Scalable algorithms for adaptive mesh refinement with arbitrary element types

Abstract

Managing adaptive meshes in parallel is a major challenge, especially when the meshes are refined and coarsened frequently during a single simulation. Important factors for scalability are for example an efficient encoding of the mesh, mesh adaptation, load-balancing and the creation of a layer of ghost(halo) elements. In the past decades the forest-of-trees approach using space-filling curves has been established as a fast and reliable method that offers both geometric flexibility and excellent parallel scalability. However, it was mostly limited to hexahedral meshes. Our work that we present in this talk is an extension of this approach to meshes with arbitrary element types with particular focus on tetrahedral and hybrid meshes. For this kind of meshes, the forest-of-trees approach is an alternative to using unstructured techniques, decreasing the overall memory footprint while improving the parallel scalability. We present our algorithms and their implementation in the t8code library and demonstrate strong and weak scalability to several hundred thousand MPI ranks.