Voro++ is a software library written in C++ for computing the Voronoi tessellation, a technique in computational geometry that is widely used for analyzing systems of particles. Voro++ was released ...in 2009 and is based on computing the Voronoi cell for each particle individually. Here, we take advantage of modern computer hardware, and extend the original serial version to allow for multithreaded computation of Voronoi cells via the OpenMP application programming interface. We test the performance of the code, and demonstrate that it can achieve parallel efficiencies greater than 95% in many cases. The multithreaded extension follows standard OpenMP programming paradigms, allowing it to be incorporated into other programs. We provide an example of this using the VoroTop software library, performing a multithreaded Voronoi cell topology analysis of up to 102.4 million particles.
Program title:Voro++
CPC Library link to program files:https://doi.org/10.17632/tddc4w4zkk.1
Developer's repository link:https://github.com/chr1shr/voro
Licensing provisions: BSD 3-clause (with LBNL modification)
Programming language: C++
External routines/libraries: OpenMP
Nature of problem: Multithreaded computation of the Voronoi tessellation in two and three dimensions
Solution method: The Voro++ library is built around several C++ classes that can be incorporated into other programs. The two largest components are the container... classes that spatially sort input particles into a grid-based data structure, allowing for efficient searches of nearby particles, and the voronoicell... classes that represent a single Voronoi cell as an arbitrary convex polygon or polyhedron. The Voronoi cell for each particle is built by considering a sequence of plane cuts based on neighboring particles, after which many different statistics (e.g. volume, centroid, number of vertices) can be computed. Since each Voronoi cell is calculated individually, the Voronoi cells can be computed using multithreading via OpenMP.
VESTA is a three‐dimensional visualization system for crystallographic studies and electronic state calculations. It has been upgraded to the latest version, VESTA 3, implementing new features ...including drawing the external morphology of crystals; superimposing multiple structural models, volumetric data and crystal faces; calculation of electron and nuclear densities from structure parameters; calculation of Patterson functions from structure parameters or volumetric data; integration of electron and nuclear densities by Voronoi tessellation; visualization of isosurfaces with multiple levels; determination of the best plane for selected atoms; an extended bond‐search algorithm to enable more sophisticated searches in complex molecules and cage‐like structures; undo and redo in graphical user interface operations; and significant performance improvements in rendering isosurfaces and calculating slices.
This paper is focused on the in-plane crushing of two-dimensional (2D) porous structures with a special attention on the effect of functionally graded (FG) porosities. The dynamic response and energy ...absorption of closed-cell metal foams with different porosity distributions are investigated by using finite element (FE) analysis. Two symmetric, two asymmetric and one uniform distributions of internal pores along the impact direction are constructed with Voronoi tessellation. The proposed porous structure is crushed under the impact of a rigid panel with a constant velocity. The deformation of cell walls is simulated using a plastic kinematic material model. The erosion criteria and hourglass control are applied to ensure the accuracy of numerical results, which are validated against the experimental data from open literature. The effects of varying parameters on the energy absorption, deformation pattern, and stress-strain curve of the FG porous structure are discussed. The dynamic response is found to be influenced by different random cell geometries, porosity gradients, cell wall thicknesses, internal pore numbers, and impact velocities. The effective way to improve the energy absorption capability of the porous structure under a constant-velocity impact is proposed, shedding new insights into the deformation mechanism of the FG porous structure for engineering design.
Display omitted
•The porosity distribution of porous structures has a significant influence on the dynamic response.•The energy absorption under high-velocity impacting can be improved with the proposed graded porosity distribution.•The absorbed energy of porous structures increases with the increasing impact velocity.•The densification of cell walls tends to localize near the impact end under high impact velocities.
The Voronoi tessellation is a fundamental geometric data structure which has numerous applications in various scientific and technological fields. For large particle datasets, computing Voronoi ...tessellations must be conducted in parallel on a distributed-memory supercomputer in order to satisfy time and memory-size constraints. However, due to load balance and communication, the parallelization of the Voronoi tessellation renders a challenge. In this paper, we present a scalable parallel algorithm for constructing 3D Voronoi tessellations, which evenly distributes the input particles between blocks through kd-tree decomposition. In order to construct the correct global Voronoi topology, we investigate both parametric and non-parametric methods for particle communication among the blocks of a spatial decomposition. The algorithm is implemented exploiting process-level and thread-level parallelization and can be used in a diverse architectural landscape. Using datasets containing up to 330 million particles, we show that our algorithm achieves parallel efficiency up to 57% using 4096 cores on a distributed-memory computer. Moreover, we compare our algorithm with previous attempts to parallelize Voronoi tessellations showing encouraging improvements in terms of computation time.
•A new parallel algorithm for computing 3D Voronoi based on kdtree decomposition.•Parametric and non-parametric methods for establish communication.•An evaluation of the algorithm, including parallel accuracy and scalability.•A publicly available library (named ParVoro++) implemented as a fork of Voro++.
Display omitted
•We propose an inverse design method for auxetic metamaterials using deep learning.•We designed novel 2D auxetic metamaterials based on Voronoi tessellation for the training ...dataset.•The trained neural network can generate 2D auxetic metamaterials with user-desired Young’s moduli and Poisson’s ratios.•The proposed method can easily be extended to the inverse design of other architected materials.
As typical mechanical metamaterials with negative Poisson’s ratios, auxetic metamaterials exhibit counterintuitive auxetic behaviors that are highly dependent on their geometric arrangements. The realization of the geometric arrangement required to achieve a negative Poisson’s ratio relies considerably on the experience of designers and trial-and-error approaches. This report proposes an inverse design method for auxetic metamaterials using deep learning, in which a batch of auxetic metamaterials with a user-defined Poisson’s ratio and Young’s modulus can be generated by a conditional generative adversarial network without prior knowledge. The network was trained based on supervised learning using a large number of geometrical patterns generated by Voronoi tessellation. The performance of the network was demonstrated by verifying the mechanical properties of the generated patterns using finite element method simulations and uniaxial compression tests. The successful realization of user-desired properties can potentially accelerate the inverse design and development of mechanical metamaterials.
A method for autonomous data partitioning Gu, Xiaowei; Angelov, Plamen P.; Príncipe, José C.
Information sciences,
September 2018, 2018-09-00, Letnik:
460-461
Journal Article
Recenzirano
Odprti dostop
In this paper, we propose a fully autonomous, local-modes-based data partitioning algorithm, which is able to automatically recognize local maxima of the data density from empirical observations and ...use them as focal points to form shape-free data clouds, i.e. a form of Voronoi tessellation. The method is free from user- and problem- specific parameters and prior assumptions. The proposed algorithm has two versions: i) offline for static data and ii) evolving for streaming data. Numerical results based on benchmark datasets prove the validity of the proposed algorithm and demonstrate its excellent performance and high computational efficiency compared with the state-of-art clustering algorithms.
A simulation-based study of the variability of remnant polarization <inline-formula> <tex-math notation="LaTeX">({P}_{r}) </tex-math></inline-formula> in a multigranular 3-D ultrathin ferroelectric ...(FE) capacitor is presented in this article. The Poisson-Voronoi tessellation (PVT) algorithm is used for the nucleation of grains in the FE region, which corresponds to the physical growth mechanism. The PVT algorithm implemented in MATLAB is coupled with TCAD simulations, to trace the FE hysteresis loop. The impact of both, area and thickness scaling on the variability of <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula>, is considered. It is found that amount of variability in <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula> increases as FE thickness decreases. In addition, FE with the smaller surface area exhibits a higher variability in <inline-formula> <tex-math notation="LaTeX">{P}_{r} </tex-math></inline-formula> compared to a larger surface area FE capacitor. Furthermore, the impact of dielectric content in the FE grains is analyzed. It is seen that the dielectric grains cause a very large amount of variability in the FE hysteresis loop. An increase in the dielectric grains also leads to a loss in the retentivity of the hysteresis loop.
It is a great challenge to evaluate the network performance of cellular mobile communication systems. In this paper, we propose new spatial spectrum and energy efficiency models for Poisson-Voronoi ...tessellation (PVT) random cellular networks. To evaluate the user access to the network, a Markov chain based wireless channel access model is first proposed for PVT random cellular networks. On that basis, the outage probability and blocking probability of PVT random cellular networks are derived, which can be computed numerically. Furthermore, taking into account the call arrival rate, the path loss exponent and the base station (BS) density in random cellular networks, spatial spectrum and energy efficiency models are proposed and analyzed for PVT random cellular networks. Numerical simulations are conducted to evaluate the network spectrum and energy efficiency in PVT random cellular networks.
PDF
