{"doi":"10.1142/s0219876205000673","title":"MESHFREE METHODS AND THEIR COMPARISONS","abstract":"<jats:p>In recent years, one of the hottest topics in computational mechanics is the meshfree or meshless method. Increasing number of researchers are devoting themselves to the research of the meshfree methods, and a group of meshfree methods have been proposed and used to solve the ordinary differential equations (ODEs) or the partial differential equations (PDE). In the meantime, meshfree methods are being applied to a growing number of practical engineering problems. In this paper, a detailed discussion will be provided on the development of meshfree methods. First, categories of meshfree methods are introduced. Second, the methods for constructing meshfree shape functions are discussed, and the interpolation qualities of them are also studied using the surface fitting. Third, several typical meshfree methods are introduced and compared with each others in terms of their accuracy, convergence and effectivity. Finally, the major technical issues in meshfree methods are discussed, and the future development of meshfree methods is addressed.</jats:p>","journal":"International Journal of Computational Methods","year":2005,"id":19695,"datarank":6.34197894955167,"base_score":4.955827057601261,"endowment":4.955827057601261,"self_citation_contribution":0.7433740586401892,"citation_network_contribution":5.598604890911481,"self_endowment_contribution":0.7433740586401892,"citer_contribution":5.598604890911481,"corpus_percentile":null,"corpus_rank":null,"citation_count":141,"citer_count":130,"citers_with_citation_signal":107,"citers_with_endowment":107,"datacite_reuse_total":0,"is_dataset":false,"is_dataset_confidence":null,"is_oa":false,"file_count":0,"downloads":0,"has_version_chain":false,"published_date":null,"algorithm_id":"datarank_citation_only_1hop_v6","ranking_scope":"data_only","authors":[{"id":132571,"name":"Y. T. GU","orcid":null,"position":0,"is_corresponding":false}],"reference_count":0,"raw_metadata":{"has_enrichment":true,"base_score":4.955827057601261,"endowment":4.955827057601261,"datacite_reuse_total":0,"file_count":0,"downloads":0,"views":0,"has_version_chain":false,"is_dataset":false,"is_oa":false,"pmid":"21071399","pmcid":null,"openalex_id":"https://openalex.org/W2043466553","authors":[],"funders":[],"total_grants":0,"fwci":6.7984,"citation_percentile":0.96608896,"influential_citations":11,"citation_trend":[{"year":2012,"count":7},{"year":2013,"count":5},{"year":2014,"count":10},{"year":2015,"count":12},{"year":2016,"count":5},{"year":2017,"count":8},{"year":2018,"count":9},{"year":2019,"count":3},{"year":2020,"count":8},{"year":2021,"count":7},{"year":2022,"count":15},{"year":2023,"count":3},{"year":2024,"count":4},{"year":2025,"count":5},{"year":2026,"count":3}],"oa_status":"closed","license":null,"oa_locations":[{"url":"https://www.worldscientific.com/doi/pdf/10.1142/S0219876205000673","host_type":"publisher"},{"url":"https://doi.org/10.1142/s0219876205000673","host_type":"journal"}],"fields_of_study":["Numerical methods in engineering","Geotechnical Engineering and Underground Structures","Advanced Numerical Methods in Computational Mathematics","Mathematics","Engineering"],"mesh_terms":[],"keywords":["Meshfree methods","Diffuse element method","Interpolation (computer graphics)","Computer science","Partial differential equation","Ordinary differential equation","Smoothed finite element method","Mathematics","Applied mathematics","Mathematical optimization","Finite element method","Differential equation","Mathematical analysis","Boundary knot method","Artificial intelligence","Structural engineering"],"sdg_mappings":[],"linked_datasets":[],"clinical_trials":[],"software_tools":[],"database_accessions":[],"source":"live","citation_network_status":"fetched"},"created_at":"2026-06-04T05:26:49.441765Z","pmid":null,"pmcid":null,"fwci":null,"citation_percentile":null,"influential_citations":0,"oa_status":null,"license":null,"views":0,"total_file_size_bytes":0,"version_count":0,"clinical_trials":[],"software_tools":[],"db_accessions":[],"linked_datasets":[],"topics":[]}