Performance Evaluation of a Parallel Algorithm for Simultaneous Untangling and Smoothing of Tetrahedral Meshes

Benítez, Domingo; Rodríguez, Eduardo; Escobar, J. M.; Montenegro, R.

doi:10.1007/978-3-319-02335-9_32

Cited by 15 publications

(14 citation statements)

References 21 publications

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“…However, it could potentially take a high number of iterations to converge in a large mesh. To solve this issue, it is possible to implement a parallel version of the untangling and smoothing process in which several nodes of the mesh are moved at the same time . Nevertheless, it is needed to ensure that the nodes that are moved simultaneously are not in the same elements to avoid using information that is being updated.…”

Section: Discussionmentioning

confidence: 99%

“…To solve this issue, it is possible to implement a parallel version of the untangling and smoothing process in which several nodes of the mesh are moved at the same time. 42 Nevertheless, it is needed to ensure that the nodes that are moved simultaneously are not in the same elements to avoid using information that is being updated. Although we do not have a proof of the convergence of the proposed method, in all the cases that we have tested the optimization-based untangling and smoother, we have obtained a valid mesh of high-quality elements.…”

Section: Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Ruiz‐Gironés

Oliver

Socorro-Marrero

et al. 2017

Numerical Meth Engineering

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This is the peer reviewed version of the following article: Ruiz Gironès , E., Oliver , A., Socorro, G., Cascón, J., Escobar, J.M., Montenegro, R., Sarrate, J. Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures. "International journal for numerical methods in engineering", 2018, which has been published in final form at http://onlinelibrary.wiley.com/doi/10.1002/nme.5706/pdf. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.In this paper, we present a new method for inserting several triangulated surfaces into an existing tetrahedral mesh generated by the meccano method. The result is a conformal mesh where each inserted surface is approximated by a set of faces of the final tetrahedral mesh. First, the tetrahedral mesh is refined around the inserted surfaces to capture their geometric features. Second, each immersed surface is approximated by a set of faces from the tetrahedral mesh. Third, following a novel approach, the nodes of the approximated surfaces are mapped to the corresponding immersed surface. Fourth, we untangle and smooth the mesh by optimizing a regularized shape distortion measure for tetrahedral elements in which we move all the nodes of the mesh, restricting the movement of the edge and surface nodes along the corresponding entity they belong to. The refining process allows approximating the immersed surface for any initial meccano tetrahedral mesh. Moreover, the proposed projection method avoids computational expensive geometric projections. Finally, the applied simultaneous untangling and smoothing process delivers a high-quality mesh and ensures that the immersed surfaces are interpolated. Several examples are presented to assess the properties of the proposed method.Peer ReviewedPostprint (author's final draft

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Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Ruiz‐Gironés

Oliver

Socorro-Marrero

et al. 2017

Numerical Meth Engineering

Self Cite

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“…Also, most existing untangling methods have limitations to untangle highly tangled meshes. Several simultaneous untangling and smoothing methods are proposed [6,11]. These methods are preferred to pure optimization-based untangling methods since they are able to untangle inverted elements while improving element qualities.…”

Section: Previous Workmentioning

confidence: 99%

“…These poor-quality elements (also, inverted elements) deteriorate the accuracy and efficiency of PDE solutions. Most existing mesh untangling methods give high cost to inverted elements and minimize the cost function by solving nonlinear optimization problems [4][5][6]. However, existing mesh untangling algorithms have limitations for highly tangled meshes and do not always untangle inverted elements.…”

Section: Introductionmentioning

confidence: 99%

An Iterative Mesh Untangling Algorithm Using Edge Flip

Kim

2017

Mathematical Problems in Engineering

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Existing mesh untangling algorithms are unable to untangle highly tangled meshes. In this study, we address this problem by proposing an iterative mesh untangling algorithm using edge flip. Our goal is to produce meshes with no inverted elements and good element qualities when inverted elements with poor element qualities are produced during mesh generation or mesh deformation process. Our proposed algorithm is composed of three steps: first, we iteratively perform edge flip; subsequently, optimizationbased mesh untangling is conducted until all inverted elements are eliminated; finally, we perform mesh smoothing for generating high-quality meshes. Numerical results show that the proposed algorithm is able to successfully generate high-quality meshes with no inverted elements for highly tangled meshes.

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“…In addition, D'Amato and Venere [7] presented an implementation of a non-Laplacian smoothing method on the GPU to optimize tetrahedral meshes in parallel. Other recent efforts attempting at parallelizing mesh smoothing include those work presented in [1,2,10].…”

Section: Introductionmentioning

confidence: 99%

On the Accelerating of Two-dimensional Smart Laplacian Smoothing on the GPU

Zhao¹

2015

J. Inf. Comput. Sci.

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This paper presents a GPU-accelerated implementation of two-dimensional Smart Laplacian smoothing. This implementation is developed under the guideline of our paradigm for accelerating Laplacianbased mesh smoothing [13]. Two types of commonly used data layouts, Array-of-Structures (AoS) and Structure-of-Arrays (SoA) are used to represent triangular meshes in our implementation. Two iteration forms that have different choices of the swapping of intermediate data are also adopted. Furthermore, the feature CUDA Dynamic Parallelism (CDP) is employed to realize the nested parallelization in Smart Laplacian smoothing. Experimental results demonstrate that: (1) our implementation can achieve the speedups of up to 44x on the GPU GT640; (2) the data layout AoS can always obtain better efficiency than the SoA layout; (3) the form that needs to swap intermediate nodal coordinates is always slower than the one that does not swap data; (4) the version of our implementation with the use of the feature CDP is slightly faster than the version where the CDP is not adopted.

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Performance Evaluation of a Parallel Algorithm for Simultaneous Untangling and Smoothing of Tetrahedral Meshes

Cited by 15 publications

References 21 publications

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

Insertion of triangulated surfaces into a meccano tetrahedral discretization by means of mesh refinement and optimization procedures

An Iterative Mesh Untangling Algorithm Using Edge Flip

On the Accelerating of Two-dimensional Smart Laplacian Smoothing on the GPU

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