{"id":"https://openalex.org/W2897565637","doi":"https://doi.org/10.1137/17m1137164","title":"A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems","display_name":"A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems","publication_year":2018,"publication_date":"2018-01-01","ids":{"openalex":"https://openalex.org/W2897565637","doi":"https://doi.org/10.1137/17m1137164","mag":"2897565637"},"language":"en","primary_location":{"id":"doi:10.1137/17m1137164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1137164","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","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/A5103110814","display_name":"Mejdi Aza\u00efez","orcid":"https://orcid.org/0000-0002-1797-4763"},"institutions":[{"id":"https://openalex.org/I4210097332","display_name":"Institut de M\u00e9canique et d'Ing\u00e9nierie","ror":"https://ror.org/00wrnm709","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210088668","https://openalex.org/I4210095849","https://openalex.org/I4210097332","https://openalex.org/I4210134562","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"M. Aza\u00efez","raw_affiliation_strings":["Institut de M\u00e9canique et d'Ing\u00e9nierie de Bordeaux"],"affiliations":[{"raw_affiliation_string":"Institut de M\u00e9canique et d'Ing\u00e9nierie de Bordeaux","institution_ids":["https://openalex.org/I4210097332"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111586176","display_name":"Faker Ben Belgacem","orcid":null},"institutions":[{"id":"https://openalex.org/I4210155549","display_name":"Laboratoire de Math\u00e9matiques","ror":"https://ror.org/05sd5r855","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I198244214","https://openalex.org/I4210141950","https://openalex.org/I4210155549"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. Ben Belgacem","raw_affiliation_strings":["Laboratoire de Math\u00e9matiques Appliqu\u00e9es de Compi\u00e8gne"],"affiliations":[{"raw_affiliation_string":"Laboratoire de Math\u00e9matiques Appliqu\u00e9es de Compi\u00e8gne","institution_ids":["https://openalex.org/I4210155549"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063248066","display_name":"Juan Casado\u2010D\u00edaz","orcid":"https://orcid.org/0000-0001-5122-7449"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"J. Casado-D\u00edaz","raw_affiliation_strings":["Departamento EDAN & IMUS, Universidad de Sevilla, C/Tarfia, s/n, 41012 Sevilla (Spain)"],"affiliations":[{"raw_affiliation_string":"Departamento EDAN & IMUS, Universidad de Sevilla, C/Tarfia, s/n, 41012 Sevilla (Spain)","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061387427","display_name":"Tom\u00e1s Chac\u00f3n Rebollo","orcid":"https://orcid.org/0000-0002-0784-1174"},"institutions":[{"id":"https://openalex.org/I4210097332","display_name":"Institut de M\u00e9canique et d'Ing\u00e9nierie","ror":"https://ror.org/00wrnm709","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I190752583","https://openalex.org/I190861549","https://openalex.org/I4210088668","https://openalex.org/I4210095849","https://openalex.org/I4210097332","https://openalex.org/I4210134562","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"T. Chac\u00f3n Rebollo","raw_affiliation_strings":["Institut de M\u00e9canique et d'Ing\u00e9nierie de Bordeaux"],"affiliations":[{"raw_affiliation_string":"Institut de M\u00e9canique et d'Ing\u00e9nierie de Bordeaux","institution_ids":["https://openalex.org/I4210097332"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5108780672","display_name":"Fran\u00e7ois Murat","orcid":null},"institutions":[{"id":"https://openalex.org/I4210158291","display_name":"Laboratoire Jacques-Louis Lions","ror":"https://ror.org/04xmteb38","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I204730241","https://openalex.org/I39804081","https://openalex.org/I4210141950","https://openalex.org/I4210158291"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. Murat","raw_affiliation_strings":["Laboratoire Jacques-Louis Lions"],"affiliations":[{"raw_affiliation_string":"Laboratoire Jacques-Louis Lions","institution_ids":["https://openalex.org/I4210158291"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5103110814"],"corresponding_institution_ids":["https://openalex.org/I4210097332"],"apc_list":null,"apc_paid":null,"fwci":0.7968,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.77973239,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"50","issue":"5","first_page":"5426","last_page":"5445"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/1804","display_name":"Statistics, Probability and Uncertainty"},"field":{"id":"https://openalex.org/fields/18","display_name":"Decision Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9994999766349792,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9976000189781189,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.6552702784538269},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.5875222682952881},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5215415954589844},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48706844449043274},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.37924525141716003},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.34517061710357666},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.05921298265457153},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.04339107871055603}],"concepts":[{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.6552702784538269},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.5875222682952881},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5215415954589844},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48706844449043274},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.37924525141716003},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34517061710357666},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.05921298265457153},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.04339107871055603},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/17m1137164","is_oa":false,"landing_page_url":"https://doi.org/10.1137/17m1137164","pdf_url":null,"source":{"id":"https://openalex.org/S74141806","display_name":"SIAM Journal on Mathematical Analysis","issn_l":"0036-1410","issn":["0036-1410","1095-7154"],"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 Mathematical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:idus.us.es:11441/81549","is_oa":false,"landing_page_url":"https://idus.us.es/handle//11441/81549","pdf_url":null,"source":{"id":"https://openalex.org/S4306400333","display_name":"idUS (Universidad de Sevilla)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79238269","host_organization_name":"Universidad de Sevilla","host_organization_lineage":["https://openalex.org/I79238269"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:HAL:hal-01939854v1","is_oa":false,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-01939854","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"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 Mathematical Analysis, 2018, 50 (5), pp.5426-5445. &#x27E8;10.1137/17M1137164&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:HAL:hal-03878565v1","is_oa":false,"landing_page_url":"https://hal.sorbonne-universite.fr/hal-03878565","pdf_url":null,"source":{"id":"https://openalex.org/S4406922276","display_name":"INRIA a CCSD electronic archive server","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ISSN: 0036-1410","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:oskar-bordeaux.fr:20.500.12278/76933","is_oa":false,"landing_page_url":"https://oskar-bordeaux.fr/handle/20.500.12278/76933","pdf_url":null,"source":{"id":"https://openalex.org/S4306402569","display_name":"Oskar-Bordeaux (Universite de Bordeaux)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article de revue"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2295037381","display_name":null,"funder_award_id":"MTM2014-53309-P","funder_id":"https://openalex.org/F4320321595","funder_display_name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras"},{"id":"https://openalex.org/G3161401281","display_name":null,"funder_award_id":"Joint program 51661135011 - PHASEFIELD","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8960730849","display_name":null,"funder_award_id":"Joint program 51661135011 - PHASEFIELD","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/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320321595","display_name":"Federaci\u00f3n Espa\u00f1ola de Enfermedades Raras","ror":"https://ror.org/0348bpk17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W1975698444","https://openalex.org/W1989793592","https://openalex.org/W1989951672","https://openalex.org/W2003455389","https://openalex.org/W2007170193","https://openalex.org/W2034801304","https://openalex.org/W2057577185","https://openalex.org/W2071128523","https://openalex.org/W2079775126","https://openalex.org/W2092189481","https://openalex.org/W2094085947","https://openalex.org/W2112823474","https://openalex.org/W2130125952","https://openalex.org/W2149384201","https://openalex.org/W2294798173","https://openalex.org/W2303196115","https://openalex.org/W2317612853","https://openalex.org/W2963858059"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2051487156","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2600246793"],"abstract_inverted_index":{"We":[0,86,125],"introduce":[1],"a":[2,88,93],"new":[3],"algorithm":[4,142],"of":[5,25,29,70,95,151],"proper":[6,72],"generalized":[7],"decomposition":[8,74],"(PGD)":[9],"for":[10,131],"parametric":[11,41,122,134],"symmetric":[12],"elliptic":[13,46,123],"partial":[14,112],"differential":[15],"equations.":[16],"For":[17],"any":[18],"given":[19],"dimension,":[20],"we":[21,108],"prove":[22,109],"the":[23,36,39,45,48,51,55,60,66,71,82,104,111,116,120,128,132,140,149,153,159,164],"existence":[24],"an":[26],"optimal":[27,100,165],"subspace":[28],"at":[30],"most":[31],"that":[32,78,110,127,162],"dimension":[33],"which":[34],"realizes":[35],"best":[37,67],"approximation---in":[38],"mean":[40,121],"norm":[42,83],"associated":[43],"to":[44,65,91,115,139],"operator---of":[47],"error":[49],"between":[50],"exact":[52],"solution":[53,57,118],"and":[54,107],"Galerkin":[56],"calculated":[58],"on":[59,98],"subspace.":[61],"This":[62,147],"is":[63,84,136],"analogous":[64],"approximation":[68],"property":[69],"orthogonal":[73],"(POD)":[75],"subspaces,":[76,101],"except":[77],"in":[79,103,119,144],"our":[80],"case":[81],"parameter-dependent.":[85],"apply":[87],"deflation":[89,141],"technique":[90],"build":[92],"series":[94],"approximating":[96],"solutions":[97],"finite-dimensional":[99],"directly":[102,157],"online":[105],"step,":[106],"sums":[113],"converge":[114],"continuous":[117],"norm.":[124],"show":[126],"standard":[129],"PGD":[130,154],"considered":[133],"problem":[135],"strongly":[137],"related":[138],"introduced":[143],"this":[145],"paper.":[146],"opens":[148],"possibility":[150],"computing":[152],"expansion":[155],"by":[156],"solving":[158],"optimization":[160],"problems":[161],"yield":[163],"subspaces.":[166]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2019,"cited_by_count":3}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
