volume | PIER Journals

Abstract

In this paper, we present a new numerical anisotropy optimization method for the three-dimensional (3D) radial point interpolation method (RPIM) in lossy media. Instead of evaluating the parameters of the artificial anisotropy or the scaling factors along the selected axes, as it is usually done in classical optimization algorithms, once the analytical expressions of these parameters have been determined, they are assigned at each node through their shape functions. By adaptive factor, we mean that its value varies in such a way to cancel the discrepancy between numerical and exact wavenumbers at each node. Doing such optimization at each node is indeed being possible during the calculation of these parameters by the RPIM dispersion relation. Therefore the numerical anisotropy is no longer optimized by averaging over the entire Cartesian grid but in each node direction. The RPIM numerical anisotropy adaptive optimization method (AOM) in lossy media is presented, and the theoretical adaptive factors are given as functions of nodes positions. Our results show that the numerical errors of the dispersion and the anisotropy are considerably reduced, after being optimized with the AOM. The proposed AOM scheme is applied for a 3D rectangular cavity in order to test its validity and evaluate the accuracy of the numerical results of our approach.

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Dr. Hichem Naamen

Dr. Ajmi Ben Hadj Hamouda

Dr. Taoufik Aguili