147710293","wikidata":"https://www.wikidata.org/wiki/Q849428","display_name":"Toeplitz matrix","level":2,"score":0.4102022051811218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3905525803565979},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.33046045899391174},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","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/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/mcom/3366","is_oa":false,"landing_page_url":"https://doi.org/10.1090/mcom/3366","pdf_url":null,"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:DiVA.org:uu-321246","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-321246","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"Report"},{"id":"pmh:oai:pure.mpg.de:item_2483092","is_oa":false,"landing_page_url":"http://hdl.handle.net/11858/00-001M-0000-002D-F6B4-6","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/lecture"},{"id":"pmh:oai:pure.mpg.de:item_3026817","is_oa":false,"landing_page_url":"http://hdl.handle.net/21.11116/0000-0002-F96D-C","pdf_url":null,"source":{"id":"https://openalex.org/S4306400654","display_name":"MPG.PuRe (Max Planck Society)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I149899117","host_organization_name":"Max Planck Society","host_organization_lineage":["https://openalex.org/I149899117"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematics of Computation","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2901836527","is_oa":false,"landing_page_url":"https://pure.mpg.de/pubman/faces/ViewItemOverviewPage.jsp?itemId=item_2483092","pdf_url":null,"source":null,"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":null}],"best_oa_location":{"id":"pmh:oai:DiVA.org:uu-321246","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-321246","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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":"","raw_type":"Report"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320311030","display_name":"Istituto Nazionale di Alta Matematica \"Francesco Severi\"","ror":"https://ror.org/01vx64p53"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2522901347","https://openalex.org/W1587478261","https://openalex.org/W2183068822","https://openalex.org/W2964244860","https://openalex.org/W122023075","https://openalex.org/W3008392526","https://openalex.org/W2558353542","https://openalex.org/W1604599717","https://openalex.org/W3119659125","https://openalex.org/W2183637989","https://openalex.org/W203254733","https://openalex.org/W2594752744","https://openalex.org/W2790431991","https://openalex.org/W2183151876","https://openalex.org/W1857993914","https://openalex.org/W3118848869","https://openalex.org/W2055610189","https://openalex.org/W2950244672","https://openalex.org/W2018814887","https://openalex.org/W2025056579"],"abstract_inverted_index":{"In":[0,204],"this":[1,175,271],"paper,":[2],"we":[3,63,77,148,185,248,298,344,356],"study":[4,78],"structural":[5],"and":[6,38,49,57,76,99,117,135,178,222,240,270,313,337,355,362],"spectral":[7,176,183,305,342],"features":[8,350],"of":[9,12,18,46,60,81,104,126,138,141,152,154,171,189,236,253,256,276,281,307,314,340,351,370],"linear":[10,53,373],"systems":[11],"equations":[13],"arising":[14],"from":[15],"Galerkin":[16],"approximations":[17],"$H(\\mathrm":[19],"{curl})$":[20],"elliptic":[21],"variational":[22],"problems,":[23,40],"based":[24,69],"on":[25,70,347],"the":[26,44,79,82,119,124,127,131,139,142,150,169,187,213,225,234,237,254,273,277,282,286,291,308,315,334,341,348,367,371],"Isogeometric":[27],"Analysis":[28],"(IgA)":[29],"approach.":[30],"Such":[31],"problems":[32],"arise":[33],"in":[34,43,133,223],"Time":[35],"Harmonic":[36],"Maxwell":[37],"Magnetostatic":[39],"as":[41,195,245],"well":[42],"preconditioning":[45],"MagnetoHydroDynamics":[47],"equations,":[48],"lead":[50],"to":[51,180,268,301],"large":[52,167,263],"systems,":[54],"with":[55,123,212],"different":[56],"severe":[58],"sources":[59],"ill-conditioning.":[61],"First,":[62],"consider":[64],"a":[65,71,96,101,105,159,198,208,228,246,303,358],"compatible":[66],"B-splines":[67],"discretization":[68],"discrete":[72,274],"de":[73],"Rham":[74],"sequence":[75],"structure":[80],"resulting":[83],"matrices":[84,309],"$\\mathcal":[85,92,257,310],"{A}_{\\mathbfit":[86,93,191,258,311],"{n}}$.":[87],"It":[88],"turns":[89],"out":[90],"that":[91,157,250,290],"{n}}$":[94,193,312],"shows":[95],"two-by-two":[97,106,199],"pattern":[98],"is":[100,112,197,207,227,265,322],"principal":[102],"submatrix":[103],"block":[107,111],"matrix,":[108],"where":[109,118],"each":[110,153,172],"two-level":[113],"banded,":[114],"almost":[115],"Toeplitz,":[116],"bandwidths":[120],"grow":[121],"linearly":[122],"degree":[125],"B-splines.":[128],"Looking":[129],"at":[130],"coefficients":[132],"detail":[134],"making":[136,338],"use":[137,339],"theory":[140,336],"Generalized":[143],"Locally":[144],"Toeplitz":[145],"(GLT)":[146],"sequences,":[147],"identify":[149],"symbol":[151,188,226],"these":[155],"blocks,":[156],"is,":[158],"function":[160],"describing":[161],"asymptotically,":[162],"i.e.,":[163],"for":[164,260,366],"$\\mathbfit":[165,261],"{n}$":[166,262],"enough,":[168,264],"spectrum":[170,255],"block.":[173],"From":[174,285],"knowledge":[177],"thanks":[179],"some":[181],"new":[182],"tools":[184],"retrieve":[186],"$\\{\\mathcal":[190],"{n}}\\}_{\\mathbfit":[192],"which":[194,216,321],"expected":[196],"matrix-valued":[200],"bivariate":[201],"trigonometric":[202],"polynomial.":[203],"particular,":[205],"there":[206],"nice":[209],"elegant":[210],"connection":[211],"continuous":[214,283],"operator,":[215],"has":[217,294],"an":[218,295],"infinite":[219,278],"dimensional":[220,279],"kernel,":[221],"fact":[224],"dyad":[229],"having":[230],"one":[231,235,241,251],"eigenvalue":[232],"like":[233],"IgA":[238],"Laplacian,":[239],"identically":[242],"zero":[243,269],"eigenvalue;":[244],"consequence,":[247],"prove":[249],"half":[252],"{n}}$,":[259],"very":[266],"close":[267],"represents":[272],"counterpart":[275],"kernel":[280],"operator.":[284],"latter":[287],"information,":[288],"showing":[289],"considered":[292],"problem":[293],"ill-posed":[296],"nature,":[297],"are":[299],"able":[300],"give":[302],"detailed":[304],"analysis":[306],"corresponding":[316],"zero-order":[317],"term":[318],"stabilized":[319],"matrices,":[320],"fully":[323],"confirmed":[324],"by":[325,330],"several":[326],"numerical":[327,368],"evidences.":[328],"Finally,":[329],"taking":[331],"into":[332],"consideration":[333],"GLT":[335],"results,":[343],"furnish":[345],"indications":[346],"convergence":[349],"known":[352],"iterative":[353,364],"solvers":[354],"suggest":[357],"further":[359],"stabilization":[360],"technique":[361],"proper":[363],"procedures":[365],"solution":[369],"involved":[372],"systems.":[374]},"counts_by_year":[{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}
