{"id":"https://openalex.org/W2929288974","doi":"https://doi.org/10.1109/access.2019.2908522","title":"Parallel Numerical Calculation on GPU for the 3-Dimensional Mathematical Model in the Walking Beam Reheating Furnace","display_name":"Parallel Numerical Calculation on GPU for the 3-Dimensional Mathematical Model in the Walking Beam Reheating Furnace","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2929288974","doi":"https://doi.org/10.1109/access.2019.2908522","mag":"2929288974"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2908522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2908522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08678757.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08678757.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5017261663","display_name":"Zhi Yang","orcid":"https://orcid.org/0000-0002-6959-8886"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhi Yang","raw_affiliation_strings":["State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China"],"raw_orcid":"https://orcid.org/0000-0002-6959-8886","affiliations":[{"raw_affiliation_string":"State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5103060588","display_name":"Xiaochuan Luo","orcid":"https://orcid.org/0000-0001-6886-1649"},"institutions":[{"id":"https://openalex.org/I9224756","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87","country_code":"CN","type":"education","lineage":["https://openalex.org/I9224756"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaochuan Luo","raw_affiliation_strings":["College of Information Science and Engineering, Northeastern University, Shenyang, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Information Science and Engineering, Northeastern University, Shenyang, China","institution_ids":["https://openalex.org/I9224756"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9224756"],"apc_list":{"value":1750,"currency":"USD","value_usd":1750},"apc_paid":{"value":1750,"currency":"USD","value_usd":1750},"fwci":0.7087,"has_fulltext":true,"cited_by_count":11,"citation_normalized_percentile":{"value":0.62712084,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"7","issue":null,"first_page":"44583","last_page":"44595"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12304","display_name":"Radiative Heat Transfer Studies","score":1.0,"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/T12304","display_name":"Radiative Heat Transfer Studies","score":1.0,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9952999949455261,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11012","display_name":"Gas Dynamics and Kinetic Theory","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7131903171539307},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7012485265731812},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.655807614326477},{"id":"https://openalex.org/keywords/graphics-processing-unit","display_name":"Graphics processing unit","score":0.6333619356155396},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.5457337498664856},{"id":"https://openalex.org/keywords/cuda","display_name":"CUDA","score":0.5324372053146362},{"id":"https://openalex.org/keywords/heat-transfer","display_name":"Heat transfer","score":0.5247951745986938},{"id":"https://openalex.org/keywords/thermal-conduction","display_name":"Thermal conduction","score":0.49723175168037415},{"id":"https://openalex.org/keywords/slab","display_name":"Slab","score":0.4949001669883728},{"id":"https://openalex.org/keywords/graphics","display_name":"Graphics","score":0.49407532811164856},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4662697911262512},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4492737054824829},{"id":"https://openalex.org/keywords/acceleration","display_name":"Acceleration","score":0.4106951355934143},{"id":"https://openalex.org/keywords/mechanics","display_name":"Mechanics","score":0.34139764308929443},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.28406429290771484},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.25241267681121826},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.15873286128044128},{"id":"https://openalex.org/keywords/computer-graphics","display_name":"Computer graphics (images)","score":0.11453679203987122},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.10328599810600281},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09512248635292053},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.07542094588279724}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7131903171539307},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7012485265731812},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.655807614326477},{"id":"https://openalex.org/C2779851693","wikidata":"https://www.wikidata.org/wiki/Q183484","display_name":"Graphics processing unit","level":2,"score":0.6333619356155396},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.5457337498664856},{"id":"https://openalex.org/C2778119891","wikidata":"https://www.wikidata.org/wiki/Q477690","display_name":"CUDA","level":2,"score":0.5324372053146362},{"id":"https://openalex.org/C50517652","wikidata":"https://www.wikidata.org/wiki/Q179635","display_name":"Heat transfer","level":2,"score":0.5247951745986938},{"id":"https://openalex.org/C172100665","wikidata":"https://www.wikidata.org/wiki/Q7465774","display_name":"Thermal conduction","level":2,"score":0.49723175168037415},{"id":"https://openalex.org/C113740112","wikidata":"https://www.wikidata.org/wiki/Q5904738","display_name":"Slab","level":2,"score":0.4949001669883728},{"id":"https://openalex.org/C21442007","wikidata":"https://www.wikidata.org/wiki/Q1027879","display_name":"Graphics","level":2,"score":0.49407532811164856},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4662697911262512},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4492737054824829},{"id":"https://openalex.org/C117896860","wikidata":"https://www.wikidata.org/wiki/Q11376","display_name":"Acceleration","level":2,"score":0.4106951355934143},{"id":"https://openalex.org/C57879066","wikidata":"https://www.wikidata.org/wiki/Q41217","display_name":"Mechanics","level":1,"score":0.34139764308929443},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.28406429290771484},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.25241267681121826},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.15873286128044128},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.11453679203987122},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.10328599810600281},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09512248635292053},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.07542094588279724},{"id":"https://openalex.org/C8058405","wikidata":"https://www.wikidata.org/wiki/Q46255","display_name":"Geophysics","level":1,"score":0.0},{"id":"https://openalex.org/C74650414","wikidata":"https://www.wikidata.org/wiki/Q11397","display_name":"Classical mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2019.2908522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2908522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08678757.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:eeed4cf4ded3487fa2956d723b7e751f","is_oa":true,"landing_page_url":"https://doaj.org/article/eeed4cf4ded3487fa2956d723b7e751f","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,"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":"IEEE Access, Vol 7, Pp 44583-44595 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2908522","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2908522","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8600701/08678757.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1584193577","display_name":null,"funder_award_id":"51634002","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3289329514","display_name":null,"funder_award_id":"2017YFB0304100","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4386282526","display_name":null,"funder_award_id":"N170708020","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6458503781","display_name":null,"funder_award_id":"2018RALKFKT008","funder_id":"https://openalex.org/F4320322429","funder_display_name":"Northeastern University"},{"id":"https://openalex.org/G7476430661","display_name":null,"funder_award_id":"51634002","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7501901109","display_name":null,"funder_award_id":"2017YFB0304100","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322429","display_name":"Northeastern University","ror":"https://ror.org/03awzbc87"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2929288974.pdf","grobid_xml":"https://content.openalex.org/works/W2929288974.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W579519726","https://openalex.org/W951087555","https://openalex.org/W1489767088","https://openalex.org/W1963967530","https://openalex.org/W1981113378","https://openalex.org/W1990662428","https://openalex.org/W2009821783","https://openalex.org/W2011015059","https://openalex.org/W2020139494","https://openalex.org/W2045281852","https://openalex.org/W2055842871","https://openalex.org/W2077470531","https://openalex.org/W2099696222","https://openalex.org/W2113190809","https://openalex.org/W2146876093","https://openalex.org/W2293642449","https://openalex.org/W2771800958","https://openalex.org/W2781504720","https://openalex.org/W3217003061","https://openalex.org/W4385293698","https://openalex.org/W6804959849","https://openalex.org/W6854960856"],"related_works":["https://openalex.org/W2119534391","https://openalex.org/W2023770367","https://openalex.org/W2503137108","https://openalex.org/W1966576946","https://openalex.org/W2020279179","https://openalex.org/W2765743988","https://openalex.org/W2062253548","https://openalex.org/W2393490604","https://openalex.org/W2393707426","https://openalex.org/W2229844714"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"the":[3,13,24,31,37,45,52,57,59,63,67,69,73,80,84,87,95,108,117,130,135,153,160,169,172,176,184,192,197],"parallel":[4,123,143],"numerical":[5],"simulations":[6],"of":[7,51,129,209],"3-dimensional":[8],"(3D)":[9],"mathematical":[10,47,90,105],"model":[11,91,119,137,162,174,178,195],"for":[12,94,134],"walking-beam":[14],"type":[15],"reheating":[16],"furnace":[17,38],"have":[18],"been":[19],"developed":[20],"and":[21,41,66,76,79,140,168,175],"implemented":[22],"on":[23,150],"graphics":[25],"processing":[26],"unit":[27],"(GPU)":[28],"architecture.":[29],"First,":[30],"detailed":[32,127],"heat":[33,54,60,70,81],"transfer":[34],"processes":[35],"in":[36,156],"are":[39],"described":[40],"categorized":[42],"when":[43],"building":[44],"3D":[46,89,131],"model.":[48],"They":[49],"consist":[50],"radiative":[53],"exchange":[55],"into":[56],"slab,":[58],"conduction":[61,82],"between":[62,72,171],"stationary":[64],"beams":[65],"slabs,":[68],"convection":[71],"gas":[74],"flow":[75],"slab":[77],"surfaces,":[78],"inside":[83],"slabs.":[85],"Moreover,":[86],"proposed":[88,118,136,161,193],"also":[92,180,213],"accounts":[93],"temperature-dependent":[96],"material":[97],"parameters,":[98],"which":[99],"is":[100,113,138,146,163,179,205],"ignored":[101],"by":[102,148],"most":[103],"published":[104],"models.":[106],"Second,":[107],"explicit":[109],"finite":[110],"difference":[111],"method":[112],"used":[114],"to":[115,120,182,202],"discretize":[116],"a":[121],"straightforward":[122],"computation":[124,198],"problem.":[125],"A":[126],"analysis":[128],"boundary":[132],"conditions":[133],"introduced":[139],"presented.":[141],"The":[142,187],"computing":[144],"problem":[145],"realized":[147],"programming":[149],"GPU":[151],"via":[152],"platform":[154],"CUDA":[155],"Tesla":[157],"P100.":[158],"Finally,":[159],"verified":[164],"with":[165],"industry":[166],"measurements":[167],"comparison":[170],"GPU-implementation":[173,194],"CPU-implementation":[177],"given":[181],"validate":[183],"great":[185],"acceleration.":[186],"experimental":[188],"results":[189],"prove":[190],"that":[191],"declines":[196],"time":[199],"from":[200],"hours":[201],"seconds.":[203],"It":[204],"not":[206],"only":[207],"orders":[208],"magnitude":[210],"faster":[211],"but":[212],"highly":[214],"accurate.":[215]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2}],"updated_date":"2026-08-28T12:50:07.497085","created_date":"2025-10-10T00:00:00"}
