Off-centre Steiner points for Delaunay-refinement on curved surfaces

Engwirda, Darren; Ivers, D. J.

doi:10.1016/j.cad.2015.10.007

Cited by 35 publications

(33 citation statements)

References 38 publications

(109 reference statements)

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“…Such grids are required to satisfy a number of constraints, including bounds on minimum element quality and adherence to user-defined mesh-spacing distributions. In this work, the applicability of a recently developed Frontal-Delaunay surface meshing algorithm (Engwirda and Ivers, 2016;) is investigated for this task.…”

Section: A Restricted Frontal-delaunay Refinement Algorithmmentioning

confidence: 99%

“…This technique is described by the author in detail in Engwirda and Ivers (2016); and differs from standard Delaunay refinement approaches in terms of the strategies used for the placement of new vertices. Specifically, the Frontal-Delaunay algorithm employs a generalisation of various off-centre pointplacement techniques (Rebay, 1993;Erten and Üngör, 2009), designed to position vertices such that element-quality and mesh-size constraints are satisfied in a locally optimal fashion.…”

Section: Restricted Frontal-delaunay Refinementmentioning

confidence: 99%

“…Specifically, the Frontal-Delaunay algorithm described here is known to generate grids with very high mean element quality, bounded minimum and maximum angles, tight conformance to grid-spacing constraints, and provable guarantees on topological consistency and convergence. A full description of the algorithm, including detailed discussions of its theoretical foundations and proofs of worst-case grid-quality bounds, can be found in Engwirda and Ivers (2016); .…”

Section: Restricted Frontal-delaunay Refinementmentioning

confidence: 99%

“…This condition ensures that new points are never positioned too close to an existing vertex, leading to provable guarantees on the performance of the algorithm. See previous work by the author (Engwirda and Ivers, 2016; for additional detail.…”

Section: Off-centre Point Placementmentioning

confidence: 99%

“…This trend necessitates the development of unstructured grid-generation algorithms designed to produce very high-resolution, guaranteedquality unstructured triangular and polygonal meshes that satisfy non-uniform mesh-spacing distributions and embedded geometrical constraints. This study investigates the applicability of a recently developed surface meshing algorithm (Engwirda and Ivers, 2016; based on restricted Frontal-Delaunay refinement and hill-climbing-type optimisation for this task.…”

Section: Introductionmentioning

confidence: 99%

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JIGSAW-GEO (1.0): locally orthogonal staggered unstructured grid generation for general circulation modelling on the sphere

Engwirda

2017

Geosci. Model Dev.

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Abstract. An algorithm for the generation of non-uniform, locally orthogonal staggered unstructured spheroidal grids is described. This technique is designed to generate very high-quality staggered Voronoi-Delaunay meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric simulation, ocean-modelling and numerical weather prediction. Using a recently developed Frontal-Delaunay refinement technique, a method for the construction of high-quality unstructured spheroidal Delaunay triangulations is introduced. A locally orthogonal polygonal grid, derived from the associated Voronoi diagram, is computed as the staggered dual. It is shown that use of the Frontal-Delaunay refinement technique allows for the generation of very high-quality unstructured triangulations, satisfying a priori bounds on element size and shape. Grid quality is further improved through the application of hill-climbing-type optimisation techniques. Overall, the algorithm is shown to produce grids with very high element quality and smooth grading characteristics, while imposing relatively low computational expense. A selection of uniform and non-uniform spheroidal grids appropriate for highresolution, multi-scale general circulation modelling are presented. These grids are shown to satisfy the geometric constraints associated with contemporary unstructured C-gridtype finite-volume models, including the Model for Prediction Across Scales (MPAS-O). The use of user-defined meshspacing functions to generate smoothly graded, non-uniform grids for multi-resolution-type studies is discussed in detail.

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Section: A Restricted Frontal-delaunay Refinement Algorithmmentioning

confidence: 99%

Section: Restricted Frontal-delaunay Refinementmentioning

confidence: 99%

Section: Restricted Frontal-delaunay Refinementmentioning

confidence: 99%

Section: Off-centre Point Placementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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