The use of polynomial-augmented RBF collocation method with ghost points for plane elastostatic equations of anisotropic functionally graded materials

Abstract

In the current study, we propose an accurate numerical method for plane elastostatic equations of anisotropic functionally graded materials. The proposed method uses radial basis functions augmented with polynomial basis functions in a collocation framework by employing ghost point centers which cover physical domain of considered problem. Unlike in classical collocation approach where the centers and collocation points are taken identically, using ghost centers different from the collocation points greatly improves the accuracy of the proposed method. Addition of polynomial basis function to the radial basis functions stabilized the method against shape parameter of radial basis functions and also increases accuracy of solution, mostly. Some numerical examples are solved via the proposed method both on regular and irregular domains. $L_{\infty }$, $L_2$ and RMS error norms are calculated and for sufficient number of collocation points their values are smaller than $1e-10$. The obtained error norms and their comparison with other methods available in literature confirm precision of the suggested numerical method.