The method of finite spheres

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.