Volume 9, Issue 1
On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method

Abderrachid Hamrani, Idir Belaidi, Eric Monteiro & Philippe Lorong

Adv. Appl. Math. Mech., 9 (2017), pp. 43-72.

Published online: 2018-05

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  • 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 terms of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

  • Keywords

Radial Basis Function, Radial Point Interpolation Methods, strain smoothing nodal integration, Galerkin weak form.

  • AMS Subject Headings

65N12, 97M50

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-43, author = {Abderrachid Hamrani , and Idir Belaidi , and Eric Monteiro , 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 = {2018}, volume = {9}, number = {1}, pages = {43--72}, 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 terms of numerical computation. The Smoothed Radial Point Interpolation Method (SRPIM) shows a higher accuracy, especially in a situation of distorted node scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2015.m1115}, url = {http://global-sci.org/intro/article_detail/aamm/12136.html} }
TY - JOUR T1 - On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method AU - Abderrachid Hamrani , AU - Idir Belaidi , AU - Eric Monteiro , AU - Philippe Lorong , JO - Advances in Applied Mathematics and Mechanics VL - 1 SP - 43 EP - 72 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2015.m1115 UR - https://global-sci.org/intro/article_detail/aamm/12136.html KW - Radial Basis Function, Radial Point Interpolation Methods, strain smoothing nodal integration, Galerkin weak form. AB -

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.

Abderrachid Hamrani, Idir Belaidi, Eric Monteiro & Philippe Lorong. (2020). On the Factors Affecting the Accuracy and Robustness of Smoothed-Radial Point Interpolation Method. Advances in Applied Mathematics and Mechanics. 9 (1). 43-72. doi:10.4208/aamm.2015.m1115
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