A Coupled RBF Method for the Solution of Elastostatic Problems

Radial basis function (RBF) has been widely used in many scientific computing and engineering applications, for instance, multidimensional scattered data interpolation and solving partial differential equations. However, the accuracy and stability of the RBF methods often strongly depend on the shape parameter. A coupled RBF (CRBF) method was proposed recently and successfully applied to solve the Poisson equation and the heat transfer equation (Appl. Math. Lett., 2019, 97: 93-98). Numerical results show that the CRBF method completely overcomes the troublesome issue of the optimal shape parameter that is a formidable obstacle to global schemes. In this paper, we further extend the CRBF method to solve the elastostatic problems. Discretization schemes are present in detail. With two elastostatic numerical examples, it is found that both numerical solutions of the CRBF method and the condition numbers of the discretized matrices are almost independent of the shape parameter. In addition, even if the traditional RBF methods take the optimal shape parameter, the CRBF method achieves better accuracy.