{"id":"https://openalex.org/W2801412278","doi":"https://doi.org/10.1137/18m1191221","title":"Tensor-based numerical method for stochastic homogenisation","display_name":"Tensor-based numerical method for stochastic homogenisation","publication_year":2018,"publication_date":"2018-05-11","ids":{"openalex":"https://openalex.org/W2801412278","doi":"https://doi.org/10.1137/18m1191221","mag":"2801412278"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:1805.04320","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1805.04320","pdf_url":"https://arxiv.org/pdf/1805.04320","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"},"type":"preprint","indexed_in":["arxiv"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1805.04320","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041055230","display_name":"Q. Ayoul-Guilmard","orcid":"https://orcid.org/0000-0002-5110-4251"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Ayoul-Guilmard, Quentin","raw_affiliation_strings":["Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5031143836","display_name":"Anthony Nouy","orcid":"https://orcid.org/0000-0002-2149-2986"},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I4210153365","display_name":"Laboratoire de Math\u00e9matiques Jean Leray","ror":"https://ror.org/04g1hjn96","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I4210141950","https://openalex.org/I4210153365","https://openalex.org/I97188460"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Nouy, Anthony","raw_affiliation_strings":["\u00c9cole Centrale de Nantes","M\u00e9thodes d'Analyse Stochastique des Codes et Traitements Num\u00e9riques","Laboratoire de Math\u00e9matiques Jean Leray"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Centrale de Nantes","institution_ids":["https://openalex.org/I100445878"]},{"raw_affiliation_string":"M\u00e9thodes d'Analyse Stochastique des Codes et Traitements Num\u00e9riques","institution_ids":[]},{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Jean Leray","institution_ids":["https://openalex.org/I4210153365"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087638067","display_name":"Christophe Bin\u00e9truy","orcid":null},"institutions":[{"id":"https://openalex.org/I100445878","display_name":"\u00c9cole Centrale de Nantes","ror":"https://ror.org/03nh7d505","country_code":"FR","type":"education","lineage":["https://openalex.org/I100445878","https://openalex.org/I97188460"]},{"id":"https://openalex.org/I4210115277","display_name":"Ingenierie des Materiaux polymeres","ror":"https://ror.org/02160my55","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210115277","https://openalex.org/I4210128300","https://openalex.org/I4405259976","https://openalex.org/I48430043"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Binetruy, Christophe","raw_affiliation_strings":["\u00c9cole Centrale de Nantes","D\u00e9partement Technologie des Polym\u00e8res et Composites & Ing\u00e9nierie M\u00e9canique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"\u00c9cole Centrale de Nantes","institution_ids":["https://openalex.org/I100445878"]},{"raw_affiliation_string":"D\u00e9partement Technologie des Polym\u00e8res et Composites & Ing\u00e9nierie M\u00e9canique","institution_ids":["https://openalex.org/I4210115277"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"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/T11558","display_name":"Composite Material Mechanics","score":0.9843000173568726,"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/tensor","display_name":"Tensor (intrinsic definition)","score":0.5160255432128906},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4095796048641205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3987146019935608},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3641868829727173},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.21376430988311768}],"concepts":[{"id":"https://openalex.org/C155281189","wikidata":"https://www.wikidata.org/wiki/Q3518150","display_name":"Tensor (intrinsic definition)","level":2,"score":0.5160255432128906},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4095796048641205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3987146019935608},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3641868829727173},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.21376430988311768}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:1805.04320","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1805.04320","pdf_url":"https://arxiv.org/pdf/1805.04320","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:1805.04320","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1805.04320","pdf_url":"https://arxiv.org/pdf/1805.04320","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/G3597637701","display_name":"Centre de Math\u00e9matiques Henri Lebesgue : fondements, interactions, applications et Formation","funder_award_id":"ANR-11-LABX-0020","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"}],"funders":[{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320323931","display_name":"Centre Technique des Industries M\u00e9caniques","ror":"https://ror.org/00c051916"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":1,"referenced_works":["https://openalex.org/W410560092"],"related_works":["https://openalex.org/W2748952813","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644"],"abstract_inverted_index":{"This":[0],"paper":[1],"addresses":[2],"the":[3,24,64,67,75,84,131],"complexity":[4],"reduction":[5,38,94,113,136],"of":[6,9,12,23,47,66,77,86,95,133],"stochastic":[7,126],"homogenisation":[8,127],"a":[10,16,29,59,96,105,117,121],"class":[11],"random":[13],"materials":[14,49,54,73,141],"for":[15,41,53,62,72,92,128],"stationary":[17],"diffusion":[18],"equation.":[19],"A":[20],"cost-efficient":[21],"approximation":[22,85],"correctors":[25],"is":[26,114],"built":[27],"using":[28],"method":[30,68],"designed":[31],"to":[32,82],"exploit":[33],"quasi-periodicity.":[34],"Accuracy":[35],"and":[36,99,130],"cost":[37,112],"are":[39,69,138],"investigated":[40],"local":[42],"perturbations":[43],"or":[44,144],"small":[45],"transformations":[46],"periodic":[48],"as":[50,52,89],"well":[51],"with":[55,120],"no":[56],"periodicity":[57,143],"but":[58],"mesoscopic":[60,145],"structure,":[61],"which":[63],"limitations":[65],"shown.":[70],"Finally,":[71],"outside":[74],"scope":[76],"this":[78,134],"method,":[79],"we":[80],"propose":[81],"use":[83],"homogenised":[87],"quantities":[88],"control":[90,122],"variates":[91],"variance":[93,135],"more":[97],"accurate":[98],"costly":[100],"Monte":[101,107],"Carlo":[102,108],"estimator":[103],"(using":[104],"multi-fidelity":[106],"method).":[109],"The":[110],"resulting":[111],"illustrated":[115],"in":[116],"numerical":[118],"experiment":[119],"variate":[123],"from":[124],"weakly":[125],"comparison,":[129],"limits":[132],"technique":[137],"tested":[139],"on":[140],"without":[142],"structure.":[146]},"counts_by_year":[],"updated_date":"2026-07-03T06:15:21.484131","created_date":"2018-05-17T00:00:00"}