{"id":"https://openalex.org/W2808314485","doi":"https://doi.org/10.1137/18m1194031","title":"Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method","display_name":"Recycling Samples in the Multigrid Multilevel (Quasi-)Monte Carlo Method","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2808314485","doi":"https://doi.org/10.1137/18m1194031","mag":"2808314485"},"language":"en","primary_location":{"id":"doi:10.1137/18m1194031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194031","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://lirias.kuleuven.be/handle/123456789/632902","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5019938458","display_name":"Pieterjan Robbe","orcid":"https://orcid.org/0000-0002-6254-8245"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Pieterjan Robbe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045125806","display_name":"Dirk Nuyens","orcid":"https://orcid.org/0000-0002-4555-2314"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5062993526","display_name":"Stefan Vandewalle","orcid":"https://orcid.org/0000-0002-8988-2374"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Stefan Vandewalle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.1614,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.57667845,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"41","issue":"5","first_page":"S37","last_page":"S60"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9997000098228455,"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":0.9997000098228455,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9987999796867371,"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"}},{"id":"https://openalex.org/T10597","display_name":"Nuclear reactor physics and engineering","score":0.9883999824523926,"subfield":{"id":"https://openalex.org/subfields/2202","display_name":"Aerospace Engineering"},"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":0.7813342213630676},{"id":"https://openalex.org/keywords/quasi-monte-carlo-method","display_name":"Quasi-Monte Carlo method","score":0.7500574588775635},{"id":"https://openalex.org/keywords/multigrid-method","display_name":"Multigrid method","score":0.6695703268051147},{"id":"https://openalex.org/keywords/variance-reduction","display_name":"Variance reduction","score":0.6477105021476746},{"id":"https://openalex.org/keywords/monte-carlo-integration","display_name":"Monte Carlo integration","score":0.5596717596054077},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5077260732650757},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5075603723526001},{"id":"https://openalex.org/keywords/hybrid-monte-carlo","display_name":"Hybrid Monte Carlo","score":0.48047345876693726},{"id":"https://openalex.org/keywords/markov-chain-monte-carlo","display_name":"Markov chain Monte Carlo","score":0.4760946035385132},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.46979841589927673},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.46142083406448364},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.44632595777511597},{"id":"https://openalex.org/keywords/sobol-sequence","display_name":"Sobol sequence","score":0.4291728138923645},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4289557933807373},{"id":"https://openalex.org/keywords/dynamic-monte-carlo-method","display_name":"Dynamic Monte Carlo method","score":0.4160270094871521},{"id":"https://openalex.org/keywords/monte-carlo-method-in-statistical-physics","display_name":"Monte Carlo method in statistical physics","score":0.4109416604042053},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.41026541590690613},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3749344050884247},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1622595489025116},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09954455494880676},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.09061053395271301}],"concepts":[{"id":"https://openalex.org/C19499675","wikidata":"https://www.wikidata.org/wiki/Q232207","display_name":"Monte Carlo method","level":2,"score":0.7813342213630676},{"id":"https://openalex.org/C63320529","wikidata":"https://www.wikidata.org/wiki/Q7269435","display_name":"Quasi-Monte Carlo method","level":5,"score":0.7500574588775635},{"id":"https://openalex.org/C137119250","wikidata":"https://www.wikidata.org/wiki/Q1413101","display_name":"Multigrid method","level":3,"score":0.6695703268051147},{"id":"https://openalex.org/C62644790","wikidata":"https://www.wikidata.org/wiki/Q3454689","display_name":"Variance reduction","level":3,"score":0.6477105021476746},{"id":"https://openalex.org/C132725507","wikidata":"https://www.wikidata.org/wiki/Q39879","display_name":"Monte Carlo integration","level":5,"score":0.5596717596054077},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5077260732650757},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5075603723526001},{"id":"https://openalex.org/C13153151","wikidata":"https://www.wikidata.org/wiki/Q1639846","display_name":"Hybrid Monte Carlo","level":4,"score":0.48047345876693726},{"id":"https://openalex.org/C111350023","wikidata":"https://www.wikidata.org/wiki/Q1191869","display_name":"Markov chain Monte Carlo","level":3,"score":0.4760946035385132},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.46979841589927673},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.46142083406448364},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.44632595777511597},{"id":"https://openalex.org/C49740808","wikidata":"https://www.wikidata.org/wiki/Q7550116","display_name":"Sobol sequence","level":3,"score":0.4291728138923645},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4289557933807373},{"id":"https://openalex.org/C122592724","wikidata":"https://www.wikidata.org/wiki/Q3855635","display_name":"Dynamic Monte Carlo method","level":3,"score":0.4160270094871521},{"id":"https://openalex.org/C204493344","wikidata":"https://www.wikidata.org/wiki/Q6904698","display_name":"Monte Carlo method in statistical physics","level":5,"score":0.4109416604042053},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.41026541590690613},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3749344050884247},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1622595489025116},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09954455494880676},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.09061053395271301},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1137/18m1194031","is_oa":false,"landing_page_url":"https://doi.org/10.1137/18m1194031","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"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 Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/632902","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/632902","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 41 (5), Art.No. 5, (S37-S60)","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:arXiv.org:1806.05619","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1806.05619","pdf_url":"https://arxiv.org/pdf/1806.05619","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"","raw_type":"text"},{"id":"pmh:oai:arXiv.org:1806.05619","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1806.05619","pdf_url":"https://arxiv.org/pdf/1806.05619","source":{"id":"https://openalex.org/S4393918464","display_name":"ArXiv.org","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"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":null,"raw_type":"text"},{"id":"mag:2808314485","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1806.05619.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.1806.05619","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1806.05619","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"article"}],"best_oa_location":{"id":"pmh:oai:lirias2repo.kuleuven.be:123456789/632902","is_oa":true,"landing_page_url":"https://lirias.kuleuven.be/handle/123456789/632902","pdf_url":null,"source":{"id":"https://openalex.org/S4306401954","display_name":"Lirias (KU Leuven)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I99464096","host_organization_name":"KU Leuven","host_organization_lineage":["https://openalex.org/I99464096"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"Siam Journal On Scientific Computing, vol. 41 (5), Art.No. 5, (S37-S60)","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3161419632","display_name":null,"funder_award_id":"140068","funder_id":"https://openalex.org/F4320321732","funder_display_name":"Agentschap voor Innovatie door Wetenschap en Technologie"},{"id":"https://openalex.org/G8973206386","display_name":null,"funder_award_id":"IWT-140068","funder_id":"https://openalex.org/F4320321732","funder_display_name":"Agentschap voor Innovatie door Wetenschap en Technologie"}],"funders":[{"id":"https://openalex.org/F4320321732","display_name":"Agentschap voor Innovatie door Wetenschap en Technologie","ror":"https://ror.org/01antkr91"},{"id":"https://openalex.org/F4320327336","display_name":"Vlaamse regering","ror":null},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W105300439","https://openalex.org/W1506342804","https://openalex.org/W1538934584","https://openalex.org/W1581764802","https://openalex.org/W1595193945","https://openalex.org/W1925297253","https://openalex.org/W1976544585","https://openalex.org/W1978501336","https://openalex.org/W2014945091","https://openalex.org/W2036766781","https://openalex.org/W2039789965","https://openalex.org/W2042083287","https://openalex.org/W2052271668","https://openalex.org/W2093625674","https://openalex.org/W2127981460","https://openalex.org/W2135459060","https://openalex.org/W2146736312","https://openalex.org/W2150175265","https://openalex.org/W2153740376","https://openalex.org/W2163715525","https://openalex.org/W2464898451","https://openalex.org/W2522607487","https://openalex.org/W2538426846","https://openalex.org/W2560947363","https://openalex.org/W2762992792","https://openalex.org/W2963592159","https://openalex.org/W2964218952","https://openalex.org/W2964295897"],"related_works":["https://openalex.org/W2135459060","https://openalex.org/W2560947363","https://openalex.org/W3203728798","https://openalex.org/W3022354188","https://openalex.org/W3017226594","https://openalex.org/W3103029122","https://openalex.org/W160467666","https://openalex.org/W3081732379","https://openalex.org/W590971457","https://openalex.org/W2787888983","https://openalex.org/W1498636934","https://openalex.org/W2988621382","https://openalex.org/W24418085","https://openalex.org/W3023358113","https://openalex.org/W2963868836","https://openalex.org/W1995089229","https://openalex.org/W2908875164","https://openalex.org/W2217072212","https://openalex.org/W2331657073","https://openalex.org/W3103019089"],"abstract_inverted_index":{"The":[0,27,130],"multilevel":[1,72],"Monte":[2,73,126],"Carlo":[3,74,103,127],"method":[4,28,36,111,132],"is":[5,29,99,119,133,167,175],"an":[6,96,114,139],"efficient":[7,169],"variance":[8,116],"reduction":[9],"technique.":[10],"It":[11],"uses":[12],"a":[13,149],"sequence":[14],"of":[15,37,124,138,151],"coarse":[16,59],"approximations":[17],"to":[18,33,54,105],"reduce":[19],"the":[20,35,56,63,71,125,136,159,171],"computational":[21],"cost":[22],"in":[23,70,122,158],"uncertainty":[24],"quantification":[25],"applications.":[26],"nowadays":[30],"often":[31],"considered":[32],"be":[34,66],"choice":[38],"for":[39,148],"solving":[40],"PDEs":[41],"with":[42,113,142,154],"random":[43,152,173],"coefficients":[44],"when":[45,170],"many":[46],"uncertainties":[47],"are":[48],"involved.":[49],"When":[50],"using":[51,101],"full":[52],"multigrid":[53],"solve":[55],"deterministic":[57],"problem,":[58],"solutions":[60],"obtained":[61],"by":[62,80],"solver":[64],"can":[65],"recycled":[67],"as":[68,76],"samples":[69],"method,":[75],"was":[77],"pointed":[78],"out":[79],"Kumar,":[81],"Oosterlee":[82],"and":[83],"Dwight":[84],"[Int.":[85],"J.":[86],"Uncertain.":[87],"Quantif.,":[88],"7":[89],"(2017),":[90],"pp.":[91],"57--81].":[92],"In":[93],"this":[94],"article,":[95],"alternative":[97],"approach":[98],"considered,":[100],"quasi-Monte":[102],"points,":[104],"speed":[106],"up":[107],"convergence.":[108],"Additionally,":[109],"our":[110],"comes":[112],"improved":[115],"estimate":[117],"which":[118],"also":[120],"valid":[121],"case":[123],"based":[128],"approach.":[129],"new":[131],"illustrated":[134],"on":[135],"example":[137],"elliptic":[140],"PDE":[141],"lognormal":[143],"diffusion":[144],"coefficient.":[145],"Numerical":[146],"results":[147],"variety":[150],"fields":[153],"different":[155],"smoothness":[156],"parameters":[157],"Mat\u00e9rn":[160],"covariance":[161],"function":[162],"show":[163],"that":[164],"sample":[165],"recycling":[166],"more":[168],"input":[172],"field":[174],"nonsmooth.":[176]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}