{"id":"https://openalex.org/W838268176","doi":"https://doi.org/10.1137/140971531","title":"A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection","display_name":"A Hyperspherical Adaptive Sparse-Grid Method for High-Dimensional Discontinuity Detection","publication_year":2015,"publication_date":"2015-01-01","ids":{"openalex":"https://openalex.org/W838268176","doi":"https://doi.org/10.1137/140971531","mag":"838268176"},"language":"en","primary_location":{"id":"doi:10.1137/140971531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140971531","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":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://www.osti.gov/biblio/1302912","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","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":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)","institution_ids":["https://openalex.org/I1289243028"]}]},{"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. Webster","raw_affiliation_strings":["Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)","institution_ids":["https://openalex.org/I1289243028"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5076283476","display_name":"Max Gunzburger","orcid":"https://orcid.org/0000-0003-0921-9079"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M. Gunzburger","raw_affiliation_strings":["Florida State Univ., Tallahassee, FL (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State Univ., Tallahassee, FL (United States)","institution_ids":["https://openalex.org/I103163165"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024090165","display_name":"John Burkardt","orcid":"https://orcid.org/0000-0003-0273-2769"},"institutions":[{"id":"https://openalex.org/I103163165","display_name":"Florida State University","ror":"https://ror.org/05g3dte14","country_code":"US","type":"education","lineage":["https://openalex.org/I103163165"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Burkardt","raw_affiliation_strings":["Florida State Univ., Tallahassee, FL (United States)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Florida State Univ., Tallahassee, FL (United States)","institution_ids":["https://openalex.org/I103163165"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.0344,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.89701284,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"53","issue":"3","first_page":"1508","last_page":"1536"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10928","display_name":"Probabilistic and Robust Engineering Design","score":0.9998999834060669,"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":0.9998999834060669,"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":0.989799976348877,"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/T11366","display_name":"Elasticity and Material Modeling","score":0.989300012588501,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical 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/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.8272085189819336},{"id":"https://openalex.org/keywords/discontinuity","display_name":"Discontinuity (linguistics)","score":0.8268260955810547},{"id":"https://openalex.org/keywords/hypersurface","display_name":"Hypersurface","score":0.6841278076171875},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.6098713874816895},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.6022098660469055},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.5941723585128784},{"id":"https://openalex.org/keywords/transformation","display_name":"Transformation (genetics)","score":0.5605061650276184},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5184606909751892},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5108491778373718},{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.5067012906074524},{"id":"https://openalex.org/keywords/computational-complexity-theory","display_name":"Computational complexity theory","score":0.48037299513816833},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4284498691558838},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.42462795972824097},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.42337608337402344},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3978808522224426},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.20504054427146912},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.16757869720458984}],"concepts":[{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.8272085189819336},{"id":"https://openalex.org/C2777042112","wikidata":"https://www.wikidata.org/wiki/Q5281658","display_name":"Discontinuity (linguistics)","level":2,"score":0.8268260955810547},{"id":"https://openalex.org/C114410712","wikidata":"https://www.wikidata.org/wiki/Q973321","display_name":"Hypersurface","level":2,"score":0.6841278076171875},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.6098713874816895},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.6022098660469055},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.5941723585128784},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.5605061650276184},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5184606909751892},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5108491778373718},{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.5067012906074524},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.48037299513816833},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4284498691558838},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.42462795972824097},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.42337608337402344},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3978808522224426},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.20504054427146912},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.16757869720458984},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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":2,"locations":[{"id":"doi:10.1137/140971531","is_oa":false,"landing_page_url":"https://doi.org/10.1137/140971531","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:osti.gov:1302912","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1302912","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null}],"best_oa_location":{"id":"pmh:oai:osti.gov:1302912","is_oa":true,"landing_page_url":"https://www.osti.gov/biblio/1302912","pdf_url":null,"source":{"id":"https://openalex.org/S4306402487","display_name":"OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I139351228","host_organization_name":"Office of Scientific and Technical Information","host_organization_lineage":["https://openalex.org/I139351228"],"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":null},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W71671705","https://openalex.org/W176737369","https://openalex.org/W1646309082","https://openalex.org/W1970476229","https://openalex.org/W1982421072","https://openalex.org/W1983156129","https://openalex.org/W1998213879","https://openalex.org/W1998917464","https://openalex.org/W2002274796","https://openalex.org/W2013576021","https://openalex.org/W2015740317","https://openalex.org/W2020717814","https://openalex.org/W2040727702","https://openalex.org/W2072205359","https://openalex.org/W2073043218","https://openalex.org/W2083845086","https://openalex.org/W2096969866","https://openalex.org/W2100474665","https://openalex.org/W2107359160","https://openalex.org/W2115225505","https://openalex.org/W2117122565","https://openalex.org/W2126447218","https://openalex.org/W2152469101","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2323190011","https://openalex.org/W3039499377","https://openalex.org/W162062087","https://openalex.org/W2085032340","https://openalex.org/W2026226327","https://openalex.org/W1989965977","https://openalex.org/W4241629433","https://openalex.org/W2056095867","https://openalex.org/W2232767080","https://openalex.org/W1756153455"],"abstract_inverted_index":{"This":[0],"work":[1],"proposes":[2],"and":[3,27],"analyzes":[4],"a":[5,42,59,63,86],"hyperspherical":[6,60,74],"adaptive":[7,32],"hierarchical":[8,115],"sparse-grid":[9,33,64],"method":[10,21,133],"for":[11,35],"detecting":[12],"jump":[13,103],"discontinuities":[14,104],"of":[15,30,45,49,54,58,66,95,130,145],"functions":[16],"in":[17,72],"high-dimensional":[18],"spaces.":[19],"The":[20],"is":[22,70,82],"motivated":[23],"by":[24,56,84],"the":[25,46,67,73,93,96,98,124,131,143,146],"theoretical":[26],"computational":[28,108],"inefficiencies":[29],"well-known":[31],"methods":[34],"discontinuity":[36,47,88],"detection.":[37],"Our":[38],"novel":[39],"approach":[40],"constructs":[41],"function":[43,69],"representation":[44],"hypersurface":[48],"an":[50],"$N$-dimensional":[51],"discontinuous":[52],"quantity":[53],"interest,":[55],"virtue":[57],"transformation.":[61],"Then,":[62],"approximation":[65],"transformed":[68],"built":[71],"coordinate":[75],"system,":[76],"whose":[77],"value":[78],"at":[79],"each":[80],"point":[81],"estimated":[83],"solving":[85],"one-dimensional":[87],"detection":[89],"problem.":[90],"Due":[91],"to":[92,111,121],"smoothness":[94],"hypersurface,":[97],"new":[99,132],"technique":[100],"can":[101],"identify":[102],"with":[105],"significantly":[106],"reduced":[107],"cost,":[109],"compared":[110],"existing":[112],"methods.":[113],"Moreover,":[114],"acceleration":[116],"techniques":[117],"are":[118,134,137],"also":[119],"incorporated":[120],"further":[122],"reduce":[123],"overall":[125],"complexity.":[126],"Rigorous":[127],"complexity":[128],"analyses":[129],"provided":[135],"as":[136],"several":[138],"numerical":[139],"examples":[140],"that":[141],"illustrate":[142],"effectiveness":[144],"approach.":[147]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}