One machine, one minute, three billion tetrahedra

Marot, Célestin; Pellerin, Jeanne; Remacle, Jean‐François

doi:10.1002/nme.5987

Cited by 39 publications

(25 citation statements)

References 53 publications

(69 reference statements)

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“…In our worst case (white noise), our implementation runs 30% faster than CGAL, but with tuned parameters and blue noise, it runs 16 times faster. Compared with the results reported in [Marot et al 2018] on many-core EPYC and MIC processors, we are up to 2x faster 2 . Note however that their method, based on a Bowyer-Watson kernel, computes the global combinatorial information.…”

Section: Performancementioning

confidence: 51%

“…The GEOGRAM library [Inria 2018] uses this strategy, with spinlocks attached to the tetrahedra. A completely different two-level approach is proposed in [Remacle 2017], and more recently, the same group of researchers proposed to insert batches of points in parallel in multiple partitionings computed from the Hilbert curve ordering of the input points [Marot et al 2018]. The latter strategy scales up very well on machines with large number of cores (Intel MIC and AMD EPYC).…”

Section: Previous Workmentioning

confidence: 99%

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Meshless voronoi on the GPU

et al. 2018

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Section: Performancementioning

confidence: 51%

Section: Previous Workmentioning

confidence: 99%

Meshless voronoi on the GPU

et al. 2018

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“…To do so, we generate a mesh T h (t) = {K} from the set of points P that is composed of non-overlapping and conforming geometrical elements K of diameter h. There are several methods to generate a mesh from a set of points, all which are studied in the computational geometry field [43]. Here, we apply Delaunay triangulation DT (P ) for several reasons: (1) the aspect ratio of the triangulated elements produce a high-quality mesh; and (2) fast Delaunay triangulation algorithms have been developed recently (see, for example, the one in [44]).…”

Section: Finite Element Methods Interpolationmentioning

confidence: 99%

Visualization of the Strain-Rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

Salazar-Llano

Bayona-Roa

2019

Applied Sciences

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One challenging problem is the representation of three-dimensional datasets that vary with time. These datasets can be thought of as a cloud of points that gradually deforms. However, point-wise variations lack information about the overall deformation pattern, and, more importantly, about the extreme deformation locations inside the cloud. This present article applies a technique in computational mechanics to derive the strain-rate state of a time-dependent and three-dimensional data distribution, by which one can characterize its main trends of shift. Indeed, the tensorial analysis methodology is able to determine the global deformation rates in the entire dataset. With the use of this technique, one can characterize the significant fluctuations in a reduced multivariate description of an urban system and identify the possible causes of those changes: calculating the strain-rate state of a PCA-based multivariate description of an urban system, we are able to describe the clustering and divergence patterns between the districts of a city and to characterize the temporal rate in which those variations happen.

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“…The first is that the aspect ratio of the triangulated elements produce a high-quality mesh. The second is because fast Delaunay triangulation algorithms have been developed recently (see for example the one in [35]).…”

Section: Finite Element Methods Interpolationmentioning

confidence: 99%

Visualization of the Strain-rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

Salazar-Llano¹,

Bayona-Roa²

2019

Preprint

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One challenging problem is the representation of three-dimensional datasets that vary with time. These datasets can be though as a cloud of points that gradually deforms. But point-wise variations lack of information about the overall deformation pattern, and more importantly, about the extreme deformation locations inside the cloud. The present article applies a technique in computational mechanics to derive the strain-rate state of a time-dependent and three-dimensional data distribution, by which one can characterize its main trends of shift. Indeed, the tensorial analysis methodology is able to determine the global deformation rates in the entire dataset. With the use of this technique, one can characterize the significant fluctuations in a reduced multivariate description of an urban system and identify the possible causes of those changes: calculating the strain-rate state of a PCA-based multivariate description of an urban system, we are able to describe the clustering and divergence patterns between the districts of the city and to characterize the temporal rate in which those variations happen.

show abstract

One machine, one minute, three billion tetrahedra

Cited by 39 publications

References 53 publications

Meshless voronoi on the GPU

Meshless voronoi on the GPU

Visualization of the Strain-Rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

Visualization of the Strain-rate State of a Data Cloud: Analysis of the Temporal Change of an Urban Multivariate Description

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