In this paper we propose for the first time an iterative approach of the Smoothed Particle Hydrodynamics (SPH) method. The method is widespread in many areas of science and engineering and despite its extensive application it suffers from several drawbacks due to inaccurate approximation at boundaries and at irregular interior regions. The presented iterative process improves the accuracy of the standard method by updating the initial estimates iterating on the residuals. It is appealing preserving the matrix-free nature of the method and avoiding to modify the kernel function. Moreover the process refines the SPH estimates and it is not affected by disordered data distribution. We discuss on the numerical scheme and experiments with a bivariate test function and different sets of data validate the adopted approach.
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