An agglomeration-based multilevel-topology concept with application to 3D-FE meshes

In this paper we focus on generating hierarchies of topological relations for unstructured three-dimensional (3D) finite element (FE) meshes. The related topological elements are agglomerates, faces, edges, and vertices. We provide practical definitions and propose efficient procedures, in particular for the setup of coarse faces and coarse edges. Moreover, we examine the agglomeration algorithm introduced by Jones and Vassilevski (AMGe based on element agglomeration, SIAM J. Sci. Comp., 23 (2001), pp. 109-133) and suggest a proper generalization for 3D meshes. This setting allows for a recursive construction of a sequence of nested coarse topologies, which can be used in different areas of finite element computations, e.g., load balancing for parallel processing, domain decomposition methods, algebraic multigrid or multilevel preconditioning methods based on incomplete factorization.