標題: A gradient reproducing kernel collocation method for boundary value problems
作者: Chi, Sheng-Wei
Chen, Jiun-Shyan
Hu, Hsin-Yun
Yang, Judy P.
土木工程學系
Department of Civil Engineering
關鍵字: reproducing kernel collocation method;gradient reproducing kernel approximation;weighted collocation method;strong form collocation
公開日期: 30-三月-2013
摘要: The 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.
URI: http://dx.doi.org/10.1002/nme.4432
http://hdl.handle.net/11536/21169
ISSN: 0029-5981
DOI: 10.1002/nme.4432
期刊: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Volume: 93
Issue: 13
起始頁: 1381
結束頁: 1402
顯示於類別:期刊論文


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