Coarse Mesh Partitioning for Tree-Based AMR

Abstract

In tree-based adaptive mesh refinement, elements are partitioned between processes using a space-filling curve. The curve establishes an ordering between all elements that derive from the same root element, the tree. When representing complex geometries by connecting several trees, the roots of these trees form an unstructured coarse mesh. We present an algorithm to partition the elements of the coarse mesh such that (a) the fine mesh can be load-balanced to equal element counts per process regardless of the element-to-tree map, and (b) each process that holds fine mesh elements has access to the meta data of all relevant trees. As an additional feature, the algorithm partitions the meta data of relevant ghost (halo) trees as well. We develop in detail how each process computes the communication pattern for the partition routine without handshaking and with minimal data movement. We demonstrate the scalability of this approach on up to 917e3 MPI ranks and 371e9 coarse mesh elements, measuring run times of one second or less.