A distributed octree structure and algorithms for parallel mesh generation

Abstract

An octree is a hierarchical data structure which is used to recursively subdivide a cubic universe into finer resolution levels. Octrees are an effective means to control element sizes which meet apriori mesh size specifications, and facilitate the retrieval of existing mesh data in specific neighborhoods around the regions of space being meshed. In the distributed memory environment, the octree is also used to divide a geometric modeling domain across a set of processors so that the individual partitions can be meshed in parallel.

The distributed octree augments a basic hierarchical octree structure to include interprocessor links to off processor octants, and also includes lateral links between octants of the same level which share common faces in the octree topology. These lateral links, known as face neighbor links, support 0(1) neighborhood queries during mesh generation. Two basic algorithms are needed to construct a distributed octree with face neighbor links. An octant migration procedure supports an arbitrary redistribution ofoctants across the processors while maintaining the octree connectivity. An octant refinement algorithm allows octants to be allocated in parallel while maintaining local tree links, and interprocessor tree links between remote octree face neighbors.

Finally, we describe how the distributed octree structure and algorithms are used inside a parallel octant template meshing procedure. Results demonstrate that template meshing scales well, and is capable of generating elements at a rate of 3660 regions/second on a single node of a 32-processor IBM SP2 (power 266 MH thin node).

In recent years, concurrent developments in finite element methods, and advances in computer hardware have given engineers and scientists the possibility to explore complex physical phenomena in the areas of structural mechanics, fluid dynamics, heat transfer, and electromagnetics. Many grand challenge problems require finite element discretizations in the millions of elements in order to get accurate solutions. As mesh sizes become this large, mesh generation in a uniprocessor environment becomes problematic in terms of time and storage. This thesis work is devoted to the development of an underlying octree data structure and algorithmic approaches which can efficiently support mesh generation on distributed memory processors.