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