A numerical scheme based on local integrated RBFNs and Cartesian grids for solving second-order elliptic problems in two dimensions

Abstract

This paper reports a new Cartesian-grid computational technique, based on local integrated radialbasis- function networks (IRBFNs), for the solution of second-order elliptic differential problems defined on two-dimensional regular and irregular domains. At each grid point, only neighbouring nodes are activated to construct the IRBFN approximations. Local IRBFNs are introduced into two different schemes for discretisation of partial differential equations, namely point collocation and control-volume (CV)/subregion-collocation. Numerical experiments indicate that the latter outperforms the former regarding accuracy. Moreover, the proposed local IRBFN CV method shows a similar level of the matrix condition number and a significant improvement in accuracy over a linear CV method.