{"id":"https://openalex.org/W2021164325","doi":"https://doi.org/10.1142/s0218654304000651","title":"SURFACE BLENDING USING A POWER SERIES SOLUTION TO FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS","display_name":"SURFACE BLENDING USING A POWER SERIES SOLUTION TO FOURTH ORDER PARTIAL DIFFERENTIAL EQUATIONS","publication_year":2004,"publication_date":"2004-12-01","ids":{"openalex":"https://openalex.org/W2021164325","doi":"https://doi.org/10.1142/s0218654304000651","mag":"2021164325"},"language":"en","primary_location":{"id":"doi:10.1142/s0218654304000651","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218654304000651","pdf_url":null,"source":{"id":"https://openalex.org/S68340538","display_name":"International Journal of Shape Modeling","issn_l":"0218-6543","issn":["0218-6543","1793-639X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Shape Modeling","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074858947","display_name":"Jianjun Zhang","orcid":"https://orcid.org/0000-0002-7069-5771"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"JIAN J. ZHANG","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Poole, Dorset BH12 5BB, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Poole, Dorset BH12 5BB, United Kingdom","institution_ids":["https://openalex.org/I9300472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101850373","display_name":"Lihua You","orcid":"https://orcid.org/0000-0001-9738-4378"},"institutions":[{"id":"https://openalex.org/I9300472","display_name":"Bournemouth University","ror":"https://ror.org/05wwcw481","country_code":"GB","type":"education","lineage":["https://openalex.org/I9300472"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"LIHUA YOU","raw_affiliation_strings":["National Centre for Computer Animation, Bournemouth University, Poole, Dorset BH12 5BB, United Kingdom"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"National Centre for Computer Animation, Bournemouth University, Poole, Dorset BH12 5BB, United Kingdom","institution_ids":["https://openalex.org/I9300472"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I9300472"],"apc_list":null,"apc_paid":null,"fwci":0.4454,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.64191534,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"10","issue":"02","first_page":"155","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9991999864578247,"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/T10514","display_name":"Numerical methods in engineering","score":0.9778000116348267,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9650999903678894,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/mathematics","display_name":"Mathematics","score":0.6767876148223877},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5828530192375183},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.5775383710861206},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5699933767318726},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5538455843925476},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5242609977722168},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5216774940490723},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.5124049782752991},{"id":"https://openalex.org/keywords/parametric-statistics","display_name":"Parametric statistics","score":0.4838389456272125},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47889605164527893},{"id":"https://openalex.org/keywords/surface","display_name":"Surface (topology)","score":0.47706520557403564},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4723162353038788},{"id":"https://openalex.org/keywords/partial-derivative","display_name":"Partial derivative","score":0.47212275862693787},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4397762417793274},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.43315985798835754},{"id":"https://openalex.org/keywords/resolution","display_name":"Resolution (logic)","score":0.43247953057289124},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.41012120246887207},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16177546977996826},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10847258567810059}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6767876148223877},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5828530192375183},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.5775383710861206},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5699933767318726},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5538455843925476},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5242609977722168},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5216774940490723},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.5124049782752991},{"id":"https://openalex.org/C117251300","wikidata":"https://www.wikidata.org/wiki/Q1849855","display_name":"Parametric statistics","level":2,"score":0.4838389456272125},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47889605164527893},{"id":"https://openalex.org/C2776799497","wikidata":"https://www.wikidata.org/wiki/Q484298","display_name":"Surface (topology)","level":2,"score":0.47706520557403564},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4723162353038788},{"id":"https://openalex.org/C53846429","wikidata":"https://www.wikidata.org/wiki/Q186475","display_name":"Partial derivative","level":2,"score":0.47212275862693787},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4397762417793274},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.43315985798835754},{"id":"https://openalex.org/C138268822","wikidata":"https://www.wikidata.org/wiki/Q1051925","display_name":"Resolution (logic)","level":2,"score":0.43247953057289124},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.41012120246887207},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16177546977996826},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10847258567810059},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0218654304000651","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0218654304000651","pdf_url":null,"source":{"id":"https://openalex.org/S68340538","display_name":"International Journal of Shape Modeling","issn_l":"0218-6543","issn":["0218-6543","1793-639X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Shape Modeling","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320324714","display_name":"Arts and Humanities Research Board","ror":"https://ror.org/0505m1554"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W575078097","https://openalex.org/W1516701337","https://openalex.org/W1602286812","https://openalex.org/W1966821837","https://openalex.org/W1967818484","https://openalex.org/W1976768276","https://openalex.org/W1978476222","https://openalex.org/W1983019655","https://openalex.org/W1984707484","https://openalex.org/W1989389927","https://openalex.org/W1997368532","https://openalex.org/W1997463783","https://openalex.org/W2008756439","https://openalex.org/W2014510891","https://openalex.org/W2022177119","https://openalex.org/W2024001333","https://openalex.org/W2028897153","https://openalex.org/W2030677490","https://openalex.org/W2031900205","https://openalex.org/W2033912262","https://openalex.org/W2035124069","https://openalex.org/W2042107141","https://openalex.org/W2045861956","https://openalex.org/W2058511943","https://openalex.org/W2061380892","https://openalex.org/W2063581946","https://openalex.org/W2073898335","https://openalex.org/W2079066051","https://openalex.org/W2082984746","https://openalex.org/W2091036616","https://openalex.org/W2131681761","https://openalex.org/W2133275054","https://openalex.org/W2146968309","https://openalex.org/W2161431717","https://openalex.org/W2168384586","https://openalex.org/W2494200982","https://openalex.org/W2506365222","https://openalex.org/W2949146770","https://openalex.org/W4205795514","https://openalex.org/W4205994512"],"related_works":["https://openalex.org/W2735653195","https://openalex.org/W2139348706","https://openalex.org/W2776138620","https://openalex.org/W2908477459","https://openalex.org/W120789411","https://openalex.org/W4295797339","https://openalex.org/W2067995173","https://openalex.org/W3081774625","https://openalex.org/W4233375541","https://openalex.org/W3211153273"],"abstract_inverted_index":{"In":[0,36,65],"our":[1,138,256],"previous":[2],"work,":[3],"we":[4,82],"proposed":[5,140,197],"a":[6,39,44,69,87,107,146,200,207,216,244],"general":[7,90,208],"fourth":[8],"order":[9,66],"partial":[10],"differential":[11],"equation":[12],"(PDE)":[13],"for":[14,27,278],"the":[15,56,60,63,77,103,121,128,131,143,157,168,178,182,188,196,225,236,264],"generation":[16],"of":[17,43,62,72,80,109,160,167,176,202,220,238,247],"blending":[18,74,222,239],"surfaces":[19],"together":[20],"with":[21,119,137,156,192],"an":[22],"accurate":[23],"closed":[24,32,40,124,132],"form":[25,33,41,79,125,133],"solution":[26,42],"special":[28],"boundary":[29,57,104,179,226],"conditions":[30,58,105,180,227],"where":[31],"solutions":[34,134],"exist.":[35],"general,":[37],"however,":[38],"PDE":[45],"is":[46,100,149,206,233,271],"often":[47],"either":[48],"not":[49,52,272],"existent":[50],"or":[51],"obtainable":[53],"depending":[54],"on":[55],"and":[59,112,120,181,211,241,250],"coefficients":[61],"PDE.":[64],"to":[67,101,214,235],"solve":[68,215],"wider":[70,218],"range":[71],"surface":[73,189,221],"problems":[75],"using":[76,93],"new":[78],"PDE,":[81],"propose":[83],"in":[84,263],"this":[85,269],"paper":[86,265],"much":[88,217],"more":[89],"resolution":[91,194,209],"method":[92,198,210,257,270],"power":[94,158],"series":[95,159],"expansion.":[96],"The":[97,164],"main":[98],"idea":[99],"decompose":[102],"into":[106,115],"number":[108,201,246],"basic":[110,154],"functions":[111,155],"separate":[113],"them":[114],"two":[116],"groups,":[117],"one":[118,161],"other":[122],"without":[123],"solutions.":[126],"For":[127,142],"first":[129],"group,":[130,145],"are":[135,171,228,253],"produced":[136],"previously":[139],"method.":[141],"second":[144],"composite":[147,169],"function":[148,170],"constructed":[150],"which":[151,186],"combines":[152],"these":[153],"parametric":[162],"variable.":[163],"unknown":[165,251],"constants":[166,252],"determined":[172],"by":[173],"making":[174,255],"use":[175],"both":[177],"weighted":[183],"residual":[184],"method,":[185],"minimizes":[187],"errors.":[190],"Compared":[191],"existing":[193],"methods,":[195],"exhibits":[199],"advantages:":[203],"1)":[204],"it":[205],"hence":[212],"able":[213],"class":[219],"problems;":[223],"2)":[224],"always":[229],"satisfied":[230],"exactly":[231],"that":[232,268],"crucial":[234],"quality":[237],"surfaces;":[240],"3)":[242],"only":[243,273],"small":[245],"collocation":[248],"points":[249],"needed,":[254],"computationally":[258],"efficient.":[259],"Several":[260],"examples":[261],"given":[262],"have":[266],"demonstrated":[267],"accurate,":[274],"but":[275],"fast":[276],"enough":[277],"interactive":[279],"applications.":[280]},"counts_by_year":[{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}