H. Rafieayan Zadeh1, M. Mohammadi1,2, E. Babolian1
CMES-Computer Modeling in Engineering & Sciences, Vol.108, No.6, pp. 375-396, 2015, DOI:10.3970/cmes.2015.108.375
Abstract A local reproducing kernel method based on spatial trial space spanned by the Newton basis functions in the native Hilbert space of the reproducing kernel is proposed. It is a truly meshless approach which uses the local sub clusters of domain nodes for approximation of the arbitrary field. It leads to a system of ordinary differential equations (ODEs) for the time-dependent partial differential equations (PDEs). An adaptive algorithm, so-called adaptive residual subsampling, is used to adjust nodes in order to remove oscillations which are caused by a sharp gradient. The method is applied for solving the Allen-Cahn and Burgers’ equations.… More >
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