A moving IRBFN-based integration-free meshless method

Abstract

A novel approximation method using integrated radial basis function networks (IRBFN) coupled with moving least square (MLS) approximants, namely moving integrated radial basis function networks (MIRBFN), is proposed in this work. In this method, the computational domain w is divided into finite sub-domains w which satisfy point-wise overlap condition. The local function interpolation is constructed by using IRBFN supported by all nodes in subdomain w. The global function is then constructed by using Partition of Unity Method (PUM), where MLS functions play the role of partition of unity. As a result, the proposed method is locally supported and yields sparse and banded interpolation matrices. The computational efficiency are excellently improved in comparison with that of the original global IRBFN method. In addition, the present method possesses the Kronecker-d property, which makes it easy to impose the essential boundary conditions. The proposed method is applicable to randomly distributed datasets and arbitrary domains. In this work, the MIRBFN method is implemented in the collocation of a first-order system formulation to solve PDEs governing various problems including heat transfer, elasticity of both compressible and incompressible materials, and linear static crack problems. The numerical results show that the present method offers high order of convergence and accuracy.