{"id":"https://openalex.org/W3211939599","doi":"https://doi.org/10.1137/21m1460016","title":"An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition","display_name":"An Online Efficient Two-Scale Reduced Basis Approach for the Localized Orthogonal Decomposition","publication_year":2023,"publication_date":"2023-07-07","ids":{"openalex":"https://openalex.org/W3211939599","doi":"https://doi.org/10.1137/21m1460016","mag":"3211939599"},"language":"en","primary_location":{"id":"doi:10.1137/21m1460016","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1460016","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":["arxiv","crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2111.08643","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5065568767","display_name":"Tim Keil","orcid":null},"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":true,"raw_author_name":"Tim Keil","raw_affiliation_strings":["Mathematics M\u00fcnster, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Einsteinstr 62, D-48149 M\u00fcnster, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematics M\u00fcnster, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Einsteinstr 62, D-48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024767834","display_name":"Stephan Rave","orcid":"https://orcid.org/0000-0003-0439-7212"},"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":"Stephan Rave","raw_affiliation_strings":["Mathematics M\u00fcnster, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Einsteinstr 62, D-48149 M\u00fcnster, Germany"],"raw_orcid":"https://orcid.org/0000-0003-0439-7212","affiliations":[{"raw_affiliation_string":"Mathematics M\u00fcnster, Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster, Einsteinstr 62, D-48149 M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5065568767"],"corresponding_institution_ids":["https://openalex.org/I22465464"],"apc_list":null,"apc_paid":null,"fwci":0.8282,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.64456497,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"45","issue":"4","first_page":"A1491","last_page":"A1518"},"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9991000294685364,"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":0.7219473123550415},{"id":"https://openalex.org/keywords/scale","display_name":"Scale (ratio)","score":0.568023681640625},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.5351278185844421},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.46445605158805847},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4113209843635559},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3740432858467102},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.18788006901741028}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7219473123550415},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.568023681640625},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.5351278185844421},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.46445605158805847},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4113209843635559},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3740432858467102},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.18788006901741028},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/21m1460016","is_oa":false,"landing_page_url":"https://doi.org/10.1137/21m1460016","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:arXiv.org:2111.08643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.08643","pdf_url":"https://arxiv.org/pdf/2111.08643","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2111.08643","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2111.08643","pdf_url":"https://arxiv.org/pdf/2111.08643","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G753995526","display_name":null,"funder_award_id":"EXC 2044 390685587","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8702963141","display_name":null,"funder_award_id":"OH 98/11-1","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":44,"referenced_works":["https://openalex.org/W1699887297","https://openalex.org/W1970934346","https://openalex.org/W1975893464","https://openalex.org/W1980404981","https://openalex.org/W1982739078","https://openalex.org/W2002174431","https://openalex.org/W2026734498","https://openalex.org/W2027239222","https://openalex.org/W2029918260","https://openalex.org/W2039055345","https://openalex.org/W2047591100","https://openalex.org/W2060368109","https://openalex.org/W2078045751","https://openalex.org/W2079799459","https://openalex.org/W2083281683","https://openalex.org/W2091917844","https://openalex.org/W2102835252","https://openalex.org/W2106401617","https://openalex.org/W2108074976","https://openalex.org/W2126028850","https://openalex.org/W2133041109","https://openalex.org/W2151177334","https://openalex.org/W2160242097","https://openalex.org/W2162992695","https://openalex.org/W2230918517","https://openalex.org/W2295099209","https://openalex.org/W2442807308","https://openalex.org/W2558443247","https://openalex.org/W2734721340","https://openalex.org/W2735270253","https://openalex.org/W2761963440","https://openalex.org/W2807389341","https://openalex.org/W2890578718","https://openalex.org/W2915756299","https://openalex.org/W2948206295","https://openalex.org/W2963415932","https://openalex.org/W2965428888","https://openalex.org/W2983397545","https://openalex.org/W3040146274","https://openalex.org/W3100174328","https://openalex.org/W3105714705","https://openalex.org/W3109896535","https://openalex.org/W4205408820","https://openalex.org/W4240395309"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W2989452537","https://openalex.org/W4313731559"],"abstract_inverted_index":{"We":[0],"are":[1,122],"concerned":[2],"with":[3],"employing":[4],"Model":[5],"Order":[6],"Reduction":[7],"(MOR)":[8],"to":[9,63,96],"efficiently":[10],"solve":[11],"parameterized":[12,144],"multiscale":[13,21,25,134,145],"problems":[14,146,175],"using":[15],"the":[16,27,30,34,47,50,54,66,69,72,80,93,102,106,126,129,133,141,160,167,172,177],"Localized":[17],"Orthogonal":[18],"Decomposition":[19],"(LOD)":[20],"method.":[22],"Like":[23],"many":[24],"methods,":[26],"LOD":[28,114],"follows":[29],"idea":[31],"of":[32,49,68,101,128,132,140,143],"separating":[33],"problem":[35],"into":[36,165],"localized":[37],"fine-scale":[38,70,174],"subproblems":[39],"and":[40,154,176],"an":[41,137],"effective":[42],"coarse-scale":[43,179],"system":[44,75],"derived":[45],"from":[46,125],"solutions":[48,142],"local":[51,173],"problems.":[52],"While":[53],"Reduced":[55,112],"Basis":[56,113],"(RB)":[57],"method":[58],"has":[59],"already":[60],"been":[61],"used":[62],"speed":[64,82],"up":[65],"solution":[67],"problems,":[71],"resulting":[73],"coarse":[74,130],"remained":[76],"untouched,":[77],"thus":[78],"limiting":[79],"achievable":[81],"up.":[83],"In":[84],"this":[85,89,110],"work":[86],"we":[87],"address":[88],"issue":[90],"by":[91],"applying":[92],"RB":[94],"methodology":[95],"a":[97,156],"new":[98],"two-scale":[99,108,111],"formulation":[100],"LOD.":[103],"By":[104],"reducing":[105],"entire":[107],"system,":[109],"(TSRBLOD)":[115],"approach,":[116,135],"yields":[117],"reduced":[118],"order":[119],"models":[120],"that":[121],"completely":[123],"independent":[124],"size":[127],"mesh":[131],"allowing":[136],"efficient":[138,155],"approximation":[139,168],"even":[147],"for":[148,170],"very":[149],"large":[150],"domains.":[151],"A":[152],"rigorous":[153],"posteriori":[157],"estimator":[158],"bounds":[159],"model":[161],"reduction":[162],"error,":[163],"taking":[164],"account":[166],"error":[169],"both":[171],"global":[178],"system.":[180]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":3}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}