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Admissible approximations for essential boundary conditions in the reproducing kernel particle method. (English) Zbl 0889.73078
Two methods of generating admissible meshless approximations are presented: one in which the RKPM (reproducing kernel particle method) correction function equals zero at the boundary, and another in which the domain of the window function is selected such that the approximate solution vanishes at the boundary. An extension of the RKPM dilation parameter is also introduced, providing the capability to generate approximations with arbitrarily shaped supports. Additional issues such as degeneration of shape functions from two dimensions to one dimension and moment matrix conditioning are also addressed.

74S30 Other numerical methods in solid mechanics (MSC2010)
Full Text: DOI
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