TY - EJOU AU - Mai-Duy, N. AU - Tran-Cong, T. TI - A Cartesian-Grid Discretisation Scheme Based on Local Integrated RBFNs for Two-Dimensional Elliptic Problems T2 - Computer Modeling in Engineering \& Sciences PY - 2009 VL - 51 IS - 3 SN - 1526-1506 AB - This paper reports a new numerical scheme based on Cartesian grids and local integrated radial-basis-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. Linear (e.g. heat flow) and nonlinear (e.g. lid-driven triangular-cavity fluid flow) problems are considered. Numerical results indicate that the local IRBFN CV scheme outperforms the local IRBFN point-collocation scheme regarding accuracy. Moreover, the former shows a similar level of the matrix condition number and a significant improvement in accuracy over a linear CV method. KW - local approximations KW - integrated RBFNs KW - point collocation KW - subregion collocation KW - second-order differential problems DO - 10.3970/cmes.2009.051.213