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, as a tool, is exploited to further elaborate RKPM in the frequency domain. Furthermore, we address error estimation and convergence properties. We present several applications which con®rm the widespread applicability of multiresolution RKPM.
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