Abstract
Abstract. A new algorithm, featuring overlapping domain decompositions, for the parallel construction of Delaunay and Voronoi tessellations is developed. Overlapping allows for the seamless stitching of the partial pieces of the global Delaunay tessellations constructed by individual processors. The algorithm is then modified, by the addition of stereographic projections, to handle the parallel construction of spherical Delaunay and Voronoi tessellations. The algorithms are then embedded into algorithms for the parallel construction of planar and spherical centroidal Voronoi tessellations that require multiple constructions of Delaunay tessellations. This combination of overlapping domain decompositions with stereographic projections provides a unique algorithm for the construction of spherical meshes that can be used in climate simulations. Computational tests are used to demonstrate the efficiency and scalability of the algorithms for spherical Delaunay and centroidal Voronoi tessellations. Compared to serial versions of the algorithm and to STRIPACK-based approaches, the new parallel algorithm results in speedups for the construction of spherical centroidal Voronoi tessellations and spherical Delaunay triangulations.
Highlights
Voronoi diagrams and their dual Delaunay tessellations have become, in many settings, natural choices for spatial griding due to their ability to handle arbitrary boundaries and refinement well
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A novel technique for the parallel construction of Delaunay triangulations is presented, utilizing unique domain decomposition techniques combined with stereographic projections
Summary
Voronoi diagrams and their dual Delaunay tessellations have become, in many settings, natural choices for spatial griding due to their ability to handle arbitrary boundaries and refinement well. Climate modelling is a specific field which has recently begun adopting Voronoi tessellations as well as triangular meshes for the spatial discretization of partial differential equations (Pain et al, 2005; Weller et al, 2009; Ju et al, 2008, 2011; Ringler et al, 2011) As this is a special interest of ours, we develop a new parallel algorithm for the generation of Voronoi and Delaunay tessellations for the entire sphere or some subregion of interest. Spherical centroidal Voronoi tessellation (SCVT) based grids are especially desirable in climate modelling because they provide for precise grid refinement, and feature smooth transition regions (Ringler et al, 2011, 2013) We show how such grids can be generated using the new parallel algorithm for spherical Delaunay tessellations.
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