A meshless technique based on integrated radial basis function networks for elliptic partial differential equations

Abstract

This paper presents a meshless technique based on radial basis function networks (RBFNs) for solving Dirichlet boundary value problems governed by the Poisson and biharmonic equations. The technique employs integrated RBFNs (IRBFNs) to approximate the field variable and point collocation to discretize the PDE. The boundary conditions are incorporated into IRBFNs via integration constants, which occurs prior to the transformation of the network-weight spaces into the physical space. Several linear and nonlinear test problems are considered to demonstrate the attractiveness of the present meshless technique.