A Galerkin approach incorporating integrated radial basis function networks for the solution of 2D biharmonic equations

Abstract

This paper is concerned with the use of integrated radial basis function networks (IRBFNs) for the discretisation of Galerkin approximations for Dirichlet biharmonic problems in two dimensions. The field variable is approximated by global high-order IRBFNs on uniform grids without suffering from Runge's phenomenon. Double boundary conditions, which can be of complicated shapes, are both satisfied identically. The proposed technique is verified through the solution of linear and nonlinear problems, including a benchmark buoyancy-driven flow in a square slot. Good accuracy and fast convergence are obtained.