Hierarchical tree-based discretization for the method of finite spheres

In this paper we report the development of a geometry-based automatic pre-processing environment for the method of finite spheres; a truly meshfree numerical technique developed for the solution of boundary value problems on geometrically complex domains. Techniques of generating open covers for the Galerkin-based as well as the point collocation-based method of finite spheres are presented for two as well as three-dimensional problems by recursive spatial subdivision using quadtrees and octrees, respectively.