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.

Keywords:

• Galerkin formulation
• integrated radial basis function networks
• biharmonic equations
• double boundary conditions
• Navier–Stokes equation

2000 AMS Subject Classifications :

• 65N30
• 65N39
• 76D05

Acknowledgements

This paper has been submitted for a special issue of the 8th CMMSE conference. This research is supported by the Australian Research Council. We would like to thank the referees for their helpful comments.