{"id":"https://openalex.org/W3158295436","doi":"https://doi.org/10.1002/nla.2388","title":"Independence of placement for local Fourier analysis","display_name":"Independence of placement for local Fourier analysis","publication_year":2021,"publication_date":"2021-05-04","ids":{"openalex":"https://openalex.org/W3158295436","doi":"https://doi.org/10.1002/nla.2388","mag":"3158295436"},"language":"en","primary_location":{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2388","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false},"type":"article","type_crossref":"journal-article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5082790650","display_name":"Yunhui He","orcid":"https://orcid.org/0000-0003-3476-2487"},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"Yunhui He","raw_affiliation_strings":["Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada","institution_ids":["https://openalex.org/I151746483"]}]}],"institution_assertions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5082790650"],"corresponding_institution_ids":["https://openalex.org/I151746483"],"apc_list":{"value":4430,"currency":"USD","value_usd":4430,"provenance":"doaj"},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":0,"max":57},"biblio":{"volume":"28","issue":"6","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998,"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":0.9998,"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":0.9995,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9992,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.5120959},{"id":"https://openalex.org/keywords/representation","display_name":"Representation","score":0.453039},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.4328955},{"id":"https://openalex.org/keywords/transfer-operator","display_name":"Transfer operator","score":0.41869298}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6571096},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5621946},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.5120959},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.47590408},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.453039},{"id":"https://openalex.org/C208081375","wikidata":"https://www.wikidata.org/wiki/Q274502","display_name":"Degrees of freedom (physics and chemistry)","level":2,"score":0.43858725},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.4328955},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.42938125},{"id":"https://openalex.org/C2777952282","wikidata":"https://www.wikidata.org/wiki/Q3354606","display_name":"Transfer operator","level":2,"score":0.41869298},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4186417},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.33499682},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3234381},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.17473844},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09168303},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"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/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"is_oa":false,"landing_page_url":"https://doi.org/10.1002/nla.2388","pdf_url":null,"source":{"id":"https://openalex.org/S60324941","display_name":"Numerical Linear Algebra with Applications","issn_l":"1070-5325","issn":["1070-5325","1099-1506"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Peace, justice, and strong institutions","id":"https://metadata.un.org/sdg/16","score":0.81}],"grants":[],"datasets":[],"versions":[],"referenced_works_count":26,"referenced_works":["https://openalex.org/W1796252776","https://openalex.org/W1984714207","https://openalex.org/W2023978888","https://openalex.org/W2070511701","https://openalex.org/W2076951688","https://openalex.org/W2080159996","https://openalex.org/W2116982324","https://openalex.org/W2117746278","https://openalex.org/W2159737710","https://openalex.org/W2163304326","https://openalex.org/W2328206302","https://openalex.org/W2762583146","https://openalex.org/W2805917124","https://openalex.org/W2806424598","https://openalex.org/W2906650913","https://openalex.org/W2917960281","https://openalex.org/W2963023415","https://openalex.org/W2963027558","https://openalex.org/W2963585082","https://openalex.org/W2982549622","https://openalex.org/W2985772874","https://openalex.org/W3003667217","https://openalex.org/W3006898615","https://openalex.org/W3025497146","https://openalex.org/W3036973740","https://openalex.org/W3149667697"],"related_works":["https://openalex.org/W2377164732","https://openalex.org/W2295047789","https://openalex.org/W2086954813","https://openalex.org/W2072647882","https://openalex.org/W2047144947","https://openalex.org/W2021837978","https://openalex.org/W2014442497","https://openalex.org/W2001529763","https://openalex.org/W1994717757","https://openalex.org/W1551381703"],"abstract_inverted_index":{"Abstract":[0],"Local":[1],"Fourier":[2],"analysis":[3],"(LFA)":[4],"serves":[5,96],"a":[6,98,109,121,146],"prominent":[7],"role":[8],"in":[9,124,145],"the":[10,13,27,53,62,72,81,84,91,113,127,130,140,153,156,161,170,173],"prediction":[11],"of":[12,16,21,29,34,52,71,74,76,83,126,129,139,155,172,175,180],"convergence":[14],"factor":[15],"multigrid":[17],"methods":[18],"for":[19,31,65,108,160,177,186],"discretizations":[20,33,181],"PDEs.":[22],"However,":[23],"few":[24],"discussions":[25],"about":[26],"implementation":[28,174],"LFA":[30,50,63,92,106,176],"complicated":[32],"PDEs":[35,68],"exist,":[36],"such":[37],"as":[38,43,97],"higher":[39,187],"order":[40,188],"finite":[41],"elements,":[42],"staggered":[44],"meshes":[45],"could":[46],"lead":[47],"to":[48,151,169],"complex":[49],"representations":[51,107],"grid\u2010transfer":[54,162],"operator.":[55],"In":[56],"this":[57],"work,":[58],"we":[59,119,136],"prove":[60],"that":[61],"representation":[64,123,166],"d":[66],"\u2010dimensional":[67],"is":[69],"independent":[70],"placement":[73],"degrees":[75],"freedom":[77],"(DoFs).":[78],"Intuitively":[79],"speaking,":[80],"seeding":[82],"unknowns":[85],"has":[86],"no":[87],"direct":[88],"effect":[89],"on":[90],"presentation,":[93],"instead,":[94],"it":[95],"unitary":[99],"transformation":[100],"between":[101],"different":[102,105,178,183],"representations.":[103],"Thus,":[104],"given":[110],"PDE":[111],"have":[112],"same":[114],"spectrum":[115],"and":[116,148,182],"norm.":[117],"Furthermore,":[118],"provide":[120],"uniform":[122],"terms":[125],"location":[128],"unknowns,":[131],"named":[132],"simple":[133,147,165],"representation,":[134],"where":[135],"allocate":[137],"all":[138],"DoFs":[141],"at":[142],"nodes,":[143],"resulting":[144],"unified":[149],"way":[150],"compute":[152],"symbols":[154],"discrete":[157],"operators,":[158],"especially":[159,185],"operators.":[163],"This":[164],"can":[167],"contribute":[168],"generalization":[171],"types":[179],"problems,":[184],"discretization":[189],"methods.":[190]},"cited_by_api_url":"https://api.openalex.org/works?filter=cites:W3158295436","counts_by_year":[],"updated_date":"2024-12-13T07:44:52.531011","created_date":"2021-05-10"}