{"id":"https://openalex.org/W2807985019","doi":"https://doi.org/10.1137/18m1193700","title":"Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification","display_name":"Improved Efficiency of a Multi-Index FEM for Computational Uncertainty Quantification","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2807985019","doi":"https://doi.org/10.1137/18m1193700","mag":"2807985019"},"language":"en","primary_location":{"id":"doi:10.1137/18m1193700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1193700","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1806.04159","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004856556","display_name":"Josef Dick","orcid":"https://orcid.org/0000-0003-0142-6022"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Josef Dick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035803720","display_name":"Michael Feischl","orcid":"https://orcid.org/0000-0001-7206-1652"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Michael Feischl","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":0.1434,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.52384689,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"57","issue":"4","first_page":"1744","last_page":"1769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998000264167786,"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":0.9998000264167786,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9966999888420105,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9926999807357788,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/discretization","display_name":"Discretization","score":0.6606367230415344},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.6351393461227417},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5894733667373657},{"id":"https://openalex.org/keywords/monte-carlo-method","display_name":"Monte Carlo method","score":0.4886808693408966},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4751536548137665},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.45615142583847046},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.44726601243019104},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.44341564178466797},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.44212037324905396},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.36884498596191406},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34270989894866943},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.18288367986679077}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6606367230415344},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.6351393461227417},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5894733667373657},{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.4886808693408966},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4751536548137665},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.45615142583847046},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.44726601243019104},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.44341564178466797},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.44212037324905396},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36884498596191406},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34270989894866943},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18288367986679077},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1137/18m1193700","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1193700","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1806.04159","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04159","pdf_url":"https://arxiv.org/pdf/1806.04159","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:EVASTAR-Karlsruhe.de:1000086907","is_oa":false,"landing_page_url":"https://publikationen.bibliothek.kit.edu/1000086907","pdf_url":null,"source":{"id":"https://openalex.org/S4306401992","display_name":"Repository KITopen (Karlsruhe Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I102335020","host_organization_name":"Karlsruhe Institute of Technology","host_organization_lineage":["https://openalex.org/I102335020"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ISSN: 2365-662X","raw_type":"info:eu-repo/semantics/book"},{"id":"mag:2807985019","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.04159","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.1806.04159","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.04159","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"},{"id":"doi:10.5445/ir/1000086907","is_oa":true,"landing_page_url":"https://doi.org/10.5445/ir/1000086907","pdf_url":null,"source":{"id":"https://openalex.org/S7407052948","display_name":"KITopen","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"report"},{"id":"mag:2964256501","is_oa":false,"landing_page_url":"https://www.research-collection.ethz.ch/handle/20.500.11850/297926","pdf_url":null,"source":{"id":"https://openalex.org/S4306529093","display_name":"SAM Research Report","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":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":"SAM Research Report","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1806.04159","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.04159","pdf_url":"https://arxiv.org/pdf/1806.04159","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1443172984","display_name":"Optimal adaptivity for uncertainty quantification","funder_award_id":"DE170100222","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G3587333238","display_name":null,"funder_award_id":"CRC 1173","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G4088550709","display_name":"Numerical Analysis of PDEs with High-Dimensional Input Data","funder_award_id":"159940","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"},{"id":"https://openalex.org/G5773529614","display_name":"Quantifying uncertainty: innovations in high dimensional computation","funder_award_id":"DP150101770","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G993971353","display_name":null,"funder_award_id":"200021","funder_id":"https://openalex.org/F4320320924","funder_display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"},{"id":"https://openalex.org/F4320320924","display_name":"Schweizerischer Nationalfonds zur F\u00f6rderung der Wissenschaftlichen Forschung","ror":"https://ror.org/00yjd3n13"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W184188664","https://openalex.org/W1595193945","https://openalex.org/W1608887775","https://openalex.org/W1630018803","https://openalex.org/W1689157804","https://openalex.org/W1851937217","https://openalex.org/W2036766781","https://openalex.org/W2066322206","https://openalex.org/W2083754610","https://openalex.org/W2126980197","https://openalex.org/W2129114523","https://openalex.org/W2135459060","https://openalex.org/W2163715525","https://openalex.org/W2274168723","https://openalex.org/W2404395639","https://openalex.org/W2538426846","https://openalex.org/W2544951676","https://openalex.org/W2559327389","https://openalex.org/W2598935221","https://openalex.org/W2782466637","https://openalex.org/W2795608305","https://openalex.org/W2950686781","https://openalex.org/W2963224214","https://openalex.org/W2964218952","https://openalex.org/W3021293439","https://openalex.org/W3102723444","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2074685901","https://openalex.org/W2750460732","https://openalex.org/W2601944466","https://openalex.org/W1554892235","https://openalex.org/W2053996530","https://openalex.org/W2914587446","https://openalex.org/W3010057631","https://openalex.org/W176737369","https://openalex.org/W2810956084","https://openalex.org/W1984671366","https://openalex.org/W2422105361","https://openalex.org/W2997662317","https://openalex.org/W2980445106","https://openalex.org/W2909211007","https://openalex.org/W2313675821","https://openalex.org/W2130284218","https://openalex.org/W2963704680","https://openalex.org/W2996414013","https://openalex.org/W2600471723","https://openalex.org/W2964791224"],"abstract_inverted_index":{"We":[0,19],"propose":[1],"a":[2,12,28,104],"multi-index":[3,40,105,127],"algorithm":[4],"for":[5,51,58,66,116,129],"the":[6,34,39,48,52,55,59,62,67,122],"Monte":[7],"Carlo":[8],"(MC)":[9],"discretization":[10],"of":[11,54,61,126],"linear,":[13],"elliptic":[14],"PDE":[15],"with":[16,42,133],"affine-parametric":[17],"input.":[18],"prove":[20],"an":[21],"error":[22],"versus":[23],"work":[24],"analysis":[25,41,108],"which":[26],"allows":[27,73],"multilevel":[29,89,114],"finite":[30],"element":[31],"approximation":[32,60],"in":[33,47,86,103],"physical":[35,49],"domain":[36,50],"and":[37,65,76,100,119],"apply":[38],"isotropic,":[43],"unstructured":[44],"mesh":[45,77],"refinement":[46],"solution":[53],"forward":[56],"problem,":[57],"random":[63,134],"field,":[64],"MC":[68,90,101],"quadrature":[69],"error.":[70],"Our":[71,107],"approach":[72],"Lipschitz":[74],"domains":[75],"hierarchies":[78],"more":[79],"general":[80],"than":[81],"tensor":[82],"grids.":[83],"The":[84],"improvement":[85],"complexity":[87],"over":[88],"FEM":[91],"is":[92],"obtained":[93],"from":[94],"combining":[95],"spatial":[96],"discretization,":[97],"dimension":[98],"truncation,":[99],"sampling":[102],"fashion.":[106],"improves":[109],"cost":[110],"estimates":[111],"compared":[112],"to":[113],"algorithms":[115,128],"similar":[117],"problems":[118],"mathematically":[120],"underpins":[121],"superior":[123],"practical":[124],"performance":[125],"partial":[130],"differential":[131],"equations":[132],"coefficients.":[135]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-08-06T08:24:18.245995","created_date":"2025-10-10T00:00:00"}
