A meshless method based on boundary integral equations and radial basis functions for biharmonic-type problems

Abstract

This paper presents a meshless method, which replaces the inhomogeneous biharmonic equation by two Poisson equations in terms of an intermediate function. The solution of the Poisson equation with the intermediate function as the right-hand term may be written as a sum of a particular solution and a homogeneous solution of a Laplace equation. The intermediate function is approximated by a series of radial basis functions. Then the particular solution is obtained via employing Kansa’s method, while the homogeneous solution is approximated by using the boundary radial point interpolation method by means of boundary integral equations. Besides, the proposed meshless method, in conjunction with the analog equation method, is further developed for solving generalized biharmonic-type problems. Some numerical tests illustrate the efficiency of the method proposed.