Abstract
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 confirm the widespread applicability of multiresolution RKPM.
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Liu, W., Hao, W., Chen, Y. et al. Multiresolution reproducing kernel particle methods. Computational Mechanics 20, 295–309 (1997). https://doi.org/10.1007/s004660050252
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DOI: https://doi.org/10.1007/s004660050252