{"id":"https://openalex.org/W2766099653","doi":"https://doi.org/10.1007/s00211-018-0968-0","title":"Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients","display_name":"Circulant embedding with QMC: analysis for elliptic PDE with lognormal coefficients","publication_year":2018,"publication_date":"2018-05-03","ids":{"openalex":"https://openalex.org/W2766099653","doi":"https://doi.org/10.1007/s00211-018-0968-0","mag":"2766099653","pmid":"https://pubmed.ncbi.nlm.nih.gov/30220739"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-018-0968-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0968-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-018-0968-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00211-018-0968-0.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064637859","display_name":"Ivan G. Graham","orcid":"https://orcid.org/0000-0002-5730-676X"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ivan G. Graham","raw_affiliation_strings":["1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK","Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045896084","display_name":"Frances Y. Kuo","orcid":"https://orcid.org/0000-0003-2123-6971"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Frances Y. Kuo","raw_affiliation_strings":["2School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052 Australia","School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052 Australia","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5045125806","display_name":"Dirk Nuyens","orcid":"https://orcid.org/0000-0002-4555-2314"},"institutions":[{"id":"https://openalex.org/I99464096","display_name":"KU Leuven","ror":"https://ror.org/05f950310","country_code":"BE","type":"education","lineage":["https://openalex.org/I99464096"]}],"countries":["BE"],"is_corresponding":true,"raw_author_name":"Dirk Nuyens","raw_affiliation_strings":["3Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium","Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"3Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium","institution_ids":[]},{"raw_affiliation_string":"Department of Computer Science, KU Leuven, Celestijnenlaan 200A, 3001, Leuven, Belgium","institution_ids":["https://openalex.org/I99464096"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050544926","display_name":"Robert Scheichl","orcid":"https://orcid.org/0000-0001-8493-4393"},"institutions":[{"id":"https://openalex.org/I51601045","display_name":"University of Bath","ror":"https://ror.org/002h8g185","country_code":"GB","type":"education","lineage":["https://openalex.org/I51601045"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Rob Scheichl","raw_affiliation_strings":["1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK","Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"1Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY UK","institution_ids":[]},{"raw_affiliation_string":"Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK","institution_ids":["https://openalex.org/I51601045"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075686837","display_name":"Ian H. Sloan","orcid":"https://orcid.org/0000-0003-3769-0538"},"institutions":[{"id":"https://openalex.org/I31746571","display_name":"UNSW Sydney","ror":"https://ror.org/03r8z3t63","country_code":"AU","type":"education","lineage":["https://openalex.org/I31746571"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Ian H. Sloan","raw_affiliation_strings":["2School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052 Australia","School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW, 2052, Australia"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"2School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW 2052 Australia","institution_ids":[]},{"raw_affiliation_string":"School of Mathematics and Statistics, UNSW Sydney, Sydney, NSW, 2052, Australia","institution_ids":["https://openalex.org/I31746571"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5045125806"],"corresponding_institution_ids":["https://openalex.org/I99464096"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":3.4727,"has_fulltext":true,"cited_by_count":32,"citation_normalized_percentile":{"value":0.93194987,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"140","issue":"2","first_page":"479","last_page":"511"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9987000226974487,"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":0.9987000226974487,"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":0.9909999966621399,"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/T13126","display_name":"Scientific Research and Discoveries","score":0.9631999731063843,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8250046372413635},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.6537333726882935},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5499722957611084},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.5007073879241943},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.481544554233551},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4721042215824127},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.32963109016418457},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.22041651606559753},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.0974663496017456}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8250046372413635},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.6537333726882935},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5499722957611084},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.5007073879241943},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.481544554233551},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4721042215824127},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.32963109016418457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.22041651606559753},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0974663496017456},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.1007/s00211-018-0968-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0968-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-018-0968-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},{"id":"pmid:30220739","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30220739","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische mathematik","raw_type":null},{"id":"pmh:oai:europepmc.org:5086117","is_oa":true,"landing_page_url":"http://europepmc.org/pmc/articles/PMC6132744","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:6132744","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/6132744","pdf_url":null,"source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Numer Math (Heidelb)","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1007/s00211-018-0968-0","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s00211-018-0968-0","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00211-018-0968-0.pdf","source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1555690208","display_name":null,"funder_award_id":"FT130100655","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G2950504642","display_name":null,"funder_award_id":"DP150101770","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G4046957151","display_name":null,"funder_award_id":"EP/K031368/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"},{"id":"https://openalex.org/G541026093","display_name":null,"funder_award_id":"OT:3E130287","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G5773529614","display_name":null,"funder_award_id":"DP150101770","funder_id":"https://openalex.org/F4320334704","funder_display_name":"Australian Research Council"},{"id":"https://openalex.org/G6467946708","display_name":null,"funder_award_id":"C3:3E150478","funder_id":"https://openalex.org/F4320322308","funder_display_name":"KU Leuven"},{"id":"https://openalex.org/G930637315","display_name":null,"funder_award_id":"EP/H051503/1","funder_id":"https://openalex.org/F4320334627","funder_display_name":"Engineering and Physical Sciences Research Council"}],"funders":[{"id":"https://openalex.org/F4320311041","display_name":"National Center for Theoretical Sciences","ror":"https://ror.org/02mfp0b67"},{"id":"https://openalex.org/F4320320322","display_name":"University of Bath","ror":"https://ror.org/002h8g185"},{"id":"https://openalex.org/F4320322308","display_name":"KU Leuven","ror":"https://ror.org/05f950310"},{"id":"https://openalex.org/F4320334627","display_name":"Engineering and Physical Sciences Research Council","ror":"https://ror.org/0439y7842"},{"id":"https://openalex.org/F4320334704","display_name":"Australian Research Council","ror":"https://ror.org/05mmh0f86"},{"id":"https://openalex.org/F4320337380","display_name":"Division of Mathematical Sciences","ror":"https://ror.org/051fftw81"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2766099653.pdf","grobid_xml":"https://content.openalex.org/works/W2766099653.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W595079961","https://openalex.org/W625796142","https://openalex.org/W1608887775","https://openalex.org/W1997321933","https://openalex.org/W2017769677","https://openalex.org/W2035455944","https://openalex.org/W2051344283","https://openalex.org/W2052271668","https://openalex.org/W2058401452","https://openalex.org/W2079222732","https://openalex.org/W2079559649","https://openalex.org/W2079884585","https://openalex.org/W2080288600","https://openalex.org/W2093294439","https://openalex.org/W2094168343","https://openalex.org/W2124413011","https://openalex.org/W2579190672","https://openalex.org/W2611887225","https://openalex.org/W2963592159","https://openalex.org/W2964295897","https://openalex.org/W2983836991"],"related_works":["https://openalex.org/W2033860025","https://openalex.org/W2139378013","https://openalex.org/W2560470131","https://openalex.org/W2049656902","https://openalex.org/W2394404719","https://openalex.org/W4287113494","https://openalex.org/W2348308003","https://openalex.org/W3148564979","https://openalex.org/W2312260908","https://openalex.org/W2088932963"],"abstract_inverted_index":{"In":[0,141],"a":[1,16,64,93,107,178,189,201],"previous":[2],"paper":[3,91],"(Graham":[4],"et":[5],"al.":[6],"in":[7,76,99,195,204],"J":[8],"Comput":[9],"Phys":[10],"230:3668-3694,":[11],"2011),":[12],"the":[13,51,60,97,100,103,119,122,133,143,151,156,163,183],"authors":[14],"proposed":[15],"new":[17],"practical":[18],"method":[19,40,98,105,169],"for":[20,28,49,58,96,162,171],"computing":[21,50],"expected":[22,52],"values":[23,53],"of":[24,26,31,71,121,132,135,150,182],"functionals":[25],"solutions":[27],"certain":[29,139],"classes":[30],"elliptic":[32],"partial":[33],"differential":[34],"equations":[35],"with":[36,54,80,192],"random":[37,61,77,157,184],"coefficients.":[38],"This":[39,90],"was":[41,68,88],"based":[42],"on":[43,63,118,188,200],"combining":[44],"quasi-Monte":[45],"Carlo":[46],"(QMC)":[47],"methods":[48,57],"circulant":[55,126],"embedding":[56],"sampling":[59,180],"field":[62],"regular":[65,179,202],"grid.":[66],"It":[67],"found":[69],"capable":[70],"handling":[72],"fluid":[73],"flow":[74],"problems":[75],"heterogeneous":[78],"media":[79],"high":[81],"stochastic":[82,136],"dimension,":[83],"but":[84],"no":[85],"convergence":[86,94,115],"theory":[87],"provided.":[89],"provides":[92],"analysis":[95,145,161],"case":[101],"when":[102],"QMC":[104,144],"is":[106],"specially":[108],"designed":[109],"randomly":[110],"shifted":[111],"lattice":[112],"rule.":[113],"The":[114,159],"result":[116],"depends":[117],"eigenvalues":[120],"underlying":[123,164],"nested":[124],"block":[125],"matrix":[127,153],"and":[128,199],"can":[129],"be":[130],"independent":[131],"number":[134],"variables":[137],"under":[138],"assumptions.":[140],"fact":[142],"applies":[146],"to":[147,154],"general":[148],"factorisations":[149],"covariance":[152],"sample":[155],"field.":[158],"error":[160],"fully":[165],"discrete":[166],"finite":[167],"element":[168],"allows":[170],"locally":[172],"refined":[173],"meshes":[174],"(via":[175],"interpolation":[176],"from":[177],"grid":[181],"field).":[185],"Numerical":[186],"results":[187],"non-regular":[190],"domain":[191,203],"corner":[193],"singularities":[194],"two":[196],"spatial":[197,206],"dimensions":[198,207],"three":[205],"are":[208],"included.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2}],"updated_date":"2026-05-11T08:15:01.531666","created_date":"2025-10-10T00:00:00"}