On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method (Advances in Applied Mathematics and Mechanics, 2018)
In order to overcome the possible singularity associated with the Point InterpolationMethod (PIM), the Radial Point Interpolation Method (RPIM) was proposedby G. R. Liu. Radial basis functions (RBF) was used in RPIM as basis functions forinterpolation. All these radial basis functions include shape parameters. The choice ofthese shape parameters has been and stays a problematic theme in RBF approximationand interpolation theory. The object of this study is to contribute to the analysis ofhow these shape parameters affect the accuracy of the radial PIM. The RPIM is studiedbased on the global Galerkin weak form performed using two integration technics:classical Gaussian integration and the strain smoothing integration scheme. The numericalperformance of this method is tested on their behavior on curve fitting, andon three elastic mechanical problems with regular or irregular nodes distributions. Arange of recommended shape parameters is obtained from the analysis of different errorindexes and also the condition number of the matrix system. All resulting RPIMmethods perform very well in terms of numerical computation. The Smoothed RadialPoint Interpolation Method (SRPIM) shows a higher accuracy, especially in a situationof distorted node scheme.