@Article{AAMM-9-1,
author = {Hamrani, Abderrachid and Idir, Belaidi and Monteiro, Eric and Philippe, Lorong},
title = {On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2017},
volume = {9},
number = {1},
pages = {43--72},
abstract = {<p style="text-align: justify;">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 terms of numerical computation. The Smoothed Radial
Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation
of distorted node scheme.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.2015.m1115},
url = {https://global-sci.com/article/73238/on-the-factors-affecting-the-accuracy-and-robustness-of-smoothed-radial-point-interpolation-method}
}