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dc.contributor.authorChi, Sheng-Weien_US
dc.contributor.authorChen, Jiun-Shyanen_US
dc.contributor.authorHu, Hsin-Yunen_US
dc.contributor.authorYang, Judy P.en_US
dc.date.accessioned2014-12-08T15:29:23Z-
dc.date.available2014-12-08T15:29:23Z-
dc.date.issued2013-03-30en_US
dc.identifier.issn0029-5981en_US
dc.identifier.urihttp://dx.doi.org/10.1002/nme.4432en_US
dc.identifier.urihttp://hdl.handle.net/11536/21169-
dc.description.abstractThe earlier work in the development of direct strong form collocation methods, such as the reproducing kernel collocation method (RKCM), addressed the domain integration issue in the Galerkin type meshfree method, such as the reproducing kernel particle method, but with increased computational complexity because of taking higher order derivatives of the approximation functions and the need for using a large number of collocation points for optimal convergence. In this work, we intend to address the computational complexity in RKCM while achieving optimal convergence by introducing a gradient reproduction kernel approximation. The proposed gradient RKCM reduces the order of differentiation to the first order for solving second-order PDEs with strong form collocation. We also show that, different from the typical strong form collocation method where a significantly large number of collocation points than the number of source points is needed for optimal convergence, the same number of collocation points and source points can be used in gradient RKCM. We also show that the same order of convergence rates in the primary unknown and its first-order derivative is achieved, owing to the imposition of gradient reproducing conditions. The numerical examples are given to verify the analytical prediction. Copyright (c) 2012 John Wiley & Sons, Ltd.en_US
dc.language.isoen_USen_US
dc.subjectreproducing kernel collocation methoden_US
dc.subjectgradient reproducing kernel approximationen_US
dc.subjectweighted collocation methoden_US
dc.subjectstrong form collocationen_US
dc.titleA gradient reproducing kernel collocation method for boundary value problemsen_US
dc.typeArticleen_US
dc.identifier.doi10.1002/nme.4432en_US
dc.identifier.journalINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERINGen_US
dc.citation.volume93en_US
dc.citation.issue13en_US
dc.citation.spage1381en_US
dc.citation.epage1402en_US
dc.contributor.department土木工程學系zh_TW
dc.contributor.departmentDepartment of Civil Engineeringen_US
dc.identifier.wosnumberWOS:000315400900002-
dc.citation.woscount2-
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