Towards an automatic discretization scheme for the method of finite spheres and its coupling with the finite element method

In this paper we report the development of a geometry-based automatic preprocessing environment as well as efficient numerical integration schemes for the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. In addition, several techniques of coupling the method of finite spheres with the traditional finite element schemes are presented which improve computational efficiency and facilitate the imposition of Dirichlet boundary conditions.