{"id":"https://openalex.org/W4415967578","doi":"https://doi.org/10.3390/computation13110262","title":"An Efficient Filter Implementation Method and Its Applications in Topology Optimization Utilizing k-d Tree Data Structure","display_name":"An Efficient Filter Implementation Method and Its Applications in Topology Optimization Utilizing k-d Tree Data Structure","publication_year":2025,"publication_date":"2025-11-06","ids":{"openalex":"https://openalex.org/W4415967578","doi":"https://doi.org/10.3390/computation13110262"},"language":"en","primary_location":{"id":"doi:10.3390/computation13110262","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13110262","pdf_url":"https://www.mdpi.com/2079-3197/13/11/262/pdf","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2079-3197/13/11/262/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111927056","display_name":"Jingbo Huang","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jingbo Huang","raw_affiliation_strings":["School of New Energy, North China Electric Power University, Beijing 102206, China"],"affiliations":[{"raw_affiliation_string":"School of New Energy, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007321625","display_name":"Amany AbdElSamea Saeed","orcid":"https://orcid.org/0009-0008-3281-5489"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ayesha Saeed","raw_affiliation_strings":["School of New Energy, North China Electric Power University, Beijing 102206, China"],"affiliations":[{"raw_affiliation_string":"School of New Energy, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102746659","display_name":"Kai Long","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Long","raw_affiliation_strings":["School of New Energy, North China Electric Power University, Beijing 102206, China"],"affiliations":[{"raw_affiliation_string":"School of New Energy, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5102843025","display_name":"Yu-Tang Chen","orcid":"https://orcid.org/0000-0003-4669-5074"},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yutang Chen","raw_affiliation_strings":["School of New Energy, North China Electric Power University, Beijing 102206, China"],"affiliations":[{"raw_affiliation_string":"School of New Energy, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108516578","display_name":"Rongrong Geng","orcid":null},"institutions":[{"id":"https://openalex.org/I153473198","display_name":"North China Electric Power University","ror":"https://ror.org/04qr5t414","country_code":"CN","type":"education","lineage":["https://openalex.org/I153473198"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Rongrong Geng","raw_affiliation_strings":["School of New Energy, North China Electric Power University, Beijing 102206, China"],"affiliations":[{"raw_affiliation_string":"School of New Energy, North China Electric Power University, Beijing 102206, China","institution_ids":["https://openalex.org/I153473198"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101775320","display_name":"Jiao Jia","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jiao Jia","raw_affiliation_strings":["Flying College, Beihang University, Beijing 100191, China"],"affiliations":[{"raw_affiliation_string":"Flying College, Beihang University, Beijing 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":null,"display_name":"Tao Tao","orcid":"https://orcid.org/0000-0002-6392-1902"},"institutions":[{"id":"https://openalex.org/I74872605","display_name":"China Southern Power Grid (China)","ror":"https://ror.org/03hkh9419","country_code":"CN","type":"company","lineage":["https://openalex.org/I74872605"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Tao Tao","raw_affiliation_strings":["China Southern Power Grid Technology Co., Ltd., Guangzhou 510080, China"],"affiliations":[{"raw_affiliation_string":"China Southern Power Grid Technology Co., Ltd., Guangzhou 510080, China","institution_ids":["https://openalex.org/I74872605"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":7,"corresponding_author_ids":["https://openalex.org/A5111927056"],"corresponding_institution_ids":["https://openalex.org/I153473198"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.33110208,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"11","first_page":"262","last_page":"262"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11115","display_name":"Topology Optimization in Engineering","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural Engineering"},"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/T11115","display_name":"Topology Optimization in Engineering","score":0.9706000089645386,"subfield":{"id":"https://openalex.org/subfields/2205","display_name":"Civil and Structural 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/T10100","display_name":"Metaheuristic Optimization Algorithms Research","score":0.007199999876320362,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/T11522","display_name":"VLSI and FPGA Design Techniques","score":0.005200000014156103,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/topology-optimization","display_name":"Topology optimization","score":0.6690000295639038},{"id":"https://openalex.org/keywords/scalability","display_name":"Scalability","score":0.6654999852180481},{"id":"https://openalex.org/keywords/design-for-manufacturability","display_name":"Design for manufacturability","score":0.5895000100135803},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.4738999903202057},{"id":"https://openalex.org/keywords/filter","display_name":"Filter (signal processing)","score":0.4731000065803528},{"id":"https://openalex.org/keywords/tree","display_name":"Tree (set theory)","score":0.46700000762939453},{"id":"https://openalex.org/keywords/constraint","display_name":"Constraint (computer-aided design)","score":0.383899986743927},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.3815999925136566},{"id":"https://openalex.org/keywords/data-structure","display_name":"Data structure","score":0.36559998989105225}],"concepts":[{"id":"https://openalex.org/C189216461","wikidata":"https://www.wikidata.org/wiki/Q2443456","display_name":"Topology optimization","level":3,"score":0.6690000295639038},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.6654999852180481},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6603999733924866},{"id":"https://openalex.org/C62064638","wikidata":"https://www.wikidata.org/wiki/Q553878","display_name":"Design for manufacturability","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.4738999903202057},{"id":"https://openalex.org/C106131492","wikidata":"https://www.wikidata.org/wiki/Q3072260","display_name":"Filter (signal processing)","level":2,"score":0.4731000065803528},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.46700000762939453},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4034000039100647},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.383899986743927},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.36559998989105225},{"id":"https://openalex.org/C110850998","wikidata":"https://www.wikidata.org/wiki/Q5377895","display_name":"Engineering optimization","level":3,"score":0.36480000615119934},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.3582000136375427},{"id":"https://openalex.org/C34972735","wikidata":"https://www.wikidata.org/wiki/Q2920267","display_name":"Engineering design process","level":2,"score":0.3540000021457672},{"id":"https://openalex.org/C199845137","wikidata":"https://www.wikidata.org/wiki/Q145490","display_name":"Network topology","level":2,"score":0.3357999920845032},{"id":"https://openalex.org/C163797641","wikidata":"https://www.wikidata.org/wiki/Q2067937","display_name":"Tree structure","level":3,"score":0.33149999380111694},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.32679998874664307},{"id":"https://openalex.org/C113775141","wikidata":"https://www.wikidata.org/wiki/Q428691","display_name":"Computer engineering","level":1,"score":0.32100000977516174},{"id":"https://openalex.org/C120314980","wikidata":"https://www.wikidata.org/wiki/Q180634","display_name":"Distributed computing","level":1,"score":0.2987000048160553},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.2953000068664551},{"id":"https://openalex.org/C20556612","wikidata":"https://www.wikidata.org/wiki/Q4469374","display_name":"Volume (thermodynamics)","level":2,"score":0.2831000089645386},{"id":"https://openalex.org/C164752517","wikidata":"https://www.wikidata.org/wiki/Q5570875","display_name":"Global optimization","level":2,"score":0.2777999937534332},{"id":"https://openalex.org/C75684735","wikidata":"https://www.wikidata.org/wiki/Q858810","display_name":"Big data","level":2,"score":0.2759999930858612},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2720000147819519},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.2700999975204468},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.25760000944137573}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/computation13110262","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13110262","pdf_url":"https://www.mdpi.com/2079-3197/13/11/262/pdf","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6f559de2a97b4cafbbb0660ce4077876","is_oa":true,"landing_page_url":"https://doaj.org/article/6f559de2a97b4cafbbb0660ce4077876","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computation, Vol 13, Iss 11, p 262 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/computation13110262","is_oa":true,"landing_page_url":"https://doi.org/10.3390/computation13110262","pdf_url":"https://www.mdpi.com/2079-3197/13/11/262/pdf","source":{"id":"https://openalex.org/S2738402919","display_name":"Computation","issn_l":"2079-3197","issn":["2079-3197"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1121271761","display_name":null,"funder_award_id":"Program","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2087396116","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2376276132","display_name":null,"funder_award_id":"China","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3317480652","display_name":null,"funder_award_id":"Science","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G4089523286","display_name":null,"funder_award_id":"2024YFE0208600","funder_id":"https://openalex.org/F4320335777","funder_display_name":"National Key Research and Development Program of China"},{"id":"https://openalex.org/G4380771912","display_name":null,"funder_award_id":"2024JC006","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G5994120800","display_name":null,"funder_award_id":"Natural","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6419518294","display_name":null,"funder_award_id":"U24B2090","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320335777","display_name":"National Key Research and Development Program of China","ror":null},{"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/W4415967578.pdf","grobid_xml":"https://content.openalex.org/works/W4415967578.grobid-xml"},"referenced_works_count":47,"referenced_works":["https://openalex.org/W1971654819","https://openalex.org/W1975383645","https://openalex.org/W1977282511","https://openalex.org/W1985881781","https://openalex.org/W2004945242","https://openalex.org/W2005703693","https://openalex.org/W2008720816","https://openalex.org/W2016413885","https://openalex.org/W2024127739","https://openalex.org/W2024978924","https://openalex.org/W2057091215","https://openalex.org/W2062523101","https://openalex.org/W2069697210","https://openalex.org/W2085015317","https://openalex.org/W2086674516","https://openalex.org/W2087210082","https://openalex.org/W2087540212","https://openalex.org/W2092801729","https://openalex.org/W2103185791","https://openalex.org/W2105836510","https://openalex.org/W2110696842","https://openalex.org/W2120191698","https://openalex.org/W2122397978","https://openalex.org/W2126092109","https://openalex.org/W2132034927","https://openalex.org/W2137726847","https://openalex.org/W2141377530","https://openalex.org/W2151041746","https://openalex.org/W2153105597","https://openalex.org/W2158783554","https://openalex.org/W2158862486","https://openalex.org/W2508135389","https://openalex.org/W2754505824","https://openalex.org/W2800367159","https://openalex.org/W3005713713","https://openalex.org/W3011719997","https://openalex.org/W3028550316","https://openalex.org/W3036097547","https://openalex.org/W3105070525","https://openalex.org/W3131165666","https://openalex.org/W4308842817","https://openalex.org/W4310118322","https://openalex.org/W4366773037","https://openalex.org/W4367047444","https://openalex.org/W4380051981","https://openalex.org/W4393135290","https://openalex.org/W4406325744"],"related_works":[],"abstract_inverted_index":{"Topology":[0],"optimization":[1,43,122,144],"(TO)":[2],"with":[3,24],"the":[4,28,42,47,99],"variable":[5],"density":[6],"concept":[7],"has":[8],"made":[9],"significant":[10],"advancements":[11],"in":[12,27,119,142,152],"academic":[13],"research":[14],"and":[15,89,124],"engineering":[16,153],"applications;":[17],"yet":[18],"it":[19],"still":[20],"encounters":[21],"obstacles":[22],"associated":[23],"computer":[25],"inefficiencies":[26],"filtering":[29],"process.":[30],"This":[31,69,132],"work":[32],"introduces":[33],"a":[34,73,135],"novel":[35],"filter":[36],"implementation":[37],"method":[38,54,70,115],"that":[39],"significantly":[40],"enhances":[41],"process":[44],"by":[45],"adapting":[46],"k-d":[48],"tree":[49],"data":[50,147],"structure.":[51],"The":[52,114],"proposed":[53,100],"converts":[55],"traditional":[56],"neighborhood":[57],"search":[58],"operations":[59],"into":[60],"extremely":[61],"efficient":[62],"spatial":[63],"searches":[64],"while":[65],"preserving":[66],"solution":[67],"accuracy.":[68],"inherently":[71],"accommodates":[72],"comprehensive":[74],"array":[75],"of":[76],"manufacturability":[77],"constraints,":[78],"including":[79],"symmetry,":[80],"local":[81],"volume":[82],"control,":[83,88],"periodic":[84],"patterning,":[85],"stamping-oriented":[86],"overhang":[87],"more,":[90],"without":[91],"compromising":[92],"computational":[93],"duration.":[94],"Extensive":[95],"numerical":[96],"examples":[97],"validate":[98],"method\u2019s":[101],"efficiency":[102],"yielding":[103],"precise,":[104],"scalable":[105],"designs,":[106],"achieving":[107],"substantial":[108],"acceleration":[109],"relative":[110],"to":[111],"conventional":[112],"methods":[113],"demonstrates":[116],"specific":[117],"advantage":[118],"large":[120],"scale":[121],"challenges":[123],"intricate":[125],"complex":[126],"geometric":[127],"restrictions,":[128],"encompassing":[129],"unstructured":[130],"meshes.":[131],"study":[133],"explores":[134],"new":[136],"paradigm":[137],"for":[138],"effective":[139],"constraint":[140],"integration":[141],"topology":[143],"through":[145],"advanced":[146],"structures,":[148],"providing":[149],"extensive":[150],"applicability":[151],"design.":[154]},"counts_by_year":[],"updated_date":"2026-04-18T07:56:08.524223","created_date":"2025-11-06T00:00:00"}
