Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

Jacobsen, Doug; Gunzburger, Max; Ringler, Todd D.; Burkardt, John; Peterson, Janet

doi:10.5194/gmd-6-1353-2013

Cited by 33 publications

(41 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Orthogonal grids are further optimised in Holleman et al (2013) to construct grids aligned to dominant flows. Additionally, algorithms are being adapted to the evolution in computational resources, with Jacobsen et al (2013) presenting algorithms enabling the construction of grids in parallel based on a Delaunay approach.…”

Section: Tessellation Algorithms and Existing Grid Generation Approachesmentioning

confidence: 99%

Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

Candy

Pietrzak

2018

Geosci. Model Dev.

View full text Add to dashboard Cite

Abstract. The approaches taken to describe and develop spatial discretisations of the domains required for geophysical simulation models are commonly ad hoc, model-or application-specific, and under-documented. This is particularly acute for simulation models that are flexible in their use of multi-scale, anisotropic, fully unstructured meshes where a relatively large number of heterogeneous parameters are required to constrain their full description. As a consequence, it can be difficult to reproduce simulations, to ensure a provenance in model data handling and initialisation, and a challenge to conduct model intercomparisons rigorously. This paper takes a novel approach to spatial discretisation, considering it much like a numerical simulation model problem of its own. It introduces a generalised, extensible, selfdocumenting approach to carefully describe, and necessarily fully, the constraints over the heterogeneous parameter space that determine how a domain is spatially discretised. This additionally provides a method to accurately record these constraints, using high-level natural language based abstractions that enable full accounts of provenance, sharing, and distribution. Together with this description, a generalised consistent approach to unstructured mesh generation for geophysical models is developed that is automated, robust and repeatable, quick-to-draft, rigorously verified, and consistent with the source data throughout. This interprets the description above to execute a self-consistent spatial discretisation process, which is automatically validated to expected discrete characteristics and metrics.Library code, verification tests, and examples available in the repository at https://github.com/shingleproject/ Shingle. Further details of the project presented at http:// shingleproject.org.

show abstract

Section: Tessellation Algorithms and Existing Grid Generation Approachesmentioning

confidence: 99%

Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

Candy

Pietrzak

2018

Geosci. Model Dev.

View full text Add to dashboard Cite

show abstract

“…Jacobsen et al [3] therefore formulate a global Delaunay criterion: If triangles with circumcenter c i and radius r i satisfy This has consequences for data-parallel execution, because simplices in the tesselation may not be Delaunay with respect to (wrt.)…”

Section: Data-parallel Algorithmmentioning

confidence: 99%

“…In contrast to [3] the parallel method therefore does not fail because of an insufficient overlap of the local Delaunay triangulations. New triangles then fill this cavity, connecting p to its edges.…”

Section: Local Algorithmmentioning

confidence: 99%

“…The special case of spherical meshes was treated, for example, in [6]. An exception is the recent publication by Jacobsen et al [3], which simplifies the technically complex merge process of local triangulations by independently triangulating spherical caps. An exception is the recent publication by Jacobsen et al [3], which simplifies the technically complex merge process of local triangulations by independently triangulating spherical caps.…”

Section: Introductionmentioning

confidence: 99%

“…However, algorithms for data-parallel execution have been studied in much less detail. Moreover, the approach in [3] is not a self-contained description in the sense that it delegates the local subproblems to planar triangulation methods. A drawback lies in the fact that the described approach theoretically suffers from breakdown situations when the spherical caps are chosen too small.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A compact parallel algorithm for spherical Delaunay triangulations

Prill

Zängl

2016

Concurrency and Computation

View full text Add to dashboard Cite

We present a data-parallel algorithm for the construction of Delaunay triangulations on the sphere. Our method combines a variant of the classical Bowyer-Watson point insertion algorithm with the recently published parallelization technique by Jacobsen et al. It resolves a breakdown situation of the latter approach and is suitable for practical implementation because of its compact formulation. Some complementary aspects are discussed such as the parallel workload and floating-point arithmetics. In a second step, the generated triangulations are reordered by a stripification algorithm. This improves cache performance and significantly reduces data-read operations and indirect addressing in multi-threaded stencil loops. This paper is an extended version of our Parallel Processing and Applied Mathematics conference contribution.

show abstract

Adaptive parallel Delaunay triangulation construction with dynamic pruned binary tree model in Cloud

Lin

Chen

et al. 2017

Concurrency and Computation

View full text Add to dashboard Cite

Summary The paper illustrates a parallel and distributed scheme for computing a planar Delaunay triangulation using a divide‐and‐conquer strategy in Cloud environment, which combines the incremental insertion algorithm and the divide‐and‐conquer method. The proposed hybrid algorithm for Delaunay triangulation construction is easy to be parallelized due to the dynamic pruned characteristic of the binary tree model used. Moreover, the Cloud platform decreases the communication overhead and improves data locality by making use of a data partitioning and integrating scheme offered by the map‐reduce architecture. The implementation of the parallel and distributed version of the algorithm relied on a robust data structure called quad‐edge, which implies the geometric relationship among the edges and vertexes adjacent. More importantly, the data are serialized easily and transmitted efficiently between different Cloud nodes; the algorithm is executed conveniently on PC clusters. We tested the parallel version of the algorithm on GeoKSCloud, a geographical knowledge service Cloud developed by our research team. Experimental results show that the proposed hybrid algorithm is efficient and competitive; it can be easily migrated and deployed in distributed and parallel computing environment, such as grid and Cloud. The parallel implementation of the hybrid algorithm has a good speed‐up, while data communication is the crucial factor for the efficiency of the parallel version. Overall, the parallel version outperforms both the sequential divide‐and‐conquer algorithm and the sequential incremental insertion algorithm.

show abstract

Parallel algorithms for planar and spherical Delaunay construction with an application to centroidal Voronoi tessellations

Cited by 33 publications

References 26 publications

Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

Shingle 2.0: generalising self-consistent and automated domain discretisation for multi-scale geophysical models

A compact parallel algorithm for spherical Delaunay triangulations

Adaptive parallel Delaunay triangulation construction with dynamic pruned binary tree model in Cloud

Contact Info

Product

Resources

About