Kansa–RBF algorithms for elliptic BVPs in annular domains with mixed boundary conditions.

We employ a Kansa–radial basis function (RBF) method for the numerical solution of elliptic boundary value problems in annular domains with mixed Dirichlet/Neumann boundary conditions. By exploiting the circular boundaries and the properties of circulant matrices we employ, in an efficient way, the pre-conditioned Krylov subspace iterative solvers GMRES and BiCGSTAB for the solution of the resulting linear systems. In particular, we employ block circulant pre-conditioners which allow for the efficient solution of the relevant systems in the iterative solution. Moreover, by exploiting the properties of circulant matrices we perform the matrix–vector multiplications involved in the iterative solvers efficiently. The feasibility of the proposed techniques is illustrated by several numerical examples. • The Kansa-RBF method is applied to elliptic BVPs in annular domains with mixed BCs. • GMRES and BiCGSTAB are used for the solution of the resulting linear systems. • The block circulant structures of the matrices are exploited. • The efficacy of the method is illustrated by several numerical examples. • Numerical experiments are also carried out in multiple precision. [ABSTRACT FROM AUTHOR]