{"id":"https://openalex.org/W4365813079","doi":"https://doi.org/10.1007/s00366-023-01819-6","title":"Near-boundary error reduction with an optimized weighted Dirichlet\u2013Neumann boundary condition for stochastic PDE-based Gaussian random field generators","display_name":"Near-boundary error reduction with an optimized weighted Dirichlet\u2013Neumann boundary condition for stochastic PDE-based Gaussian random field generators","publication_year":2023,"publication_date":"2023-04-15","ids":{"openalex":"https://openalex.org/W4365813079","doi":"https://doi.org/10.1007/s00366-023-01819-6"},"language":"en","primary_location":{"id":"doi:10.1007/s00366-023-01819-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00366-023-01819-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-023-01819-6.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"Engineering with Computers","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s00366-023-01819-6.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5004293946","display_name":"Evan John Ricketts","orcid":"https://orcid.org/0000-0001-8056-070X"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Evan John Ricketts","raw_affiliation_strings":["School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK"],"raw_orcid":"https://orcid.org/0000-0001-8056-070X","affiliations":[{"raw_affiliation_string":"School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK","institution_ids":["https://openalex.org/I79510175"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051229649","display_name":"Peter John Cleall","orcid":"https://orcid.org/0000-0002-4005-5319"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Peter John Cleall","raw_affiliation_strings":["School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK"],"raw_orcid":"https://orcid.org/0000-0002-4005-5319","affiliations":[{"raw_affiliation_string":"School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK","institution_ids":["https://openalex.org/I79510175"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085761291","display_name":"Tony Jefferson","orcid":"https://orcid.org/0000-0002-2050-2521"},"institutions":[{"id":"https://openalex.org/I79510175","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41","country_code":"GB","type":"education","lineage":["https://openalex.org/I79510175"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Tony Jefferson","raw_affiliation_strings":["School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK"],"raw_orcid":"https://orcid.org/0000-0002-2050-2521","affiliations":[{"raw_affiliation_string":"School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK","institution_ids":["https://openalex.org/I79510175"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014555327","display_name":"Pierre Kerfriden","orcid":"https://orcid.org/0000-0002-7749-3996"},"institutions":[{"id":"https://openalex.org/I2746051580","display_name":"Universit\u00e9 Paris Sciences et Lettres","ror":"https://ror.org/013cjyk83","country_code":"FR","type":"education","lineage":["https://openalex.org/I2746051580"]},{"id":"https://openalex.org/I4210108605","display_name":"Centre des Mat\u00e9riaux","ror":"https://ror.org/01q5ge486","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I4210091621","https://openalex.org/I4210095849","https://openalex.org/I4210108605","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Pierre Kerfriden","raw_affiliation_strings":["Centre de Mat\u00e9riaux, Mines Paris/PSL University, Evry, France"],"raw_orcid":"https://orcid.org/0000-0002-7749-3996","affiliations":[{"raw_affiliation_string":"Centre de Mat\u00e9riaux, Mines Paris/PSL University, Evry, France","institution_ids":["https://openalex.org/I4210108605","https://openalex.org/I2746051580"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111798354","display_name":"Paul Lyons","orcid":null},"institutions":[{"id":"https://openalex.org/I4210092143","display_name":"LUSAS (United Kingdom)","ror":"https://ror.org/00e7hrn50","country_code":"GB","type":"company","lineage":["https://openalex.org/I4210092143"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Paul Lyons","raw_affiliation_strings":["LUSAS, Surrey, UK"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"LUSAS, Surrey, UK","institution_ids":["https://openalex.org/I4210092143"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5004293946"],"corresponding_institution_ids":["https://openalex.org/I79510175"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":1.2636,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.81082505,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"39","issue":"6","first_page":"3821","last_page":"3833"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9994000196456909,"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":0.9994000196456909,"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/T11046","display_name":"Geotechnical Engineering and Analysis","score":0.9941999912261963,"subfield":{"id":"https://openalex.org/subfields/2213","display_name":"Safety, Risk, Reliability and Quality"},"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/T10770","display_name":"Soil Geostatistics and Mapping","score":0.9926000237464905,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7260552644729614},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.7002716064453125},{"id":"https://openalex.org/keywords/neumann-boundary-condition","display_name":"Neumann boundary condition","score":0.6921632289886475},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.5509931445121765},{"id":"https://openalex.org/keywords/weighting","display_name":"Weighting","score":0.5443971753120422},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.49601325392723083},{"id":"https://openalex.org/keywords/dirichlet-distribution","display_name":"Dirichlet distribution","score":0.49201056361198425},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4898383319377899},{"id":"https://openalex.org/keywords/mixed-boundary-condition","display_name":"Mixed boundary condition","score":0.48084506392478943},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.47627586126327515},{"id":"https://openalex.org/keywords/random-field","display_name":"Random field","score":0.451757550239563},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4457100033760071},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11052295565605164},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08098158240318298}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7260552644729614},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.7002716064453125},{"id":"https://openalex.org/C163681178","wikidata":"https://www.wikidata.org/wiki/Q1149279","display_name":"Neumann boundary condition","level":3,"score":0.6921632289886475},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.5509931445121765},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.5443971753120422},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.49601325392723083},{"id":"https://openalex.org/C169214877","wikidata":"https://www.wikidata.org/wiki/Q981016","display_name":"Dirichlet distribution","level":3,"score":0.49201056361198425},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4898383319377899},{"id":"https://openalex.org/C42045870","wikidata":"https://www.wikidata.org/wiki/Q2992268","display_name":"Mixed boundary condition","level":3,"score":0.48084506392478943},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.47627586126327515},{"id":"https://openalex.org/C130402806","wikidata":"https://www.wikidata.org/wiki/Q5361768","display_name":"Random field","level":2,"score":0.451757550239563},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4457100033760071},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11052295565605164},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08098158240318298},{"id":"https://openalex.org/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1007/s00366-023-01819-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00366-023-01819-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-023-01819-6.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"Engineering with Computers","raw_type":"journal-article"},{"id":"pmh:oai:https://orca.cardiff.ac.uk:158544","is_oa":true,"landing_page_url":null,"pdf_url":"https://orca.cardiff.ac.uk/id/eprint/158544/4/s00366-023-01819-6.pdf","source":{"id":"https://openalex.org/S4306401195","display_name":"ORCA Online Research @Cardiff (Cardiff University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I79510175","host_organization_name":"Cardiff University","host_organization_lineage":["https://openalex.org/I79510175"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:HAL:hal-04528224v1","is_oa":false,"landing_page_url":"https://hal.science/hal-04528224","pdf_url":null,"source":{"id":"https://openalex.org/S4406922466","display_name":"SPIRE - Sciences Po Institutional REpository","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Engineering with Computers, 2023, 39 (6), pp.3821-3833. ⟨10.1007/s00366-023-01819-6⟩","raw_type":"Journal articles"}],"best_oa_location":{"id":"doi:10.1007/s00366-023-01819-6","is_oa":true,"landing_page_url":"http://dx.doi.org/10.1007/s00366-023-01819-6","pdf_url":"https://link.springer.com/content/pdf/10.1007/s00366-023-01819-6.pdf","source":{"id":"https://openalex.org/S89333158","display_name":"Engineering With Computers","issn_l":"0177-0667","issn":["0177-0667","1435-5663"],"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":"Engineering with Computers","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320320350","display_name":"Cardiff University","ror":"https://ror.org/03kk7td41"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4365813079.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W1550944210","https://openalex.org/W1560225635","https://openalex.org/W1837874438","https://openalex.org/W2014619115","https://openalex.org/W2018476056","https://openalex.org/W2021218138","https://openalex.org/W2024825055","https://openalex.org/W2053739471","https://openalex.org/W2072660879","https://openalex.org/W2081010329","https://openalex.org/W2323750980","https://openalex.org/W2414025222","https://openalex.org/W2524251113","https://openalex.org/W2549108856","https://openalex.org/W2755742938","https://openalex.org/W2810932392","https://openalex.org/W2884854305","https://openalex.org/W2923135078","https://openalex.org/W2962980151","https://openalex.org/W2963199582","https://openalex.org/W2963824728","https://openalex.org/W2965144800","https://openalex.org/W2972777349","https://openalex.org/W3012672502","https://openalex.org/W3080110401","https://openalex.org/W4211049957","https://openalex.org/W4226291750"],"related_works":["https://openalex.org/W1514481392","https://openalex.org/W4322770021","https://openalex.org/W2020502833","https://openalex.org/W2100405323","https://openalex.org/W2059354999","https://openalex.org/W2767841216","https://openalex.org/W3203194254","https://openalex.org/W1988058848","https://openalex.org/W3098770929","https://openalex.org/W3155098563"],"abstract_inverted_index":{"Abstract":[0],"Random":[1],"field":[2,221],"generation":[3],"through":[4],"the":[5,36,51,55,59,63,71,78,82,87,97,101,118,122,134,150,155,161,175,183,196,202,211,215,220,224],"solution":[6],"of":[7,17,54,62,100,116,154,174,219],"stochastic":[8],"partial":[9],"differential":[10],"equations":[11],"is":[12,25,43,111,163,187],"a":[13,44,106,114,129,138,146,208,231],"computationally":[14],"inexpensive":[15],"method":[16],"introducing":[18],"spatial":[19],"variability":[20],"into":[21],"numerical":[22],"analyses.":[23],"This":[24,68],"particularly":[26],"important":[27],"in":[28,50,70,81,96,121,201],"systems":[29],"where":[30],"material":[31],"heterogeneity":[32],"has":[33],"influence":[34],"over":[35],"response":[37,80],"to":[38,58,94,136,149,189],"certain":[39],"stimuli.":[40],"Whilst":[41],"it":[42],"convenient":[45],"method,":[46],"spurious":[47],"values":[48,173],"arise":[49],"near":[52],"boundary":[53,65,89,109,198],"domain":[56],"due":[57],"non-exact":[60],"nature":[61],"specific":[64],"condition":[66,110,126],"applied.":[67],"change":[69],"correlation":[72,152,193],"structure":[73,120,153],"can":[74,92,227],"amplify":[75],"or":[76,142],"dampen":[77],"system":[79],"near-boundary":[83,123],"region":[84],"depending":[85],"on":[86,128,159],"chosen":[88,229],"condition,":[90],"and":[91,171,214],"lead":[93],"inconsistencies":[95],"overall":[98],"behaviour":[99],"system.":[102],"In":[103],"this":[104],"study,":[105],"weighted":[107,184],"Dirichlet\u2013Neumann":[108,185],"proposed":[112,170],"as":[113],"way":[115],"controlling":[117],"resulting":[119],"region.":[124],"The":[125],"relies":[127],"weighting":[130,167,176,212],"parameter":[131,177,213,218],"which":[132,160],"scales":[133],"application":[135],"have":[137],"more":[139,191],"dominant":[140],"Dirichlet":[141],"Neumann":[143],"component,":[144],"giving":[145],"closer":[147],"approximation":[148],"true":[151],"Mat\u00e9rn":[156],"autocorrelation":[157],"function":[158],"formulation":[162],"based":[164],"on.":[165],"Two":[166],"coefficients":[168],"are":[169,178],"optimal":[172,225],"provided.":[179],"Through":[180],"parametric":[181],"investigation,":[182],"approach":[186],"shown":[188],"yield":[190],"consistent":[192],"structures":[194],"than":[195],"common":[197],"conditions":[199],"applied":[200],"current":[203],"literature.":[204],"We":[205],"also":[206],"propose":[207],"relationship":[209],"between":[210],"desired":[216],"length-scale":[217],"such":[222],"that":[223],"value":[226],"be":[228],"for":[230],"given":[232],"problem.":[233]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}