An automatic methodology for obtaining optimum shape factors for the radial point interpolation method

• Main Authors: Péricles L. Machado, Rodrigo M.S. de Oliveira, Washington C.B. Souza, Ramon C.F. Araújo, Maria E.L. Tostes, Cláudio Gonçalves
• Format: Article
• Language: English
• Published: Sociedade Brasileira de Microondas e Optoeletrônica; Sociedade Brasileira de Eletromagnetismo
• Series: Journal of Microwaves, Optoelectronics and Electromagnetic Applications
• Subjects: improved numerical precision; matrix inversion difficulties; optimum shape factor calculation; radial point interpolation method (RPIM)
• Online Access: http://www.scielo.br/scielo.php?script=sci_arttext&pid=S2179-10742011000200009&lng=en&tlng=en

In this letter, a methodology is proposed for automatically (and locally) obtaining the shape factor c for the Gaussian basis functions, for each support domain, in order to increase numerical precision and mainly to avoid matrix inversion impossibilities. The concept of calibration function is introduced, which is used for obtaining c. The methodology developed was applied for a 2-D numerical experiment, which results are compared to analytical solution. This comparison revels that the results associated to the developed methodology are very close to the analytical solution for the entire bandwidth of the excitation pulse. The proposed methodology is called in this work Local Shape Factor Calibration Method (LSFCM).