{"id":"https://openalex.org/W2148930331","doi":"https://doi.org/10.1155/2013/398438","title":"Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems","display_name":"Efficient CUDA Polynomial Preconditioned Conjugate Gradient Solver for Finite Element Computation of Elasticity Problems","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2148930331","doi":"https://doi.org/10.1155/2013/398438","mag":"2148930331"},"language":"en","primary_location":{"id":"doi:10.1155/2013/398438","doi":"https://doi.org/10.1155/2013/398438","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/398438","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/398438.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"volume":null,"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://downloads.hindawi.com/journals/mpe/2013/398438.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100716809","display_name":"Jianfei Zhang","orcid":"https://orcid.org/0000-0003-3432-7637","observed_orcids":["https://orcid.org/0000-0003-3432-7637","https://orcid.org/0000-0002-6739-8688"]},"institutions":[{"id":"https://openalex.org/I163340411","display_name":"Hohai University","ror":"https://ror.org/01wd4xt90","country_code":"CN","type":"education","lineage":["https://openalex.org/I163340411"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jianfei Zhang","raw_affiliation_strings":["College of Mechanics and Materials, Hohai University, 1 Xikang Road, Nanjing 210098, China"],"raw_orcid":"https://orcid.org/0000-0003-3432-7637","affiliations":[{"raw_affiliation_string":"College of Mechanics and Materials, Hohai University, 1 Xikang Road, Nanjing 210098, China","institution_ids":["https://openalex.org/I163340411"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080088278","display_name":"Lei Zhang","orcid":"https://orcid.org/0000-0001-6149-1630","observed_orcids":["https://orcid.org/0000-0001-6149-1630"]},"institutions":[{"id":"https://openalex.org/I4210092032","display_name":"China Institute of Water Resources and Hydropower Research","ror":"https://ror.org/00m4czf33","country_code":"CN","type":"facility","lineage":["https://openalex.org/I4210092032"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["China Institute of Water Resources and Hydropower Research, Beijing 100044, China"],"raw_orcid":"https://orcid.org/0000-0001-6149-1630","affiliations":[{"raw_affiliation_string":"China Institute of Water Resources and Hydropower Research, Beijing 100044, China","institution_ids":["https://openalex.org/I4210092032"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100716809"],"corresponding_institution_ids":["https://openalex.org/I163340411"],"apc_list":{"value":2550,"currency":"USD","value_usd":2550},"apc_paid":{"value":2550,"currency":"USD","value_usd":2550},"fwci":3.2879,"has_fulltext":true,"cited_by_count":15,"citation_normalized_percentile":{"value":0.92222794,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2013","issue":null,"first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9413999915122986,"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"}},"topics":[{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9413999915122986,"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/T10054","display_name":"Parallel Computing and Optimization Techniques","score":0.05480000004172325,"subfield":{"id":"https://openalex.org/subfields/1708","display_name":"Hardware and Architecture"},"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.0012000000569969416,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/polynomial-preconditioning","display_name":"polynomial preconditioning","score":0.8840000033378601},{"id":"https://openalex.org/keywords/conjugate-gradient-solver","display_name":"conjugate gradient solver","score":0.8840000033378601},{"id":"https://openalex.org/keywords/gpu-computing","display_name":"GPU computing","score":0.7170000076293945},{"id":"https://openalex.org/keywords/cuda","display_name":"CUDA","score":0.9819999933242798},{"id":"https://openalex.org/keywords/elasticity-problems","display_name":"elasticity problems","score":0.7919999957084656},{"id":"https://openalex.org/keywords/finite-element-discretization","display_name":"finite element discretization","score":0.875},{"id":"https://openalex.org/keywords/sparse-matrix-storage","display_name":"sparse matrix storage","score":0.8230000138282776},{"id":"https://openalex.org/keywords/ellpack","display_name":"ELLPACK","score":0.7590000033378601},{"id":"https://openalex.org/keywords/mixed-precision","display_name":"mixed precision","score":0.8650000095367432},{"id":"https://openalex.org/keywords/sparse-linear-systems","display_name":"sparse linear systems","score":0.5419999957084656}],"concepts":[{"id":"https://openalex.org/C167431342","wikidata":"https://www.wikidata.org/wiki/Q1754327","display_name":"Preconditioner","level":3,"score":0.7980477213859558},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7422719597816467},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.6738635301589966},{"id":"https://openalex.org/C81184566","wikidata":"https://www.wikidata.org/wiki/Q1191895","display_name":"Conjugate gradient method","level":2,"score":0.6653640270233154},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.640407919883728},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6392847299575806},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.5848413705825806},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.5755656361579895},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5176118612289429},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5008265972137451},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.4907001256942749},{"id":"https://openalex.org/C2779851693","wikidata":"https://www.wikidata.org/wiki/Q183484","display_name":"Graphics processing unit","level":2,"score":0.4843684136867523},{"id":"https://openalex.org/C121854251","wikidata":"https://www.wikidata.org/wiki/Q62932","display_name":"Elasticity (physics)","level":2,"score":0.475000262260437},{"id":"https://openalex.org/C188045654","wikidata":"https://www.wikidata.org/wiki/Q17148339","display_name":"Memory bandwidth","level":2,"score":0.425582617521286},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.42215585708618164},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.376284658908844},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.2898062765598297},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.27559787034988403},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2013/398438","doi":"https://doi.org/10.1155/2013/398438","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/398438","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/398438.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},{"id":"pmh:oai:RePEc:hin:jnlmpe:398438","doi":null,"is_oa":false,"landing_page_url":"http://downloads.hindawi.com/journals/MPE/2013/398438.xml","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:8a3d1b6ab60c4cb79007800dbbed6ad3","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/8a3d1b6ab60c4cb79007800dbbed6ad3","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Mathematical Problems in Engineering, Vol 2013 (2013)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2013/398438","doi":"https://doi.org/10.1155/2013/398438","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2013/398438","pdf_url":"https://downloads.hindawi.com/journals/mpe/2013/398438.pdf","source":{"id":"https://openalex.org/S178238111","display_name":"Mathematical Problems in Engineering","issn_l":"1024-123X","issn":["1024-123X","1026-7077","1563-5147"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-scientific","cwts-core","poland-20","vabb-shw"],"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematical Problems in Engineering","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3789126216","display_name":null,"funder_award_id":"51109072","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2148930331.pdf","grobid_xml":"https://content.openalex.org/works/W2148930331.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W168866822","https://openalex.org/W1506342804","https://openalex.org/W1541162015","https://openalex.org/W1588915715","https://openalex.org/W1965034778","https://openalex.org/W1965512225","https://openalex.org/W1983771518","https://openalex.org/W1995649289","https://openalex.org/W2010580757","https://openalex.org/W2021261510","https://openalex.org/W2054316636","https://openalex.org/W2065721576","https://openalex.org/W2065816298","https://openalex.org/W2076485756","https://openalex.org/W2078391824","https://openalex.org/W2108157916","https://openalex.org/W2116808829","https://openalex.org/W2117686912","https://openalex.org/W2117752372","https://openalex.org/W2128539477","https://openalex.org/W2135063202","https://openalex.org/W2167622672","https://openalex.org/W2295862081","https://openalex.org/W4250981202"],"related_works":["https://openalex.org/W2516005922","https://openalex.org/W2055685501","https://openalex.org/W1970627903","https://openalex.org/W357369717","https://openalex.org/W2588911004","https://openalex.org/W2552618867","https://openalex.org/W4372359475","https://openalex.org/W1900162302","https://openalex.org/W3139976910","https://openalex.org/W387381159"],"abstract_inverted_index":{"Graphics":[0],"processing":[1],"unit":[2],"(GPU)":[3],"has":[4],"obtained":[5],"great":[6],"success":[7],"in":[8,83,102],"scientific":[9],"computations":[10],"for":[11,34,112],"its":[12,113],"tremendous":[13],"computational":[14],"horsepower":[15],"and":[16,85,138,155],"very":[17],"high":[18],"memory":[19],"bandwidth.":[20],"This":[21],"paper":[22],"discusses":[23],"the":[24,35,89,92,121,133,146,149,159],"efficient":[25],"way":[26],"to":[27,57,105,131,141,171],"implement":[28],"polynomial":[29,95],"preconditioned":[30,162],"conjugate":[31],"gradient":[32],"solver":[33,104],"finite":[36,63,106],"element":[37,64,107],"computation":[38],"of":[39,66,145,148,168],"elasticity":[40,67,111],"on":[41,116],"NVIDIA":[42],"GPUs":[43],"using":[44],"compute":[45],"unified":[46],"device":[47],"architecture":[48],"(CUDA).":[49],"Sliced":[50],"block":[51],"ELLPACK":[52],"(SBELL)":[53],"format":[54,154],"is":[55,97,127],"introduced":[56],"store":[58],"sparse":[59],"matrix":[60],"arising":[61],"from":[62,110],"discretization":[65],"with":[68],"fewer":[69],"padding":[70],"zeros":[71],"than":[72],"traditional":[73],"ELLPACK-based":[74],"formats.":[75],"Polynomial":[76],"preconditioning":[77],"methods":[78],"have":[79],"been":[80],"investigated":[81],"both":[82],"convergence":[84],"running":[86],"time.":[87],"From":[88],"overall":[90,134],"performance,":[91],"least-squares":[93],"(L-S)":[94],"method":[96],"chosen":[98],"as":[99],"a":[100,166],"preconditioner":[101],"PCG":[103,122],"equations":[108],"derived":[109],"best":[114],"results":[115],"different":[117],"example":[118],"meshes.":[119],"In":[120],"solver,":[123],"mixed":[124,156],"precision":[125,157],"algorithm":[126],"used":[128],"not":[129],"only":[130],"reduce":[132],"computational,":[135],"storage":[136],"requirements":[137],"bandwidth":[139],"but":[140],"make":[142],"full":[143],"use":[144],"capacity":[147],"GPU":[150],"devices.":[151],"With":[152],"SBELL":[153],"algorithm,":[158],"GPU-based":[160],"L-S":[161],"CG":[163],"can":[164],"get":[165],"speedup":[167],"about":[169],"7\u20139":[170],"CPU-implementation.":[172]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":2}],"updated_date":"2026-10-14T16:39:01.820549","created_date":"2016-06-24T00:00:00"}