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Advances in multiple scale kernel particle methods. (English) Zbl 0868.73091
A novel approach to multiresolution analysis based on reproducing kernel particle methods (RKPM) and wavelets is presented. The concepts of reproducing conditions, discrete convolutions, and multiple scale analysis are described. By means of a newly proposed semidiscrete Fourier analysis, RKPM is further elaborated in the frequency domain, and the interpolation estimate and the convergence of Galerkin solutions are given. The current application areas of RKPM include structural acoustics, structural dynamics, elastic-plastic deformation, computational fluid dynamics and hyperelasticity.

74S99 Numerical and other methods in solid mechanics
76M99 Basic methods in fluid mechanics
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