Coarse mesh partitioning for tree based AMR

TL;DR

This paper introduces a scalable algorithm for partitioning coarse meshes in tree-based adaptive mesh refinement, enabling efficient load balancing and metadata access across processes in complex geometries.

Contribution

The paper presents a novel partitioning algorithm for unstructured coarse meshes in tree-based AMR, supporting load balancing and metadata sharing without handshaking.

Findings

Scalable to over 917,000 MPI ranks.

Handles up to 3.7 trillion coarse mesh elements.

Partitioning runs in one second or less.

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 more complex geometries by patching together 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 .37e12 coarse mesh elements, measuring run times of one second or less.