{"id":"https://openalex.org/W2164694224","doi":"https://doi.org/10.1080/00207160802647365","title":"A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations","display_name":"A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations","publication_year":2009,"publication_date":"2009-09-25","ids":{"openalex":"https://openalex.org/W2164694224","doi":"https://doi.org/10.1080/00207160802647365","mag":"2164694224"},"language":"en","primary_location":{"id":"doi:10.1080/00207160802647365","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802647365","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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":null,"display_name":"N. Mai-Duy","orcid":null},"institutions":[{"id":"https://openalex.org/I185523456","display_name":"University of Southern Queensland","ror":"https://ror.org/04sjbnx57","country_code":"AU","type":"education","lineage":["https://openalex.org/I185523456"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"N. Mai-Duy","raw_affiliation_strings":["Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia","institution_ids":["https://openalex.org/I185523456"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032770069","display_name":"D. Ho-Minh","orcid":null},"institutions":[{"id":"https://openalex.org/I185523456","display_name":"University of Southern Queensland","ror":"https://ror.org/04sjbnx57","country_code":"AU","type":"education","lineage":["https://openalex.org/I185523456"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"D. Ho-Minh","raw_affiliation_strings":["Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia","institution_ids":["https://openalex.org/I185523456"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5042503126","display_name":"Ton Tran-Cong","orcid":null},"institutions":[{"id":"https://openalex.org/I185523456","display_name":"University of Southern Queensland","ror":"https://ror.org/04sjbnx57","country_code":"AU","type":"education","lineage":["https://openalex.org/I185523456"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"T. Tran-Cong","raw_affiliation_strings":["Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia"],"affiliations":[{"raw_affiliation_string":"Computational Engineering and Science Research Centre, Faculty of Engineering and Surveying , The University of Southern Queensland , Toowoomba, QLD, Australia","institution_ids":["https://openalex.org/I185523456"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I185523456"],"apc_list":null,"apc_paid":null,"fwci":3.9757,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92749162,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"86","issue":"10-11","first_page":"1746","last_page":"1759"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10514","display_name":"Numerical methods in engineering","score":0.9997000098228455,"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":0.9997000098228455,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.998199999332428,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9980000257492065,"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/biharmonic-equation","display_name":"Biharmonic equation","score":0.9309626817703247},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8136855363845825},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.7614361047744751},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6759467720985413},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.5823388695716858},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5385938286781311},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5333459377288818},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4784969389438629},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4637485146522522},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.43029019236564636},{"id":"https://openalex.org/keywords/basis","display_name":"Basis (linear algebra)","score":0.4291658103466034},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.42399224638938904},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.4153987765312195},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.36289072036743164},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.17289605736732483},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08591660857200623}],"concepts":[{"id":"https://openalex.org/C145784156","wikidata":"https://www.wikidata.org/wiki/Q859808","display_name":"Biharmonic equation","level":3,"score":0.9309626817703247},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8136855363845825},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.7614361047744751},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6759467720985413},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.5823388695716858},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5385938286781311},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5333459377288818},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4784969389438629},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4637485146522522},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.43029019236564636},{"id":"https://openalex.org/C12426560","wikidata":"https://www.wikidata.org/wiki/Q189569","display_name":"Basis (linear algebra)","level":2,"score":0.4291658103466034},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.42399224638938904},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.4153987765312195},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.36289072036743164},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.17289605736732483},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08591660857200623},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160802647365","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160802647365","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11","score":0.5199999809265137}],"awards":[],"funders":[{"id":"https://openalex.org/F4320310921","display_name":"University of Guelph","ror":"https://ror.org/01r7awg59"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W56087484","https://openalex.org/W1966820249","https://openalex.org/W1979325693","https://openalex.org/W2019791415","https://openalex.org/W2026656818","https://openalex.org/W2111352333","https://openalex.org/W2123658362","https://openalex.org/W2131778920","https://openalex.org/W4298060601"],"related_works":["https://openalex.org/W2503543076","https://openalex.org/W2738351852","https://openalex.org/W2064104303","https://openalex.org/W256613907","https://openalex.org/W2441614350","https://openalex.org/W1984726292","https://openalex.org/W2005394642","https://openalex.org/W1685120052","https://openalex.org/W2156202908","https://openalex.org/W603561220"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,30,60],"concerned":[3],"with":[4],"the":[5,15,63],"use":[6],"of":[7,17,50,65],"integrated":[8],"radial":[9],"basis":[10],"function":[11],"networks":[12],"(IRBFNs)":[13],"for":[14,20],"discretisation":[16],"Galerkin":[18],"approximations":[19],"Dirichlet":[21],"biharmonic":[22],"problems":[23],"in":[24,75],"two":[25],"dimensions.":[26],"The":[27,57],"field":[28],"variable":[29],"approximated":[31],"by":[32],"global":[33],"high-order":[34],"IRBFNs":[35],"on":[36],"uniform":[37],"grids":[38],"without":[39],"suffering":[40],"from":[41],"Runge's":[42],"phenomenon.":[43],"Double":[44],"boundary":[45],"conditions,":[46],"which":[47],"can":[48],"be":[49],"complicated":[51],"shapes,":[52],"are":[53,84],"both":[54],"satisfied":[55],"identically.":[56],"proposed":[58],"technique":[59],"verified":[61],"through":[62],"solution":[64],"linear":[66],"and":[67,81],"nonlinear":[68],"problems,":[69],"including":[70],"a":[71,76],"benchmark":[72],"buoyancy-driven":[73],"flow":[74],"square":[77],"slot.":[78],"Good":[79],"accuracy":[80],"fast":[82],"convergence":[83],"obtained.":[85]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":2}],"updated_date":"2026-04-16T08:26:57.006410","created_date":"2025-10-10T00:00:00"}
