RBF–DQ algorithms for elliptic problems in axisymmetric domains.

A radialbasis function (RBF)–differentialquadrature (DQ) method is applied for the numerical solution of elliptic boundary value problems (BVPs) in three-dimensional axisymmetric domains. By appropriately selecting the collocation points, for any choice of RBF, the proposed discretization leads to linear systems in which the coefficient matrices possess block circulant structures. Matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs) are employed for the efficient solution of these systems. Three types of BVPs are considered, namely ones governed by the Poisson equation, the inhomogeneous biharmonic equation, and the inhomogeneous Cauchy–Navier equations of elasticity. The high accuracy of the proposed technique as well as its ability to solve large-scale problems is demonstrated on several numerical examples. [ABSTRACT FROM AUTHOR]