Array-based Hierarchical Mesh Generation in Parallel

In this paper, we describe an array-based hierarchical mesh generation capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework "Mesh Oriented dAtaBase" a.k.a MOAB [16]. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. We also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.