{"id":"https://openalex.org/W2952498200","doi":"https://doi.org/10.1109/access.2019.2922292","title":"Learning Solutions for Electromagnetic Problems Using RBF Network-Based FE-LSSVM","display_name":"Learning Solutions for Electromagnetic Problems Using RBF Network-Based FE-LSSVM","publication_year":2019,"publication_date":"2019-01-01","ids":{"openalex":"https://openalex.org/W2952498200","doi":"https://doi.org/10.1109/access.2019.2922292","mag":"2952498200"},"language":"en","primary_location":{"id":"doi:10.1109/access.2019.2922292","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2922292","pdf_url":null,"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://doi.org/10.1109/access.2019.2922292","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5101405299","display_name":"Xiaoming Han","orcid":"https://orcid.org/0000-0002-5648-0483"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoming Han","raw_affiliation_strings":["School of Electrical Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100423680","display_name":"Zheng Liu","orcid":"https://orcid.org/0000-0002-2879-5859"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zheng Liu","raw_affiliation_strings":["School of Electrical Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100746489","display_name":"Jinjun Wang","orcid":"https://orcid.org/0000-0003-3733-7275"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jinjun Wang","raw_affiliation_strings":["School of Electrical Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100935793","display_name":"Ziku Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I146773158","display_name":"Qingdao Agricultural University","ror":"https://ror.org/051qwcj72","country_code":"CN","type":"education","lineage":["https://openalex.org/I146773158"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ziku Wu","raw_affiliation_strings":["Science and Information College, Qingdao Agricultural University, Qingdao, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Science and Information College, Qingdao Agricultural University, Qingdao, China","institution_ids":["https://openalex.org/I146773158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112412580","display_name":"Guofeng Li","orcid":null},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Guofeng Li","raw_affiliation_strings":["School of Electrical Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":"https://orcid.org/0000-0001-9403-2158","affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5047015759","display_name":"Yan Wu","orcid":"https://orcid.org/0000-0003-4293-9430"},"institutions":[{"id":"https://openalex.org/I27357992","display_name":"Dalian University of Technology","ror":"https://ror.org/023hj5876","country_code":"CN","type":"education","lineage":["https://openalex.org/I27357992"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yan Wu","raw_affiliation_strings":["School of Electrical Engineering, Dalian University of Technology, Dalian, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical Engineering, Dalian University of Technology, Dalian, China","institution_ids":["https://openalex.org/I27357992"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.3663,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.56099968,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"7","issue":null,"first_page":"80247","last_page":"80261"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.996999979019165,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"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/T10221","display_name":"Composite Structure Analysis and Optimization","score":0.9932000041007996,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/lagrange-multiplier","display_name":"Lagrange multiplier","score":0.7627443075180054},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.7247338891029358},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.5649375915527344},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.532912015914917},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.49039626121520996},{"id":"https://openalex.org/keywords/quadratic-programming","display_name":"Quadratic programming","score":0.47682541608810425},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46431657671928406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4439292848110199},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.43653643131256104},{"id":"https://openalex.org/keywords/electromagnetics","display_name":"Electromagnetics","score":0.42388927936553955},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.35947418212890625},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2461339235305786},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12895846366882324}],"concepts":[{"id":"https://openalex.org/C73684929","wikidata":"https://www.wikidata.org/wiki/Q598870","display_name":"Lagrange multiplier","level":2,"score":0.7627443075180054},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.7247338891029358},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.5649375915527344},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.532912015914917},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.49039626121520996},{"id":"https://openalex.org/C81845259","wikidata":"https://www.wikidata.org/wiki/Q290117","display_name":"Quadratic programming","level":2,"score":0.47682541608810425},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46431657671928406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4439292848110199},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.43653643131256104},{"id":"https://openalex.org/C2909720056","wikidata":"https://www.wikidata.org/wiki/Q11406","display_name":"Electromagnetics","level":2,"score":0.42388927936553955},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.35947418212890625},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2461339235305786},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12895846366882324},{"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/C24326235","wikidata":"https://www.wikidata.org/wiki/Q126095","display_name":"Electronic engineering","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:10.1109/access.2019.2922292","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2922292","pdf_url":null,"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:37c93bae4316405abefdedafe8bd82e1","is_oa":true,"landing_page_url":"https://doaj.org/article/37c93bae4316405abefdedafe8bd82e1","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 80247-80261 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2019.2922292","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2019.2922292","pdf_url":null,"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/G3859804199","display_name":null,"funder_award_id":"51607023","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G5275262758","display_name":null,"funder_award_id":"20170540179","funder_id":"https://openalex.org/F4320323086","funder_display_name":"Natural Science Foundation of Liaoning Province"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320323086","display_name":"Natural Science Foundation of Liaoning Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W1535382688","https://openalex.org/W1536466900","https://openalex.org/W1538983967","https://openalex.org/W1605773447","https://openalex.org/W2005195748","https://openalex.org/W2006338052","https://openalex.org/W2007052736","https://openalex.org/W2020087720","https://openalex.org/W2024303446","https://openalex.org/W2025574765","https://openalex.org/W2026656818","https://openalex.org/W2029546093","https://openalex.org/W2048763981","https://openalex.org/W2055139292","https://openalex.org/W2055223918","https://openalex.org/W2071849871","https://openalex.org/W2080977367","https://openalex.org/W2083691506","https://openalex.org/W2096318771","https://openalex.org/W2102871258","https://openalex.org/W2105561225","https://openalex.org/W2139557571","https://openalex.org/W2142136198","https://openalex.org/W2142151081","https://openalex.org/W2148666448","https://openalex.org/W2158150998","https://openalex.org/W2158985775","https://openalex.org/W2160425262","https://openalex.org/W2166789864","https://openalex.org/W2597142455","https://openalex.org/W2620253406","https://openalex.org/W4231132678","https://openalex.org/W4244829582","https://openalex.org/W4247533770","https://openalex.org/W6829038324"],"related_works":["https://openalex.org/W2074745806","https://openalex.org/W1600454385","https://openalex.org/W1997033546","https://openalex.org/W3120556963","https://openalex.org/W1979241556","https://openalex.org/W2105377028","https://openalex.org/W4379919368","https://openalex.org/W2370558260","https://openalex.org/W2157978609","https://openalex.org/W2973952456"],"abstract_inverted_index":{"Solutions":[0],"to":[1,81,121,139,186],"most":[2],"electromagnetic":[3,38,77,148,166],"problems":[4,78,167],"use":[5],"numerical":[6],"methods,":[7,30],"such":[8],"as":[9,68,103,184],"the":[10,25,55,61,65,69,97,110,114,125,135,142,147,153,158,161,172,188,191],"finite":[11,46],"element":[12,15,47],"method":[13,17,63,137,177,192],"(FEM),":[14],"free":[16],"(EFM),":[18],"and":[19,85,150,178],"soft":[20],"computing":[21],"method.":[22,72,174],"To":[23,156],"decrease":[24],"computational":[26],"complexities":[27],"of":[28,57,76,88,105,127,130,134,146,160,165,190],"these":[29],"this":[31,195],"paper":[32],"presents":[33],"an":[34,106],"approach":[35],"for":[36],"solving":[37],"problems,":[39],"called":[40],"radial":[41],"basis":[42],"function":[43],"(RBF)":[44],"network-based":[45],"least":[48],"square":[49],"support":[50],"vector":[51],"machine":[52],"(FE-LSSVM).":[53],"First,":[54],"expansion":[56],"approximate":[58],"solutions":[59],"by":[60,170],"proposed":[62,136,173,193],"uses":[64],"same":[66],"structure":[67],"RBF":[70],"network":[71],"Second,":[73],"governing":[74],"equations":[75,149],"are":[79,94,101,138,168,180],"transformed":[80,120],"weak":[82],"integral":[83],"forms":[84],"variational":[86],"formulations":[87],"FEM.":[89],"Finally,":[90],"Dirichlet":[91],"boundary":[92,144],"conditions":[93,145],"handled":[95],"in":[96,194],"LS-SVM":[98],"framework,":[99],"which":[100],"considered":[102],"constraints":[104],"optimization":[107],"problem.":[108],"By":[109],"Lagrange":[111],"multiplier":[112],"method,":[113,162],"quadratic":[115],"programming":[116],"problem":[117,123],"can":[118],"be":[119],"a":[122,128],"requiring":[124],"solution":[126],"system":[129],"equations.":[131],"The":[132],"advantages":[133,189],"directly":[140],"satisfy":[141],"natural":[143],"remarkably":[151],"improve":[152],"calculation":[154],"accuracy.":[155],"verify":[157],"efficiency":[159],"four":[163],"categories":[164],"investigated":[169],"using":[171],"An":[175],"analytical":[176],"FEM":[179],"also":[181],"carried":[182],"out":[183],"comparisons":[185],"prove":[187],"paper.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}