The method of finite spheres

Abstract

 The objective of this paper is to present some of our recent developments in meshless methods. In particular, a technique is given – the method of finite spheres – that is truly meshless in nature in the sense that the nodes are placed and the numerical integration is performed without a mesh. The method can be viewed as a special case of the general formulation known as the meshless local Petrov–Galerkin (MLPG) procedure. Some of the novel features of the method of finite spheres are the numerical integration scheme and the way in which the Dirichlet boundary conditions are incorporated. A new way of modeling doubly-connected domains is also presented. Various example problems are solved to demonstrate the method.