A Hybrid RBF Collocation Method and Its Application in the Elastostatic Symmetric Problems

Abstract

In this paper, a new hybrid radial basis function collocation method (HRBF-CM) is proposed to help resolve two-dimensional elastostatic symmetric problems. In the new approach, the hybrid radial basis function (HRBF) combines the infinitely smooth RBF and piecewise smooth RBF, containing two parameters (the shape parameter and the weight parameter). Discretization schemes are presented in detail. We use MATLAB to implement the HRBF-CM and produce numerical results which demonstrate the potential of this method. The new method’s accuracy is higher than that of the traditional methods, especially in the case of a more significant number of nodes. We discuss the new method’s effectiveness compared to the widely used traditional RBF and also investigate the effect of parameters on the method’s performance under the new method.

A Study of the Effects of the Shape Parameter and Type of Data Points Locations on the Accuracy of the Hermite-Based Symmetric Approach Using Positive Definite Radial Kernels

“…In Equation (3), D x j refer to the same differential operator as D c but now acting on the radial kernel as a function of the x variable. This makes the coefficient matrix of the Equations ( 2) and (3) a symmetric one, which make its assembling and solution of the problem easier (Chen et al, 2022). This system can be rewritten in a more convenient and simplified way using the matrix notation:…”