{"id":"https://openalex.org/W3019022790","doi":"https://doi.org/10.1137/18m120035x","title":"An Embedded Corrector Problem for Homogenization. Part I: Theory","display_name":"An Embedded Corrector Problem for Homogenization. Part I: Theory","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3019022790","doi":"https://doi.org/10.1137/18m120035x","mag":"3019022790"},"language":"en","primary_location":{"id":"doi:10.1137/18m120035x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m120035x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},"type":"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/A5107049443","display_name":"\u00c9ric Canc\u00e8s","orcid":"https://orcid.org/0000-0002-8876-8254"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Eric Canc\u00e8s","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","MATHERIALS - MATHematics for MatERIALS (France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]},{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043821615","display_name":"Virginie Ehrlacher","orcid":"https://orcid.org/0000-0001-6540-4784"},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Virginie Ehrlacher","raw_affiliation_strings":["MATHERIALS - MATHematics for MatERIALS (France)","CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]},{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108100026","display_name":"Fr\u00e9d\u00e9ric Legoll","orcid":"https://orcid.org/0000-0002-2334-5058"},"institutions":[{"id":"https://openalex.org/I142631665","display_name":"\u00c9cole nationale des ponts et chauss\u00e9es","ror":"https://ror.org/02nwvxz07","country_code":"FR","type":"education","lineage":["https://openalex.org/I142631665","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210115903","display_name":"Laboratoire Navier","ror":"https://ror.org/029hkd614","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210095849","https://openalex.org/I4210115903","https://openalex.org/I4210145102","https://openalex.org/I4210154111"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Fr\u00e9d\u00e9ric Legoll","raw_affiliation_strings":["MATHERIALS - MATHematics for MatERIALS (France)","NAVIER UMR 8205 - Laboratoire Navier (\u00c9cole des Ponts ParisTech, 6-8 avenue Blaise Pascal, 77455 Champs-sur-Marne - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"MATHERIALS - MATHematics for MatERIALS (France)","institution_ids":[]},{"raw_affiliation_string":"NAVIER UMR 8205 - Laboratoire Navier (\u00c9cole des Ponts ParisTech, 6-8 avenue Blaise Pascal, 77455 Champs-sur-Marne - France)","institution_ids":["https://openalex.org/I142631665","https://openalex.org/I4210115903"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5036554395","display_name":"Benjamin Stamm","orcid":"https://orcid.org/0000-0003-3375-483X"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Benjamin Stamm","raw_affiliation_strings":["RWTH - Rheinisch-Westf\u00e4lische Technische Hochschule Aachen University (RWTH Aachen\r\n\r\nTemplergraben 55\r\n52062 Aachen (Hausanschrift)\r\n52056 Aachen (Postanschrift) - Germany)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RWTH - Rheinisch-Westf\u00e4lische Technische Hochschule Aachen University (RWTH Aachen\r\n\r\nTemplergraben 55\r\n52062 Aachen (Hausanschrift)\r\n52056 Aachen (Postanschrift) - Germany)","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089028110","display_name":"Shuyang Xiang","orcid":null},"institutions":[{"id":"https://openalex.org/I4210128309","display_name":"CERMICS","ror":"https://ror.org/03wct8w46","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I142631665","https://openalex.org/I4210128309","https://openalex.org/I4210145102"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Shuyang Xiang","raw_affiliation_strings":["CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CERMICS - Centre d'Enseignement et de Recherche en Math\u00e9matiques et Calcul Scientifique (6 et 8 avenue Blaise Pascal Cit\u00e9 Descartes - Champs sur Marne 77455 Marne la Vall\u00e9e Cedex 2 - France)","institution_ids":["https://openalex.org/I4210128309"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7286,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.76355582,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"18","issue":"3","first_page":"1179","last_page":"1209"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":1.0,"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":1.0,"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":0.9998999834060669,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/homogenization","display_name":"Homogenization (climate)","score":0.9267343282699585},{"id":"https://openalex.org/keywords/homogeneous","display_name":"Homogeneous","score":0.6135294437408447},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5921021699905396},{"id":"https://openalex.org/keywords/predictor\u2013corrector-method","display_name":"Predictor\u2013corrector method","score":0.527504563331604},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5172474980354309},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4413769543170929},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4175824820995331},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3519274592399597},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.08152410387992859}],"concepts":[{"id":"https://openalex.org/C2778722038","wikidata":"https://www.wikidata.org/wiki/Q17030643","display_name":"Homogenization (climate)","level":3,"score":0.9267343282699585},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.6135294437408447},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5921021699905396},{"id":"https://openalex.org/C157977623","wikidata":"https://www.wikidata.org/wiki/Q2650267","display_name":"Predictor\u2013corrector method","level":2,"score":0.527504563331604},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5172474980354309},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4413769543170929},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4175824820995331},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3519274592399597},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.08152410387992859},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C130217890","wikidata":"https://www.wikidata.org/wiki/Q47041","display_name":"Biodiversity","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/18m120035x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m120035x","pdf_url":null,"source":{"id":"https://openalex.org/S4357572","display_name":"Multiscale Modeling and Simulation","issn_l":"1540-3459","issn":["1540-3459","1540-3467"],"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":"Multiscale Modeling &amp; Simulation","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01840993v1","is_oa":false,"landing_page_url":"https://hal.science/hal-01840993","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Multiscale Modeling and Simulation: A SIAM Interdisciplinary Journal, 2020, 18 (3), pp.1179-1209. &#x27E8;10.1137/18M120035X&#x27E9;","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3234747200","display_name":null,"funder_award_id":"N00014-15-1-2777","funder_id":"https://openalex.org/F4320338298","funder_display_name":"Office of Naval Research Global"},{"id":"https://openalex.org/G4793870349","display_name":null,"funder_award_id":"ANR-11-LABX-0022","funder_id":"https://openalex.org/F4320320883","funder_display_name":"Agence Nationale de la Recherche"},{"id":"https://openalex.org/G8062333962","display_name":null,"funder_award_id":"FA9550-17-1-0294","funder_id":"https://openalex.org/F4320338503","funder_display_name":"European Office of Aerospace Research and Development"},{"id":"https://openalex.org/G8101003307","display_name":null,"funder_award_id":"57317909","funder_id":"https://openalex.org/F4320321114","funder_display_name":"Bundesministerium f\u00fcr Bildung und Forschung"}],"funders":[{"id":"https://openalex.org/F4320320875","display_name":"Deutscher Akademischer Austauschdienst","ror":"https://ror.org/039djdh30"},{"id":"https://openalex.org/F4320320883","display_name":"Agence Nationale de la Recherche","ror":"https://ror.org/00rbzpz17"},{"id":"https://openalex.org/F4320321114","display_name":"Bundesministerium f\u00fcr Bildung und Forschung","ror":"https://ror.org/04pz7b180"},{"id":"https://openalex.org/F4320338298","display_name":"Office of Naval Research Global","ror":"https://ror.org/00rk2pe57"},{"id":"https://openalex.org/F4320338503","display_name":"European Office of Aerospace Research and Development","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W1537785329","https://openalex.org/W1989589317","https://openalex.org/W1993130704","https://openalex.org/W2004534757","https://openalex.org/W2008588630","https://openalex.org/W2021211036","https://openalex.org/W2040550846","https://openalex.org/W2052947161","https://openalex.org/W2072176741","https://openalex.org/W2072954894","https://openalex.org/W2083715576","https://openalex.org/W2092871579","https://openalex.org/W2096105657","https://openalex.org/W2118745850","https://openalex.org/W2125887644","https://openalex.org/W2165084730","https://openalex.org/W2535698354","https://openalex.org/W2962899060","https://openalex.org/W2963875859","https://openalex.org/W2964167860","https://openalex.org/W3000342366","https://openalex.org/W3105352918","https://openalex.org/W3194996585"],"related_works":["https://openalex.org/W2104620528","https://openalex.org/W140119233","https://openalex.org/W2757910772","https://openalex.org/W4249473811","https://openalex.org/W2394422079","https://openalex.org/W2025913943","https://openalex.org/W166351930","https://openalex.org/W2312674383","https://openalex.org/W4318052229","https://openalex.org/W2884768316"],"abstract_inverted_index":{"This":[0],"article":[1,122],"is":[2,14,93,116,137],"the":[3,10,15,27,39,42,58,89,120,140,150,156,164,168,171,174],"first":[4],"part":[5],"of":[6,12,21,29,41,60,88,142,167,173],"a":[7,84,96,133],"two-fold":[8],"study,":[9],"objective":[11],"which":[13],"theoretical":[16],"analysis":[17],"and":[18],"numerical":[19],"investigation":[20],"new":[22,36],"approximate":[23],"corrector":[24,63,114],"problems":[25,47,115,144],"in":[26,69,95,119],"context":[28],"stochastic":[30],"homogenization.":[31],"We":[32],"present":[33,151],"here":[34],"three":[35,157],"alternatives":[37],"for":[38,45,110,139,145],"approximation":[40],"homogenized":[43,165],"matrix":[44,166],"diffusion":[46,101],"with":[48],"highly":[49,90],"oscillatory":[50,91],"coefficients.":[51],"These":[52],"different":[53,158],"approximations":[54,159],"all":[55],"rely":[56],"on":[57],"use":[59],"an":[61],"embedded":[62,94,113,175],"problem":[64],"(that":[65],"we":[66,153,160],"previously":[67],"introduced":[68],"[Canc\u00e8s":[70,123],"et":[71,124],"al.,":[72,125],"C.":[73],"R.":[74],"Math.":[75],"Acad.":[76],"Sci.":[77],"Paris,":[78],"353":[79],"(2015),":[80],"pp.":[81],"801--806]),":[82],"where":[83,132],"finite-size":[85],"domain":[86,176],"made":[87,117],"material":[92],"homogeneous":[97],"infinite":[98],"medium":[99,169],"whose":[100],"coefficients":[102],"have":[103],"to":[104,163,178],"be":[105],"appropriately":[106],"determined.":[107],"The":[108],"motivation":[109],"considering":[111],"such":[112,143],"clear":[118],"companion":[121],"J.":[126],"Comput.":[127],"Phys.,":[128],"407":[129],"(2020),":[130],"109254],":[131],"very":[134],"efficient":[135],"algorithm":[136],"presented":[138],"resolution":[141],"particular":[146],"heterogeneous":[147],"materials.":[148],"In":[149],"article,":[152],"prove":[154],"that":[155],"introduce":[161],"converge":[162],"when":[170],"size":[172],"goes":[177],"infinity.":[179]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":4},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-20T22:02:38.213706","created_date":"2020-05-01T00:00:00"}
