Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks

This paper reports a new indirect radial-basis-function (RBF) collocation method for numerically solving biharmonic boundary-value problems. The RBF approximations are constructed through an integration process. The new feature here is that integration constants are eliminated pointwise using the prescribed boundary conditions rather than employed as network weights. This treatment of integration constants is particularly well suited for the case of discretizing the governing differential equations on a set of scattered points. The proposed method is verified through the solution of benchmark test problems. Accurate results and high convergence rates are obtained.