{"id":"https://openalex.org/W2963283735","doi":"https://doi.org/10.1137/15m1019568","title":"Accelerating Stochastic Collocation Methods for Partial Differential Equations with Random Input Data","display_name":"Accelerating Stochastic Collocation Methods for Partial Differential Equations with Random Input Data","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2963283735","doi":"https://doi.org/10.1137/15m1019568","mag":"2963283735"},"language":"en","primary_location":{"id":"doi:10.1137/15m1019568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019568","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","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/A5107905536","display_name":"D. Galindo","orcid":null},"institutions":[{"id":"https://openalex.org/I4210159558","display_name":"Joint Institute for Computational Sciences","ror":"https://ror.org/05277x335","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294","https://openalex.org/I4210159558","https://openalex.org/I75027704"]},{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"D. Galindo","raw_affiliation_strings":["Joint Institute for Computational Sciences, University of Tennessee, 1 Bethel Valley Road, Oak Ridge, TN 37831"],"affiliations":[{"raw_affiliation_string":"Joint Institute for Computational Sciences, University of Tennessee, 1 Bethel Valley Road, Oak Ridge, TN 37831","institution_ids":["https://openalex.org/I4210159558","https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089231890","display_name":"Peter Jantsch","orcid":null},"institutions":[{"id":"https://openalex.org/I75027704","display_name":"University of Tennessee at Knoxville","ror":"https://ror.org/020f3ap87","country_code":"US","type":"education","lineage":["https://openalex.org/I75027704"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"P. Jantsch","raw_affiliation_strings":["Department of Mathematics, University of Tennessee, Knoxville, TN 37996"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Tennessee, Knoxville, TN 37996","institution_ids":["https://openalex.org/I75027704"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5009338966","display_name":"Clayton Webster","orcid":"https://orcid.org/0000-0002-1375-0359"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"C. G. Webster","raw_affiliation_strings":["Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831"],"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046509521","display_name":"Guannan Zhang","orcid":"https://orcid.org/0000-0001-7256-150X"},"institutions":[{"id":"https://openalex.org/I1289243028","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56","country_code":"US","type":"facility","lineage":["https://openalex.org/I1289243028","https://openalex.org/I1330989302","https://openalex.org/I39565521","https://openalex.org/I4210159294"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"G. Zhang","raw_affiliation_strings":["Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831"],"affiliations":[{"raw_affiliation_string":"Department of Computational and Applied Mathematics, Oak Ridge National Laboratory, Oak Ridge, TN 37831","institution_ids":["https://openalex.org/I1289243028"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5107905536"],"corresponding_institution_ids":["https://openalex.org/I4210159558","https://openalex.org/I75027704"],"apc_list":null,"apc_paid":null,"fwci":0.2928,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.74566985,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"4","issue":"1","first_page":"1111","last_page":"1137"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":1.0,"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":1.0,"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/T11371","display_name":"Wind and Air Flow Studies","score":0.9962999820709229,"subfield":{"id":"https://openalex.org/subfields/2305","display_name":"Environmental Engineering"},"field":{"id":"https://openalex.org/fields/23","display_name":"Environmental Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10968","display_name":"Statistical Distribution Estimation and Applications","score":0.9821000099182129,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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/collocation","display_name":"Collocation (remote sensing)","score":0.7117221355438232},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6550882458686829},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.6470820307731628},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5539280772209167},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5251650214195251},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5231503248214722},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5116408467292786},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.49973559379577637},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.43920373916625977},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4167514443397522},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3777092397212982},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3316619396209717},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.27744850516319275},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.2424660325050354},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.14654213190078735}],"concepts":[{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.7117221355438232},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6550882458686829},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.6470820307731628},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5539280772209167},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5251650214195251},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5231503248214722},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5116408467292786},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.49973559379577637},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.43920373916625977},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4167514443397522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3777092397212982},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3316619396209717},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.27744850516319275},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.2424660325050354},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.14654213190078735},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/15m1019568","is_oa":false,"landing_page_url":"https://doi.org/10.1137/15m1019568","pdf_url":null,"source":{"id":"https://openalex.org/S2911293512","display_name":"SIAM/ASA Journal on Uncertainty Quantification","issn_l":"2166-2525","issn":["2166-2525"],"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/ASA Journal on Uncertainty Quantification","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1489425746","display_name":null,"funder_award_id":"DE-AC05-00OR22725","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G1553423244","display_name":null,"funder_award_id":"1854-V521-12","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G1645119126","display_name":null,"funder_award_id":"AC05-00OR22725","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G1719536385","display_name":null,"funder_award_id":"DE-AC05-00OR22725","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G2042897603","display_name":null,"funder_award_id":"DE-AC05-00OR2272","funder_id":"https://openalex.org/F4320316892","funder_display_name":"UT-Battelle"},{"id":"https://openalex.org/G2296932962","display_name":null,"funder_award_id":"DE-AC05-00OR227","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G236881256","display_name":null,"funder_award_id":"ERKJE45","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3299391273","display_name":null,"funder_award_id":"E-AC05-00OR22725","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G3704101847","display_name":null,"funder_award_id":"ERKJ259","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G3841132129","display_name":null,"funder_award_id":"ERKJ259","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G4044773326","display_name":null,"funder_award_id":"ERKJE45","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G4370606643","display_name":null,"funder_award_id":"DE-AC05-00OR22725","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G4423657506","display_name":null,"funder_award_id":"AC05-00OR22725","funder_id":"https://openalex.org/F4320338287","funder_display_name":"Oak Ridge National Laboratory"},{"id":"https://openalex.org/G4694431782","display_name":null,"funder_award_id":"DE-AC05-00OR2272","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G5680552350","display_name":null,"funder_award_id":"ERKJ259","funder_id":"https://openalex.org/F4320337506","funder_display_name":"Advanced Scientific Computing Research"},{"id":"https://openalex.org/G5726405315","display_name":null,"funder_award_id":"DE-AC05","funder_id":"https://openalex.org/F4320306250","funder_display_name":"Battelle"},{"id":"https://openalex.org/G6129992089","display_name":null,"funder_award_id":"DE-AC05-","funder_id":"https://openalex.org/F4320316892","funder_display_name":"UT-Battelle"},{"id":"https://openalex.org/G6488227018","display_name":null,"funder_award_id":"DE-AC05-00OR227","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G67284079","display_name":null,"funder_award_id":"ERKJE45","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G6864165199","display_name":null,"funder_award_id":"DE-AC05-00OR22725","funder_id":"https://openalex.org/F4320306250","funder_display_name":"Battelle"},{"id":"https://openalex.org/G691578896","display_name":null,"funder_award_id":"DE-AC05-00OR2272","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G7114708214","display_name":null,"funder_award_id":"DE-AC05-00OR2272","funder_id":"https://openalex.org/F4320338287","funder_display_name":"Oak Ridge National Laboratory"},{"id":"https://openalex.org/G7995982022","display_name":null,"funder_award_id":"DE-AC05","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8269158468","display_name":null,"funder_award_id":"AC05-00OR22725","funder_id":"https://openalex.org/F4320332359","funder_display_name":"Office of Science"},{"id":"https://openalex.org/G8414908677","display_name":null,"funder_award_id":"DE-AC0","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8799952057","display_name":null,"funder_award_id":"DE-AC05-00OR22","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8906985441","display_name":null,"funder_award_id":"00OR22725","funder_id":"https://openalex.org/F4320306084","funder_display_name":"U.S. Department of Energy"},{"id":"https://openalex.org/G8943143067","display_name":null,"funder_award_id":"AC05-00OR22725","funder_id":"https://openalex.org/F4320316892","funder_display_name":"UT-Battelle"}],"funders":[{"id":"https://openalex.org/F4320306084","display_name":"U.S. Department of Energy","ror":"https://ror.org/01bj3aw27"},{"id":"https://openalex.org/F4320306250","display_name":"Battelle","ror":"https://ror.org/01h5tnr73"},{"id":"https://openalex.org/F4320316892","display_name":"UT-Battelle","ror":"https://ror.org/04nza6677"},{"id":"https://openalex.org/F4320332359","display_name":"Office of Science","ror":"https://ror.org/00mmn6b08"},{"id":"https://openalex.org/F4320332467","display_name":"U.S. Air Force","ror":"https://ror.org/006gmme17"},{"id":"https://openalex.org/F4320337506","display_name":"Advanced Scientific Computing Research","ror":"https://ror.org/0012c7r22"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"},{"id":"https://openalex.org/F4320338287","display_name":"Oak Ridge National Laboratory","ror":"https://ror.org/01qz5mb56"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W208376040","https://openalex.org/W838268176","https://openalex.org/W1828419635","https://openalex.org/W1971099220","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W1999723468","https://openalex.org/W2014490899","https://openalex.org/W2018159038","https://openalex.org/W2032916960","https://openalex.org/W2033022456","https://openalex.org/W2036242000","https://openalex.org/W2041509689","https://openalex.org/W2045116180","https://openalex.org/W2048791667","https://openalex.org/W2065120373","https://openalex.org/W2069379427","https://openalex.org/W2072205359","https://openalex.org/W2072282162","https://openalex.org/W2083845086","https://openalex.org/W2100880455","https://openalex.org/W2102031020","https://openalex.org/W2109744909","https://openalex.org/W2963862882","https://openalex.org/W3021293439"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2031073114","https://openalex.org/W2000247808"],"abstract_inverted_index":{"This":[0],"work":[1],"proposes":[2],"and":[3,48,139,142,154,158,163],"analyzes":[4],"a":[5,42,86,96,124],"generalized":[6],"technique":[7,169],"for":[8],"decreasing":[9],"the":[10,31,34,66,70,73,89,92,104,130,144,160,164],"computational":[11,126],"complexity":[12,127],"of":[13,33,72,91,106,113,129,146,167],"stochastic":[14],"collocation":[15,39,77],"(SC)":[16],"methods":[17],"to":[18,52,63],"solve":[19],"partial":[20],"differential":[21],"equations":[22],"(PDEs)":[23],"with":[24,58,138,171],"random":[25],"input":[26],"data.":[27],"Specifically,":[28],"we":[29,99],"predict":[30],"solution":[32],"parametrized":[35,156],"PDE":[36],"at":[37],"each":[38],"point":[40],"using":[41],"previously":[43],"assembled":[44,84],"lower":[45],"fidelity":[46],"interpolant":[47],"use":[49],"this":[50,168],"prediction":[51],"provide":[53],"deterministic":[54],"(linear/nonlinear)":[55],"iterative":[56],"solvers":[57],"initial":[59],"approximations":[60],"which":[61],"continue":[62],"improve":[64],"as":[65,85],"algorithm":[67],"progresses":[68],"through":[69],"levels":[71],"interpolant.":[74,94],"With":[75],"nested":[76,119],"points,":[78],"these":[79],"coarse":[80],"predictions":[81],"can":[82],"be":[83],"substep":[87],"in":[88,103],"construction":[90],"high-fidelity":[93],"As":[95],"concrete":[97],"example,":[98],"develop":[100],"our":[101,147],"approach":[102],"context":[105],"SC":[107,136],"approaches":[108],"employing":[109],"sparse":[110,134],"tensor":[111],"products":[112],"globally":[114],"defined":[115],"Lagrange":[116],"polynomials":[117],"on":[118],"one-dimensional":[120],"Clenshaw--Curtis":[121],"abscissas,":[122],"providing":[123],"rigorous":[125],"analysis":[128],"resulting":[131],"fully":[132],"discrete":[133],"grid":[135],"approximation,":[137],"without":[140],"acceleration,":[141],"demonstrating":[143],"effectiveness":[145],"proposed":[148],"algorithm.":[149],"Numerical":[150],"examples":[151],"include":[152],"linear":[153],"nonlinear":[155],"PDEs":[157],"illustrate":[159],"theoretical":[161],"results":[162],"improved":[165],"efficiency":[166],"compared":[170],"several":[172],"others.":[173]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
