{"id":"https://openalex.org/W2091280316","doi":"https://doi.org/10.1137/100787842","title":"Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems","display_name":"Efficient Spectral Sparse Grid Methods and Applications to High-Dimensional Elliptic Problems","publication_year":2010,"publication_date":"2010-01-01","ids":{"openalex":"https://openalex.org/W2091280316","doi":"https://doi.org/10.1137/100787842","mag":"2091280316"},"language":"en","primary_location":{"id":"doi:10.1137/100787842","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100787842","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":"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/A5028981574","display_name":"Jie Shen","orcid":"https://orcid.org/0000-0002-4885-5732"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jie Shen","raw_affiliation_strings":["shen7@purdue.edu#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"shen7@purdue.edu#TAB#","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080825351","display_name":"Haijun Yu","orcid":"https://orcid.org/0000-0002-5742-0327"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Haijun Yu","raw_affiliation_strings":["hyu@lsec.cc.ac.cn#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"hyu@lsec.cc.ac.cn#TAB#","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":3.0874,"has_fulltext":false,"cited_by_count":81,"citation_normalized_percentile":{"value":0.91716203,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":99},"biblio":{"volume":"32","issue":"6","first_page":"3228","last_page":"3250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/sparse-grid","display_name":"Sparse grid","score":0.878778338432312},{"id":"https://openalex.org/keywords/sparse-matrix","display_name":"Sparse matrix","score":0.6401005983352661},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6221304535865784},{"id":"https://openalex.org/keywords/solver","display_name":"Solver","score":0.6221051812171936},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5587060451507568},{"id":"https://openalex.org/keywords/sparse-approximation","display_name":"Sparse approximation","score":0.540979266166687},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.5335692763328552},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5181490182876587},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.4936927258968353},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4896469712257385},{"id":"https://openalex.org/keywords/discontinuous-galerkin-method","display_name":"Discontinuous Galerkin method","score":0.4734960198402405},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.47112083435058594},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.457690566778183},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.45450833439826965},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.4427162706851959},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4141170382499695},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.3300333023071289},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2884829640388489},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.20639029145240784},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15417107939720154},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.1183755099773407},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08463191986083984}],"concepts":[{"id":"https://openalex.org/C156439662","wikidata":"https://www.wikidata.org/wiki/Q7573793","display_name":"Sparse grid","level":2,"score":0.878778338432312},{"id":"https://openalex.org/C56372850","wikidata":"https://www.wikidata.org/wiki/Q1050404","display_name":"Sparse matrix","level":3,"score":0.6401005983352661},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6221304535865784},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.6221051812171936},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5587060451507568},{"id":"https://openalex.org/C124066611","wikidata":"https://www.wikidata.org/wiki/Q28684319","display_name":"Sparse approximation","level":2,"score":0.540979266166687},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.5335692763328552},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5181490182876587},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.4936927258968353},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4896469712257385},{"id":"https://openalex.org/C92244383","wikidata":"https://www.wikidata.org/wiki/Q428273","display_name":"Discontinuous Galerkin method","level":3,"score":0.4734960198402405},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47112083435058594},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.457690566778183},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.45450833439826965},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.4427162706851959},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4141170382499695},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3300333023071289},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2884829640388489},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.20639029145240784},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15417107939720154},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.1183755099773407},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08463191986083984},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","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/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"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/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/100787842","is_oa":false,"landing_page_url":"https://doi.org/10.1137/100787842","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:CiteSeerX.psu:10.1.1.299.5394","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.299.5394","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.math.purdue.edu/~shen/pub/SISC10.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1523888516","display_name":null,"funder_award_id":"FA9550-","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G5919228138","display_name":null,"funder_award_id":"FA9550-11-1-0328","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"},{"id":"https://openalex.org/G7807745527","display_name":null,"funder_award_id":"FA9550-11","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":21,"referenced_works":["https://openalex.org/W1494602634","https://openalex.org/W1601540052","https://openalex.org/W1646309082","https://openalex.org/W1987902628","https://openalex.org/W1997701847","https://openalex.org/W2001257392","https://openalex.org/W2012708209","https://openalex.org/W2046683716","https://openalex.org/W2051917325","https://openalex.org/W2052806039","https://openalex.org/W2061496185","https://openalex.org/W2075490698","https://openalex.org/W2082849992","https://openalex.org/W2132119675","https://openalex.org/W2142863015","https://openalex.org/W2165083863","https://openalex.org/W2167512083","https://openalex.org/W2403013574","https://openalex.org/W2410898212","https://openalex.org/W2948315021","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2980465122","https://openalex.org/W2361346113","https://openalex.org/W2963412993","https://openalex.org/W2372064402","https://openalex.org/W3115345692","https://openalex.org/W2002575138","https://openalex.org/W2253211697","https://openalex.org/W2549535467","https://openalex.org/W2515728595","https://openalex.org/W2998356720"],"abstract_inverted_index":{"We":[0],"develop":[1,31],"in":[2,51],"this":[3],"paper":[4],"some":[5],"efficient":[6,66],"algorithms":[7],"which":[8],"are":[9,119],"essential":[10],"to":[11,81,121],"implementations":[12],"of":[13,49,90,95,127],"spectral":[14],"methods":[15,69,99],"on":[16,24,101],"the":[17,36,40,43,47,58,77,123],"sparse":[18,44,67,83,97,114],"grid":[19,45,98],"by":[20,56,111],"Smolyak's":[21],"construction":[22],"based":[23,100],"a":[25,32,52,71,82,86,112],"nested":[26],"quadrature.":[27],"More":[28],"precisely,":[29],"we":[30,62],"fast":[33,60],"algorithm":[34],"for":[35,70],"discrete":[37],"transform":[38],"between":[39],"values":[41],"at":[42],"and":[46,55,106,125],"coefficients":[48],"expansion":[50],"hierarchical":[53],"basis;":[54],"using":[57],"aforementioned":[59],"transform,":[61],"construct":[63],"two":[64],"very":[65],"spectral-Galerkin":[68],"model":[72],"elliptic":[73],"equation.":[74],"In":[75],"particular,":[76],"Chebyshev\u2013Legendre\u2013Galerkin":[78],"method":[79],"leads":[80],"matrix":[84],"with":[85],"much":[87],"lower":[88],"number":[89],"nonzero":[91],"elements":[92,103],"than":[93],"that":[94],"low-order":[96],"finite":[102],"or":[104],"wavelets,":[105],"can":[107],"be":[108],"efficiently":[109],"solved":[110],"suitable":[113],"solver.":[115],"Ample":[116],"numerical":[117],"results":[118],"presented":[120],"demonstrate":[122],"efficiency":[124],"accuracy":[126],"our":[128],"algorithms.":[129]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":9},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
