Load-Balancing for Parallel Delaunay Triangulations

Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two partial triangulations by re-triangulating a small subset of their vertices - the border vertices - and combining the three triangulations efficiently via parallel hash table lookups. The input point division should therefore yield roughly equal-sized partitions for good load-balancing and also result in a small number of border vertices for fast merging. In this paper, we present a novel divide-step based on partitioning the triangulation of a small sample of the input points. In experiments on synthetic and real-world data sets, we achieve nearly perfectly balanced partitions and small border triangulations. This almost cuts running time in half compared to non-data-sensitive division schemes on inputs exhibiting an exploitable underlying structure.Comment: Short version submitted to EuroPar 201

Method of up-front load balancing for local memory parallel processors

In a parallel processing computer system with multiple processing units and shared memory, a method is disclosed for uniformly balancing the aggregate computational load in, and utilizing minimal memory by, a network having identical computations to be executed at each connection therein. Read-only and read-write memory are subdivided into a plurality of process sets, which function like artificial processing units. Said plurality of process sets is iteratively merged and reduced to the number of processing units without exceeding the balance load. Said merger is based upon the value of a partition threshold, which is a measure of the memory utilization. The turnaround time and memory savings of the instant method are functions of the number of processing units available and the number of partitions into which the memory is subdivided. Typical results of the preferred embodiment yielded memory savings of from sixty to seventy five percent

A parallel edge orientation algorithm for quadrilateral meshes

One approach to achieving correct finite element assembly is to ensure that the local orientation of facets relative to each cell in the mesh is consistent with the global orientation of that facet. Rognes et al. have shown how to achieve this for any mesh composed of simplex elements, and deal.II contains a serial algorithm to construct a consistent orientation of any quadrilateral mesh of an orientable manifold. The core contribution of this paper is the extension of this algorithm for distributed memory parallel computers, which facilitates its seamless application as part of a parallel simulation system. Furthermore, our analysis establishes a link between the well-known Union-Find algorithm and the construction of a consistent orientation of a quadrilateral mesh. As a result, existing work on the parallelisation of the Union-Find algorithm can be easily adapted to construct further parallel algorithms for mesh orientations.Comment: Second revision: minor change