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On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method

Article dans une revue avec comité de lecture
Author
HAMRANI, Abderrachid
302807 Université M'Hamed Bougara Boumerdes [UMBB]
BELAIDI, Idir
302807 Université M'Hamed Bougara Boumerdes [UMBB]
ccMONTEIRO, Eric
86289 Laboratoire Procédés et Ingénierie en Mécanique et Matériaux [PIMM]
LORONG, Philippe

URI
http://hdl.handle.net/10985/11874
DOI
10.4208/aamm.2015.m1115
Date
2017
Journal
Advances in Applied Mathematics and Mechanics

Abstract

In order to overcome the possible singularity associated with the Point Interpolation Method (PIM), the Radial Point Interpolation Method (RPIM) was proposed by G. R. Liu. Radial basis functions (RBF) was used in RPIM as basis functions for interpolation. All these radial basis functions include shape parameters. The choice of these shape parameters has been and stays a problematic theme in RBF approximation and interpolation theory. The object of this study is to contribute to the analysis of how these shape parameters affect the accuracy of the radial PIM. The RPIM is studied based on the global Galerkin weak form performed using two integration technics: classical Gaussian integration and the strain smoothing integration scheme. The numerical performance of this method is tested on their behavior on curve fitting, and on three elastic mechanical problems with regular or irregular nodes distributions. A range of recommended shape parameters is obtained from the analysis of different error indexes and also the condition number of the matrix system. All resulting RPIM methods perform very well in term of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

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