The Radial Basis Function-Differential Quadrature Method for Elliptic Problems In Annular Domains
We employ a radial basis function (RBF) - differential quadrature (DQ) method for the numerical solution of elliptic boundary value problems in annular domains. With an appropriate selection of collocation points, for any choice of RBF, both the coefficient and right hand side matrices in the systems appearing in this discretization possess block circulant structures. These linear systems can thus be solved efficiently using matrix decomposition algorithms (MDAs) and fast Fourier transforms (FFTs). In particular, we consider problems governed by the Poisson equation, the inhomogeneous biharmonic equation and the inhomogeneous Cauchy–Navier equations of elasticity. In addition to its simplicity, the proposed method can both achieve high accuracy and solve large-scale problems. The feasibility of the proposed techniques is illustrated by several numerical examples.