A moving IRBFN-based integration-free meshless method

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 domainω is divided into finite sub-domains ω₁ which satisfy point-wise overlap condition. The local function interpolation is constructed by using IRBFN supported by all nodes in subdomain ω₁.The global function is then constructed by using Partition of Unity Method (PUM), where MLS functions play the role ofpartition 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 ofthe 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 [Le, Mai-Duy, Tran-Cong, and Baker (2010)] to solve PDEs governing various problems including heat transfer, elasticity of bothcompressible and incompressible materials, and linear static crack problems.The numerical results show that the present method offers highorder of convergence and accuracy.