{"id":"https://openalex.org/W2105425058","doi":"https://doi.org/10.1137/120894725","title":"Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs","display_name":"Multilevel Monte Carlo Methods for Stochastic Elliptic Multiscale PDEs","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2105425058","doi":"https://doi.org/10.1137/120894725","mag":"2105425058"},"language":"en","primary_location":{"id":"doi:10.1137/120894725","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120894725","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 & Simulation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/182185","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066396148","display_name":"Assyr Abdulle","orcid":"https://orcid.org/0000-0002-5687-9742"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Assyr Abdulle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112275965","display_name":"Andrea Barth","orcid":"https://orcid.org/0000-0003-1642-3625"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Andrea Barth","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5110448103","display_name":"Christoph Schwab","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Christoph Schwab","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.5664,"has_fulltext":false,"cited_by_count":40,"citation_normalized_percentile":{"value":0.93138731,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"4","first_page":"1033","last_page":"1070"},"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":0.9997000098228455,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9994999766349792,"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/monte-carlo-method","display_name":"Monte Carlo method","score":0.8031669855117798},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7720504999160767},{"id":"https://openalex.org/keywords/mixed-finite-element-method","display_name":"Mixed finite element method","score":0.5829012393951416},{"id":"https://openalex.org/keywords/smoothed-finite-element-method","display_name":"Smoothed finite element method","score":0.5676529407501221},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.5338726043701172},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.5284794569015503},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4922257959842682},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4919428527355194},{"id":"https://openalex.org/keywords/monte-carlo-molecular-modeling","display_name":"Monte Carlo molecular modeling","score":0.4741363227367401},{"id":"https://openalex.org/keywords/dynamic-monte-carlo-method","display_name":"Dynamic Monte Carlo method","score":0.4716326892375946},{"id":"https://openalex.org/keywords/extended-finite-element-method","display_name":"Extended finite element method","score":0.47038283944129944},{"id":"https://openalex.org/keywords/quantum-monte-carlo","display_name":"Quantum Monte Carlo","score":0.4526195824146271},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4518912434577942},{"id":"https://openalex.org/keywords/hp-fem","display_name":"hp-FEM","score":0.4450485110282898},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.4174303412437439},{"id":"https://openalex.org/keywords/finite-element-limit-analysis","display_name":"Finite element limit analysis","score":0.3688673973083496},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3280341923236847},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.28439080715179443},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.2105427086353302},{"id":"https://openalex.org/keywords/boundary-knot-method","display_name":"Boundary knot method","score":0.1636238992214203},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06218290328979492}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.8031669855117798},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7720504999160767},{"id":"https://openalex.org/C144468803","wikidata":"https://www.wikidata.org/wiki/Q16965966","display_name":"Mixed finite element method","level":3,"score":0.5829012393951416},{"id":"https://openalex.org/C177605945","wikidata":"https://www.wikidata.org/wiki/Q11007230","display_name":"Smoothed finite element method","level":5,"score":0.5676529407501221},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.5338726043701172},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.5284794569015503},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4922257959842682},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4919428527355194},{"id":"https://openalex.org/C37669827","wikidata":"https://www.wikidata.org/wiki/Q6904703","display_name":"Monte Carlo molecular modeling","level":4,"score":0.4741363227367401},{"id":"https://openalex.org/C122592724","wikidata":"https://www.wikidata.org/wiki/Q3855635","display_name":"Dynamic Monte Carlo method","level":3,"score":0.4716326892375946},{"id":"https://openalex.org/C24810621","wikidata":"https://www.wikidata.org/wiki/Q3333647","display_name":"Extended finite element method","level":3,"score":0.47038283944129944},{"id":"https://openalex.org/C16016025","wikidata":"https://www.wikidata.org/wiki/Q3861408","display_name":"Quantum Monte Carlo","level":3,"score":0.4526195824146271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4518912434577942},{"id":"https://openalex.org/C4349628","wikidata":"https://www.wikidata.org/wiki/Q17027720","display_name":"hp-FEM","level":5,"score":0.4450485110282898},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.4174303412437439},{"id":"https://openalex.org/C93949632","wikidata":"https://www.wikidata.org/wiki/Q5450392","display_name":"Finite element limit analysis","level":4,"score":0.3688673973083496},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3280341923236847},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.28439080715179443},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.2105427086353302},{"id":"https://openalex.org/C52890695","wikidata":"https://www.wikidata.org/wiki/Q4949966","display_name":"Boundary knot method","level":4,"score":0.1636238992214203},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06218290328979492},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/120894725","is_oa":false,"landing_page_url":"https://doi.org/10.1137/120894725","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 & Simulation","raw_type":"journal-article"},{"id":"pmh:oai:infoscience.epfl.ch:182185","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/182185","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:182185","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/182185","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I5124864","host_organization_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","host_organization_lineage":["https://openalex.org/I5124864"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320915","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052"},{"id":"https://openalex.org/F4320321652","display_name":"Eidgen\u00f6ssische Technische Hochschule Z\u00fcrich","ror":"https://ror.org/05a28rw58"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W39412911","https://openalex.org/W74748254","https://openalex.org/W1492326914","https://openalex.org/W1521778258","https://openalex.org/W1542004730","https://openalex.org/W1547249381","https://openalex.org/W1586623601","https://openalex.org/W1594572592","https://openalex.org/W1599423952","https://openalex.org/W1825216778","https://openalex.org/W1835030294","https://openalex.org/W1966480196","https://openalex.org/W1971634471","https://openalex.org/W1974309308","https://openalex.org/W1987902628","https://openalex.org/W1990157709","https://openalex.org/W1991395770","https://openalex.org/W2001772063","https://openalex.org/W2005788407","https://openalex.org/W2008987050","https://openalex.org/W2018941619","https://openalex.org/W2019592395","https://openalex.org/W2028402684","https://openalex.org/W2029450279","https://openalex.org/W2036766781","https://openalex.org/W2036810845","https://openalex.org/W2041523977","https://openalex.org/W2047368043","https://openalex.org/W2049222546","https://openalex.org/W2051917325","https://openalex.org/W2056624361","https://openalex.org/W2063909992","https://openalex.org/W2068543948","https://openalex.org/W2069366742","https://openalex.org/W2070980742","https://openalex.org/W2083754610","https://openalex.org/W2093294439","https://openalex.org/W2117358914","https://openalex.org/W2138940269","https://openalex.org/W2163715525","https://openalex.org/W2341283081","https://openalex.org/W2342119047","https://openalex.org/W2685500084","https://openalex.org/W2741480250","https://openalex.org/W2934526567","https://openalex.org/W3021293439","https://openalex.org/W3214098784"],"related_works":["https://openalex.org/W1567939749","https://openalex.org/W1977906733","https://openalex.org/W2367880982","https://openalex.org/W2382979343","https://openalex.org/W2185206193","https://openalex.org/W2165887158","https://openalex.org/W2350502375","https://openalex.org/W3196813885","https://openalex.org/W1989473560","https://openalex.org/W2021654023"],"abstract_inverted_index":{"In":[0,39,202],"this":[1],"paper":[2],"Monte":[3,32,74,93,107,122,151],"Carlo":[4,33,75,94,108,123,152],"finite":[5,34,47,59,85,95,109,124,136,142,153,207],"element":[6,35,48,60,96,110,125,137,143,154,208],"approximations":[7],"for":[8,82],"elliptic":[9],"homogenization":[10],"problems":[11],"with":[12,187,217],"random":[13,185],"coefficients,":[14],"which":[15,161],"oscillate":[16],"on":[17],"$n\\in\\mathbb{N}$":[18],"a":[19,133,198],"priori":[20],"known,":[21],"separated":[22],"microscopic":[23],"length":[24,54,165,222],"scales,":[25,166],"are":[26,159],"considered.":[27],"The":[28],"convergence":[29],"of":[30,115,180,183,197,205],"multilevel":[31,46,73,92,121,150],"discretizations":[36],"is":[37,42,79,128,192],"analyzed.":[38],"particular,":[40],"it":[41],"considered":[43],"that":[44,65,81,130,191],"the":[45,51,57,66,91,100,104,113,120,141,149,181,184,195,203,206,212,220],"discretization":[49],"resolves":[50],"finest":[52],"physical":[53,164,221],"scale,":[55],"but":[56],"coarsest":[58],"mesh":[61],"does":[62],"not,":[63],"so":[64],"so-called":[67],"resonance":[68],"case":[69,204],"occurs":[70],"at":[71,99],"intermediate":[72],"sampling":[76],"levels.":[77],"It":[78,127],"shown":[80],"first":[83],"order":[84],"elements":[86],"in":[87,119],"two":[88],"space":[89],"dimensions,":[90],"method":[97,138,146,211],"converges":[98],"same":[101],"rate":[102],"as":[103,140],"corresponding":[105],"single-level":[106],"method,":[111],"despite":[112],"majority":[114],"samples":[116],"being":[117],"underresolved":[118],"estimator.":[126],"proved":[129],"switching":[131],"to":[132,147,177,194,219],"hierarchic":[134],"multiscale":[135,145,210],"such":[139],"heterogeneous":[144,209],"compute":[148],"estimator,":[155],"when":[156],"only":[157],"meshes":[158],"used":[160],"underresolve":[162],"all":[163],"implies":[167],"optimal":[168],"convergence.":[169],"Specifically,":[170],"both":[171],"methods":[172],"proposed":[173],"here":[174],"allow":[175],"one":[176],"obtain":[178],"estimates":[179],"expectation":[182],"solution,":[186],"accuracy":[188],"versus":[189],"work":[190],"identical":[193],"solution":[196],"single":[199],"deterministic":[200],"problem.":[201],"estimate":[213],"is,":[214],"moreover,":[215],"robust":[216],"respect":[218],"scales.":[223],"Numerical":[224],"experiments":[225],"corroborate":[226],"our":[227],"analytical":[228],"findings.":[229]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":5},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-08-13T07:04:57.449891","created_date":"2025-10-10T00:00:00"}