{"id":"https://openalex.org/W3114620291","doi":"https://doi.org/10.3390/sym13010015","title":"An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction","display_name":"An RBF-Based h-Adaptive Cartesian Grid Refinement Method for Arbitrary Single/Multi-Body Hull Modeling and Reconstruction","publication_year":2020,"publication_date":"2020-12-23","ids":{"openalex":"https://openalex.org/W3114620291","doi":"https://doi.org/10.3390/sym13010015","mag":"3114620291"},"language":"en","primary_location":{"id":"doi:10.3390/sym13010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13010015","pdf_url":"https://www.mdpi.com/2073-8994/13/1/15/pdf?version=1609144659","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/1/15/pdf?version=1609144659","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5103172321","display_name":"Lin Ma","orcid":"https://orcid.org/0000-0003-4140-0302"},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin Ma","raw_affiliation_strings":["School of Transportation, Wuhan University of Technology (WUT), Wuhan 430063, China","Wuhan University of Technology (WUT)-University of Southampton (UoS) High Performance Ship Technology Joint Centre, Wuhan University of Technology (WUT), Wuhan 430063, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Transportation, Wuhan University of Technology (WUT), Wuhan 430063, China","institution_ids":["https://openalex.org/I196699116"]},{"raw_affiliation_string":"Wuhan University of Technology (WUT)-University of Southampton (UoS) High Performance Ship Technology Joint Centre, Wuhan University of Technology (WUT), Wuhan 430063, China","institution_ids":["https://openalex.org/I196699116"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013166375","display_name":"Tingqiu Li","orcid":null},"institutions":[{"id":"https://openalex.org/I196699116","display_name":"Wuhan University of Technology","ror":"https://ror.org/03fe7t173","country_code":"CN","type":"education","lineage":["https://openalex.org/I196699116"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Tingqiu Li","raw_affiliation_strings":["School of Transportation, Wuhan University of Technology (WUT), Wuhan 430063, China","Wuhan University of Technology (WUT)-University of Southampton (UoS) High Performance Ship Technology Joint Centre, Wuhan University of Technology (WUT), Wuhan 430063, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Transportation, Wuhan University of Technology (WUT), Wuhan 430063, China","institution_ids":["https://openalex.org/I196699116"]},{"raw_affiliation_string":"Wuhan University of Technology (WUT)-University of Southampton (UoS) High Performance Ship Technology Joint Centre, Wuhan University of Technology (WUT), Wuhan 430063, China","institution_ids":["https://openalex.org/I196699116"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5013166375"],"corresponding_institution_ids":["https://openalex.org/I196699116"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.24295879,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"13","issue":"1","first_page":"15","last_page":"15"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T10996","display_name":"Computational Geometry and Mesh Generation","score":0.9987999796867371,"subfield":{"id":"https://openalex.org/subfields/1704","display_name":"Computer Graphics and Computer-Aided Design"},"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/T13067","display_name":"Geological Modeling and Analysis","score":0.9954000115394592,"subfield":{"id":"https://openalex.org/subfields/1906","display_name":"Geochemistry and Petrology"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10719","display_name":"3D Shape Modeling and Analysis","score":0.9915000200271606,"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/cartesian-coordinate-system","display_name":"Cartesian coordinate system","score":0.7710806131362915},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.7619094252586365},{"id":"https://openalex.org/keywords/regular-grid","display_name":"Regular grid","score":0.6744958162307739},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6501232981681824},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.616235077381134},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5920326113700867},{"id":"https://openalex.org/keywords/ellipsoid","display_name":"Ellipsoid","score":0.4992861747741699},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49753454327583313},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.4876755475997925},{"id":"https://openalex.org/keywords/hull","display_name":"Hull","score":0.4859982430934906},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.43689581751823425},{"id":"https://openalex.org/keywords/convex-hull","display_name":"Convex hull","score":0.4330509901046753},{"id":"https://openalex.org/keywords/hierarchical-rbf","display_name":"Hierarchical RBF","score":0.4239589273929596},{"id":"https://openalex.org/keywords/conic-section","display_name":"Conic section","score":0.41105014085769653},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.38186904788017273},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.347351610660553},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.2746877670288086},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.23204666376113892},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2255311906337738},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.17601445317268372},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.15704289078712463},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.10615432262420654}],"concepts":[{"id":"https://openalex.org/C16038011","wikidata":"https://www.wikidata.org/wiki/Q62912","display_name":"Cartesian coordinate system","level":2,"score":0.7710806131362915},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.7619094252586365},{"id":"https://openalex.org/C43173174","wikidata":"https://www.wikidata.org/wiki/Q2646942","display_name":"Regular grid","level":3,"score":0.6744958162307739},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6501232981681824},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.616235077381134},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5920326113700867},{"id":"https://openalex.org/C57489055","wikidata":"https://www.wikidata.org/wiki/Q190046","display_name":"Ellipsoid","level":2,"score":0.4992861747741699},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49753454327583313},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.4876755475997925},{"id":"https://openalex.org/C37423430","wikidata":"https://www.wikidata.org/wiki/Q6750281","display_name":"Hull","level":2,"score":0.4859982430934906},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.43689581751823425},{"id":"https://openalex.org/C206194317","wikidata":"https://www.wikidata.org/wiki/Q1138624","display_name":"Convex hull","level":3,"score":0.4330509901046753},{"id":"https://openalex.org/C182016430","wikidata":"https://www.wikidata.org/wiki/Q17029399","display_name":"Hierarchical RBF","level":4,"score":0.4239589273929596},{"id":"https://openalex.org/C108598597","wikidata":"https://www.wikidata.org/wiki/Q124255","display_name":"Conic section","level":2,"score":0.41105014085769653},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.38186904788017273},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.347351610660553},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.2746877670288086},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.23204666376113892},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2255311906337738},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.17601445317268372},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.15704289078712463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10615432262420654},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C199104240","wikidata":"https://www.wikidata.org/wiki/Q118291","display_name":"Marine engineering","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13010015","pdf_url":"https://www.mdpi.com/2073-8994/13/1/15/pdf?version=1609144659","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:d022e9b03eb34c8c95279fff2d9caf2b","is_oa":true,"landing_page_url":"https://doaj.org/article/d022e9b03eb34c8c95279fff2d9caf2b","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":"Symmetry, Vol 13, Iss 1, p 15 (2020)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/1/15/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13010015","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13010015","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13010015","pdf_url":"https://www.mdpi.com/2073-8994/13/1/15/pdf?version=1609144659","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Life below water","id":"https://metadata.un.org/sdg/14","score":0.8700000047683716}],"awards":[{"id":"https://openalex.org/G2293620595","display_name":null,"funder_award_id":"2016-YB-013","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G6086197363","display_name":null,"funder_award_id":"51579196","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/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W1492713652","https://openalex.org/W1964722081","https://openalex.org/W1973308526","https://openalex.org/W1975943852","https://openalex.org/W1978574709","https://openalex.org/W1999758431","https://openalex.org/W2005539970","https://openalex.org/W2043824713","https://openalex.org/W2049449714","https://openalex.org/W2074797641","https://openalex.org/W2081306995","https://openalex.org/W2095769364","https://openalex.org/W2112463414","https://openalex.org/W2127689830","https://openalex.org/W2144598163","https://openalex.org/W2169990827","https://openalex.org/W2194317022","https://openalex.org/W2229412420","https://openalex.org/W2346308695","https://openalex.org/W2400104698","https://openalex.org/W2497628886","https://openalex.org/W2739589480","https://openalex.org/W2790155557","https://openalex.org/W2899677740","https://openalex.org/W2944412207","https://openalex.org/W2959004956","https://openalex.org/W2993873782","https://openalex.org/W3004427254","https://openalex.org/W3006899429","https://openalex.org/W3023383054","https://openalex.org/W3032945520","https://openalex.org/W3097788968","https://openalex.org/W4292169137","https://openalex.org/W4382891143","https://openalex.org/W6669145261","https://openalex.org/W6676779952"],"related_works":["https://openalex.org/W2410216726","https://openalex.org/W2794503223","https://openalex.org/W2294862180","https://openalex.org/W2024184249","https://openalex.org/W2162647716","https://openalex.org/W1969044629","https://openalex.org/W2186005834","https://openalex.org/W1785485394","https://openalex.org/W2020488014","https://openalex.org/W100820662"],"abstract_inverted_index":{"Complex":[0],"single/multi-body":[1,182],"structures":[2,27],"are":[3,143],"generally":[4],"found":[5],"in":[6,21],"ship":[7],"and":[8,17,94,137,154,174,185,196],"ocean":[9],"engineering.":[10],"They":[11],"have":[12],"the":[13,26,29,35,78,86,112,117,123,130,140,146,149,155,166,181,190,194,197],"smooth,":[14],"sharp,":[15],"concave,":[16],"convex":[18],"surface":[19,153],"features":[20],"common.":[22],"Precise":[23],"modeling":[24,40,76],"of":[25,31,99,125,139,148,180,193,199],"is":[28,48,71,88],"basis":[30,59],"numerical":[32],"simulation.":[33],"However,":[34],"most":[36],"widely":[37],"used":[38],"explicit":[39],"method":[41,142,201],"requires":[42],"considerable":[43],"manual":[44],"operations.":[45],"The":[46,69,104,134,177],"result":[47],"also":[49],"difficult":[50],"to":[51,82,90,115,202],"reproduce.":[52],"Therefore,":[53],"this":[54],"paper":[55],"presents":[56],"a":[57,97],"Radial":[58],"function":[60],"(RBF)":[61],"based":[62],"hierarchical":[63],"(h-)":[64],"adaptive":[65],"Cartesian":[66,79,132],"grid":[67,119],"method.":[68],"RBF":[70,87,113,172],"introduced":[72],"for":[73,102],"arbitrary":[74],"implicit":[75],"over":[77],"framework.":[80],"Thanks":[81],"its":[83],"natural":[84],"properties,":[85],"easy":[89],"use,":[91],"highly":[92],"automated,":[93],"only":[95],"needs":[96],"set":[98],"scatter":[100],"points":[101,127],"modeling.":[103],"block-based":[105],"h-adaptive":[106],"mesh":[107],"refinement":[108],"(AMR)":[109],"combined":[110],"with":[111,129],"aims":[114],"enhance":[116],"local":[118],"resolution.":[120],"It":[121],"accelerates":[122],"calculation":[124],"intersecting":[126],"compared":[128],"uniform":[131],"grid.":[133],"accuracy,":[135],"efficiency,":[136],"robustness":[138],"proposed":[141],"validated":[144],"by":[145],"simulation":[147,178],"3D":[150],"analytical":[151],"ellipsoidal":[152],"unclosed":[156],"conic":[157],"surface.":[158],"To":[159],"select":[160],"suitable":[161],"parameters,":[162],"we":[163],"thoroughly":[164],"investigated":[165],"uncertainty":[167],"factors":[168,195],"including":[169],"sample":[170],"points,":[171],"functions,":[173],"h-AMR":[175],"grids.":[176],"results":[179],"Wigley":[183],"hull":[184,187],"KCS":[186],"forms":[188],"verified":[189],"proper":[191],"selection":[192],"feasibility":[198],"our":[200],"solve":[203],"practical":[204],"problems.":[205]},"counts_by_year":[{"year":2024,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
