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Multiresolution reproducing kernel particle methods. (English) Zbl 0893.73078
Summary: Reproducing kernel particle methods (RKPM) with a built-in feature of multiresolution analysis are addressed. Some fundamental concepts such as reproducing conditions, and correction function are constructed to systematize the framework of RKPM. In particular, Fourier analysis is exploited to further elaborate RKPM in the frequency domain. Furthermore, we address error estimation and convergence properties. We present several applications which confirm the applicability of multiresolution RKPM.

MSC:
74S30 Other numerical methods in solid mechanics (MSC2010)
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