{"id":"https://openalex.org/W2080159996","doi":"https://doi.org/10.1137/070679119","title":"Local Fourier Analysis of Multigrid for the Curl-Curl Equation","display_name":"Local Fourier Analysis of Multigrid for the Curl-Curl Equation","publication_year":2008,"publication_date":"2008-01-01","ids":{"openalex":"https://openalex.org/W2080159996","doi":"https://doi.org/10.1137/070679119","mag":"2080159996"},"language":"en","primary_location":{"id":"doi:10.1137/070679119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679119","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":"http://eprints.uwe.ac.uk/12792/","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5013093910","display_name":"Tim J. Boonen","orcid":"https://orcid.org/0000-0001-9186-416X"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Tim Boonen","raw_affiliation_strings":["Tim.Boonen@cs.kuleuven.be and Stefan.Vandewalle@cs.kuleuven.be#TAB#"],"affiliations":[{"raw_affiliation_string":"Tim.Boonen@cs.kuleuven.be and Stefan.Vandewalle@cs.kuleuven.be#TAB#","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062264386","display_name":"Jan Van lent","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jan Van lent","raw_affiliation_strings":["j.van.lent@maths.bath.ac.uk#TAB#"],"affiliations":[{"raw_affiliation_string":"j.van.lent@maths.bath.ac.uk#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Vandewalle","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5013093910"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.292,"has_fulltext":false,"cited_by_count":29,"citation_normalized_percentile":{"value":0.88348256,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"30","issue":"4","first_page":"1730","last_page":"1755"},"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":0.9994999766349792,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/curl","display_name":"Curl (programming language)","score":0.9325679540634155},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.8096861839294434},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7177661657333374},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.5579302310943604},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5114237666130066},{"id":"https://openalex.org/keywords/laplace-operator","display_name":"Laplace operator","score":0.5067628026008606},{"id":"https://openalex.org/keywords/fourier-analysis","display_name":"Fourier analysis","score":0.4141748547554016},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3942943513393402},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2630126178264618},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14184173941612244}],"concepts":[{"id":"https://openalex.org/C147663694","wikidata":"https://www.wikidata.org/wiki/Q1144631","display_name":"Curl (programming language)","level":2,"score":0.9325679540634155},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.8096861839294434},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7177661657333374},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.5579302310943604},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5114237666130066},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.5067628026008606},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.4141748547554016},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3942943513393402},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2630126178264618},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14184173941612244},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1137/070679119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/070679119","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:eprints.uwe.ac.uk:12792","is_oa":true,"landing_page_url":"http://eprints.uwe.ac.uk/12792/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401464","display_name":"UWE Research Repository (UWE Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I178535277","host_organization_name":"University of the West of England","host_organization_lineage":["https://openalex.org/I178535277"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/157087","is_oa":false,"landing_page_url":"https://lirias.kuleuven.be/bitstream/123456789/157087/2/067911.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"SIAM Journal on Scientific Computing, vol. 30 (4), Art.No. 4, (1730-1755)","raw_type":"info:eu-repo/semantics/publishedVersion"}],"best_oa_location":{"id":"pmh:oai:eprints.uwe.ac.uk:12792","is_oa":true,"landing_page_url":"http://eprints.uwe.ac.uk/12792/","pdf_url":null,"source":{"id":"https://openalex.org/S4306401464","display_name":"UWE Research Repository (UWE Bristol)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I178535277","host_organization_name":"University of the West of England","host_organization_lineage":["https://openalex.org/I178535277"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W634415007","https://openalex.org/W1572639095","https://openalex.org/W1582734821","https://openalex.org/W1985506636","https://openalex.org/W1987419872","https://openalex.org/W1994183034","https://openalex.org/W2006895912","https://openalex.org/W2008438865","https://openalex.org/W2009860245","https://openalex.org/W2028703925","https://openalex.org/W2130970049","https://openalex.org/W2135615508","https://openalex.org/W2148147555","https://openalex.org/W2151317657"],"related_works":["https://openalex.org/W2102602799","https://openalex.org/W2363841656","https://openalex.org/W2999785843","https://openalex.org/W2180012347","https://openalex.org/W3006898615","https://openalex.org/W3003667217","https://openalex.org/W2357962721","https://openalex.org/W4289305094","https://openalex.org/W2898992040","https://openalex.org/W2181789249"],"abstract_inverted_index":{"We":[0,129],"present":[1],"a":[2],"local":[3],"Fourier":[4,56,91,103],"analysis":[5],"of":[6,14,45,48,72,80,110,118,154],"multigrid":[7,82],"methods":[8],"for":[9,58,126],"the":[10,18,25,43,49,55,69,73,77,81,87,107,111,116,119,123,132],"two-dimensional":[11,46],"curl-curl":[12,51,120],"formulation":[13],"Maxwell's":[15],"equations.":[16],"Both":[17],"hybrid":[19],"smoother":[20,28],"proposed":[21,29],"by":[22,30,53],"Hiptmair":[23],"and":[24,33,76,115,122,143,148,150],"overlapping":[26],"block":[27],"Arnold,":[31],"Falk,":[32],"Winther":[34],"are":[35],"considered.":[36],"The":[37],"key":[38],"to":[39,67,99,141,151],"our":[40],"approach":[41,133],"is":[42,65],"identification":[44],"eigenspaces":[47],"discrete":[50],"problem":[52],"decoupling":[54],"modes":[57],"edges":[59],"with":[60],"different":[61],"orientations.":[62],"This":[63,93],"procedure":[64],"used":[66,134],"quantify":[68],"smoothing":[70],"properties":[71,98,109],"considered":[74],"smoothers":[75],"convergence":[78],"behavior":[79],"methods.":[83],"Additionally,":[84],"we":[85],"identify":[86],"Helmholtz":[88],"splitting":[89],"in":[90,102,135,146],"space.":[92],"allows":[94],"several":[95],"well":[96],"known":[97],"be":[100,139],"recovered":[101],"space,":[104],"such":[105],"as":[106],"commutation":[108],"classical":[112],"N\u00e9d\u00e9lec":[113],"prolongator":[114],"equivalence":[117],"operator":[121],"vector":[124],"Laplacian":[125],"divergence-free":[127],"vectors.":[128],"show":[130],"how":[131],"this":[136],"paper":[137],"can":[138],"generalized":[140],"two-":[142],"three-dimensional":[144],"problems":[145],"H(curl)":[147],"H(div)":[149],"other":[152],"types":[153],"regular":[155],"meshes.":[156]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}