Fitting Laguerre tessellation approximations to tomographic image data

Spettl, Aaron; Brereton, Tim; Duan, Qibin; Werz, Thomas; Krill, Carl E.; Kroese, Dirk P.; Schmidt, Volker

doi:10.1080/14786435.2015.1125540

Cited by 35 publications

(36 citation statements)

References 51 publications

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“…In the context of tessellations these points are called generators. The basic Voronoi tessellation [5] is often too simple to be used for fitting polycrystals [18], on the other hand the Laguerre tessellation [12] became quite popular for microstructures with approximately convex grains [13], [23]. More complex models exhibiting anisotropy or curved boundaries [1], [22] rely on higher-dimensional marks and are thus more difficult to handle.…”

Section: Introductionmentioning

confidence: 99%

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Seitl

Petrich²,

Staněk

et al. 2020

Methodol Comput Appl Probab

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Random tessellations are well suited for the probabilistic modeling of three-dimensional (3D) grain microstructure of polycrystalline metals. The present paper deals with so-called Gibbs-Laguerre tessellations where the generators of a Laguerre tessellation form a Gibbs point process. The goal is to construct an energy function of the Gibbs point process from a suitable set of potentials, such that the resulting Gibbs-Laguerre tessellation matches some desired geometrical properties. Since the model is analytically hardly tractable, our main tool of analysis are stochastic simulations based on Markov chain Monte Carlo. These enable us to investigate the properties of the models, and, in the next step, to apply the thus gained knowledge to do a statistical reconstruction of an aluminum alloy based on 3D tomographic image data.

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Section: Introductionmentioning

confidence: 99%

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Seitl

Petrich²,

Staněk

et al. 2020

Methodol Comput Appl Probab

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“…Concerning materials science, great interest has been devoted to the application of convex tessellation models, in which the grains are convex polyhedra; see, e.g., Lyckegaard et al (2011). The simplicity of these models allows a simple evaluation of size and shape characteristics of the grains (Lautensack and Zuyev, 2008) and relatively fast and accurate fitting to empirical data (Spettl et al, 2016). However, in connection with recent progress in microscopic research, the interest of scientists has significantly increased regarding more general tessellations with curved boundaries, which can better describe real grain shapes.…”

Section: Introductionmentioning

confidence: 99%

Description of the 3d Morphology of Grain Boundaries in Aluminum Alloys Using Tessellation Models Generated by Ellipsoids

Šedivý

Dake²,

Krill³

et al. 2017

Image Anal Stereol

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Parametric tessellation models are often used to approximate complex grain morphologies of polycrystalline microstructures. A big advantage of such models is the substantial reduction in disk space required to store large, three-dimensional data sets, especially when compared with voxel-based alternatives. By selection of an appropriate tessellation model, a reasonably small loss of information on the real grain shapes can usually be achieved. Special attention has recently been devoted to models based on ellipsoidal approximations fitted to each grain. Faces of these tessellations are portions of quadric surfaces whose parameters can be derived easily. In this paper, we deal with geometric features of the structure, notably curvatures and dihedral angles, which are closely related to the kinetics of grain growth. These characteristics are computed for ellipsoidbased tessellations fitted to two different aluminum alloys with nominal composition Al-3 wt% Mg-0.2 wt% Sc and Al-1 wt% Mg. The results are then compared with estimations based on meshed empirical data. We observe that the model offers more consistent estimations of grain shape characteristics than do the meshed empirical data. Precise description of grain boundaries by the model is also promising with respect to possible applications of these tessellations in stochastic space-time modeling of grain growth.

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“…Microstructures of polycrystalline materials are generally not Laguerre tessellations and using a solver for the Laguerre inverse problem (LIP) as in [77] will not necessarily provide a good result. However one can try to find a Laguerre tessellation that approximates a certain microstructure as in [78] and [79]. In the following a very simple way to solve the Laguerre approximation problem (LAP) for results of phase field simulation using simulated annealing [80] .…”

Section: Inverse Laguerre Tessellationmentioning

confidence: 99%

Massively Parallel Multiphase Field Simulations

Tegeler¹,

Sutmann

Monas³

Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering

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The multiphase field method is a commonly used tool to simulate the evolution of microstructure during materials processing. Even when using a concept called active parameter tracking, which substantially reduces the computational complexity, the resource demands of the multiphase field method remain significant in both time and memory. A hybrid-parallelization is presented, that combines MPI and OpenMP and allows considerably larger system sizes. Due to the utilization of active parameter tracking the computational load can be heterogeneously distributed in the system, which makes load-balancing necessary in order to obtain an efficient parallelization. In this thesis two different load-balancing schemes are presented. The first uses graphpartitioning and an adaptive sub-domain decomposition. The second is based on the multiphase field method itself. Results are presented for performance benchmarks as well as for a variety of applications, including grain growth in polycrystalline materials with hundreds of thousands of different phase fields and Mg-Al alloy solidification as well as a coupling with the Lattice-Boltzmann method. One of the load-balancing schemes is also applied to a cell-based particle method. In addition a way of utilizing the multiphase field method is shown that allows the construction of microstructures and the corresponding Laguerre generator points with a given grain size distribution. 4Declaration/Erklärung I, Marvin Tegeler, born on July, 31st, 1985 in Gelsenkirchen, hereby declare that this dissertation is my own work.

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Fitting Laguerre tessellation approximations to tomographic image data

Cited by 35 publications

References 51 publications

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Exploration of Gibbs-Laguerre Tessellations for Three-Dimensional Stochastic Modeling

Description of the 3d Morphology of Grain Boundaries in Aluminum Alloys Using Tessellation Models Generated by Ellipsoids

Massively Parallel Multiphase Field Simulations

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