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Journal articles on the topic 'Tetrahedral mesh'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 June 2025

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1

Peng, Biao, Chunhua Zhou, and Junqiang Ai. "Solution Reconstruction on Unstructured Tetrahedral Meshes Using P1-Conservative Interpolation." Advances in Applied Mathematics and Mechanics 8, no. 5 (2016): 847–70. http://dx.doi.org/10.4208/aamm.2015.m1087.

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AbstractThis paper extends an algorithm of P1-conservative interpolation on triangular meshes to tetrahedral meshes and thus constructs an approach of solution reconstruction for three-dimensional problems. The conservation property is achieved by local mesh intersection and the mass of a tetrahedron of the current mesh is calculated by the integral on its intersection with the background mesh. For each current tetrahedron, the overlapped background tetrahedrons are detected efficiently. A mesh intersection algorithm is proposed to construct the intersection of a current tetrahedron with the overlapped background tetrahedron and mesh the intersection region by tetrahedrons. A localization algorithm is employed to search the host units in background mesh for each vertex of the current mesh. In order to enforce the maximum principle and avoid the loss of monotonicity, correction of nodal interpolated solution on tetrahedral meshes is given. The performance of the present solution reconstruction method is verified by numerical experiments on several analytic functions and the solution of the flow around a sphere.

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2

Pébay, Philippe P., and David Thompson. "Communication-Free Streaming Mesh Refinement." Journal of Computing and Information Science in Engineering 5, no. 4 (2005): 309–16. http://dx.doi.org/10.1115/1.2052806.

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This article presents a technique for the adaptive refinement of tetrahedral meshes. What makes this method new is that no neighbor information is required for the refined mesh to be compatible everywhere. Refinement consists of inserting new vertices at edge midpoints until some tolerance (geometric or otherwise) is met. For a tetrahedron, the six edges present 26=64 possible subdivision combinations. The challenge is to triangulate the new vertices (i.e., the original vertices plus some subset of the edge midpoints) in a way that neighboring tetrahedra always generate the same triangles on their shared boundary. A geometric solution based on edge lengths was developed previously, but did not account for geometric degeneracies (edges of equal length). This article provides a solution that works in all cases, while remaining entirely communication-free.

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3

SAVCHENKO, Maria, Olga EGOROVA, Ichiro HAGIWARA, and Vladimir SAVCHENKO. "Tetrahedral Mesh Reduction Technique." Journal of Computational Science and Technology 3, no. 1 (2009): 183–95. http://dx.doi.org/10.1299/jcst.3.183.

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4

Guo, YuFei, YongQing Hai, and JianFei Liu. "Direct modifications of tetrahedral meshes." Engineering Computations 37, no. 9 (2020): 3361–85. http://dx.doi.org/10.1108/ec-12-2019-0573.

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Purpose During the industrial design process, a product is usually modified and analyzed repeatedly until reaching the final design. Modifying the model and regenerating a mesh for every update during this process is very time consuming. To improve efficiency, it is necessary to circumvent the computer-aided design modeling stage when possible and directly modify the meshes to save valuable time. The purpose of this paper is to develop a method for mesh modifications. Design/methodology/approach In contrast to existing studies, which focus on one or a class of modifications, this paper comprehensively studies mesh union, mesh gluing, mesh cutting and mesh partitioning. To improve the efficiency of the method, the paper presents a fast and effective surface mesh remeshing algorithm based on a ball-packing method and controls the remeshing regions with a size field. Findings Examples and results show that the proposed mesh modification method is efficient and effective. The proposed method can be also applied to meshes with different material properties, which is very different with previous work that is only suitable for the meshes with same material property. Originality/value This paper proposes an efficient and comprehensive tetrahedral mesh modification method, through which engineers can directly modify meshes instead of models and save time.

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Meshkat, Sia, and Dafna Talmor. "Generating a mixed mesh of hexahedra, pentahedra and tetrahedra from an underlying tetrahedral mesh." International Journal for Numerical Methods in Engineering 49, no. 1-2 (2000): 17–30. http://dx.doi.org/10.1002/1097-0207(20000910/20)49:1/2<17::aid-nme920>3.0.co;2-u.

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Luo, Dan, Yu Zhang, and Jia Li. "Research on Several Key Problems of Medical Image Segmentation and Virtual Surgery." Contrast Media & Molecular Imaging 2022 (April 11, 2022): 1–18. http://dx.doi.org/10.1155/2022/3463358.

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Medical images play an important role in modern medical diagnosis. Many clinicians make correct and appropriate diagnosis and treatment plans by means of medical images. With the development of science and technology, the application of medical image needs not only to simply read the image, but also to fuse advanced technology to analyze and process the image from a deeper level, such as the proposal of virtual surgery. Therefore, this article focuses on several key issues of medical image segmentation and virtual surgery. First, medical images are preprocessed by gray level transformation, interpolation, and noise elimination techniques. Second, level set model-based segmentation algorithm is adopted and improved. Finally, a constrained Delaunay tetrahedron method based on a point-by-point insertion method is proposed to reconstruct the tetrahedron mesh model. In order to eliminate the thin element, the tetrahedron mesh model is optimized. The simulation results show that this article improves the segmentation algorithm based on the level set model, which effectively improves the contradiction between the convergence accuracy and the convergence speed of the algorithm. The proposed tetrahedral mesh reconstruction algorithm realizes the generation of tetrahedral finite element meshes with complex boundaries and improves the quality of the volume model by optimizing the model.

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7

姜, 文芳. "Lagrange Interpolation on Tetrahedral Mesh." Advances in Applied Mathematics 07, no. 12 (2018): 1486–89. http://dx.doi.org/10.12677/aam.2018.712172.

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8

Danilov, A. A. "Unstructured tetrahedral mesh generation technology." Computational Mathematics and Mathematical Physics 50, no. 1 (2010): 139–56. http://dx.doi.org/10.1134/s0965542510010124.

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9

Knupp, P. M. "Hexahedral and Tetrahedral Mesh Untangling." Engineering with Computers 17, no. 3 (2001): 261–68. http://dx.doi.org/10.1007/s003660170006.

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10

Au, Kin Man, and Kai Ming Yu. "Balanced Octree for Tetrahedral Mesh Generation." Materials Science Forum 471-472 (December 2004): 608–12. http://dx.doi.org/10.4028/www.scientific.net/msf.471-472.608.

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Nowadays, with the advances of Finite Element Analysis (FEA) packages, some of the engineering and design problems such as stress or thermal deformation can be successfully solved. These are convenient for better incorporating the design constraints of various tasks such as injection molded parts, or rapid prototyping and tooling. Mesh generation is the major step of finite element method for numerical computation. Common types of mesh include triangulation or tetrahedralization. During the mesh generation process, we always find difficulty in the formation of a uniform, non-conformal mesh. The undesirable mesh will adversely influence the accuracy and meshing time of the model. This paper will, thus, propose an effective approach to extend to threedimensional (3D) mesh generation by octree balancing method so as to adjust the mesh pattern. In this paper, the implementation of octree balancing will be explained and illustrated with real life example. The proposed method includes three main steps. Problematic unbalanced octants will be detected and Steiner points will be added as appropriate before the tetrahedral mesh generation. The balanced octree will form good tetrahedral meshes for further analysis. Then the balanced and unbalanced meshes will be compared for efficiency and accuracy for mesh generation.

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11

Cai, Jian, Lan Chen, and Umezuruike Linus Opara. "Numerical Simulation of Powder Dispersion Performance by Different Mesh Types." Key Engineering Materials 680 (February 2016): 82–85. http://dx.doi.org/10.4028/www.scientific.net/kem.680.82.

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OBJECTIVE To investigate the influence of mesh type on numerical simulating the dispersion performance of micro-powders through a home-made tube. METHODS With the computational fluid dynamics (CFD) method, a powder dispersion tube was meshed in three different types, namely, tetrahedral, unstructured hexahedral and prismatic-tetrahedral hybrid meshes. The inner flow field and the kinetic characteristics of the particles were investigated. Results of the numerical simulation were compared with literature evidences. RESULTS The results showed that using tetrahedral mesh had the highest computational efficiency, while employing the unstructured hexahedral mesh obtained more accurate outlet velocity. The simulation results of the inner flow field and the kinetic characteristics of the particles were slightly different among the three mesh types. The calculated particle velocity using the tetrahedral mesh had the best correlation with the changing trend of the fine particle mass in the first 4 stages of the new generation impactor (NGI) (R2 = 0.91 and 0.89 for powder A and B, respectively). Conclusions Mesh type affected computational time, accuracy of simulation results and the prediction abilities of fine particle deposition.

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12

Borisenko, V. V., N. S. Serova, and A. M. Chepovskiy. "Reconstruction of Three-Dimensional Geometry of the Vessels by Computed Tomography Data." Vestnik NSU. Series: Information Technologies 17, no. 3 (2019): 5–17. http://dx.doi.org/10.25205/1818-7900-2019-17-3-5-17.

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We consider algorithms of 3D reconstruction for the internal surface of cardiac vessels. The precise reconstruction of vessel geometry is necessary for the creating a hydrodynamic model of blood supply for the heart and computing various parameters of blood flow. To compute a triangulation of blood vessel walls, we use the combination of two methods. At the first stage we apply the 3D seeded region growing algorithm to reconstruct a set of voxels inside vessels. At the second stage we use the isosurface reconstruction algorithm based on the tessellation of 3D space into small tetrahedral cells. We use the tetrahedral mesh, which was proposed in the works of S. Chan, E. Purisima (1998), and V. Skala (2000). Tetrahedra in this mesh are constructed on common faces of adjacent cubes in a cubic lattice, so it fits well with the voxel model. The mesh is constructed only in the neighborhood of the border of voxel set obtained at the first stage as the result of seeded region growing algorithms.

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13

Yamakawa, Soji, and Kenji Shimada. "Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency." International Journal for Numerical Methods in Engineering 80, no. 1 (2009): 74–102. http://dx.doi.org/10.1002/nme.2634.

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14

Zhang, Zi Xian, Ichiro Hagiwara, Maria Savchenko, Yi Xiong Feng, and Junichi Shinoda. "A Novel Tetrahedral Mesh Generation Algorithm for Finite Element Analysis." Advanced Materials Research 189-193 (February 2011): 545–48. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.545.

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In this paper, a robust tetrahedral mesh generation method based on Advancing Front technique is proposed. The proposed method inherits advantages of Delaunay method and Advancing Front method, such as efficiency of Delaunay method and maintaining the given boundary triangle mesh exactly of advancing front method. Tetrahedral mesh is generated from the given triangle surface mesh. This method mainly includes three stages. Firstly, the minimum container box of the triangular surface mesh is calculated and points are inserted into the box. Then the proper point is selected out to generate tetrahedron’s layers from surface to the interior volume of the model, so g the surface mesh can be maintained. The operation is simplified, and calculation efficiency is also higher than common Advancing Front method. At last, triangle intersection is examined. This technique allows generating the tetrahedral mesh with high quality elements with surface mesh preservation. A shoes model with both convex and concave surface is chosen for the experiment. The result clarified the robust and high efficiency of the proposed algorithm.

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15

Lu, Shenglian, Xinyu Guo, Chunjiang Zhao, and Changfeng Li. "Physical Model for Interactive Deformation of 3D Plant." International Journal of Virtual Reality 10, no. 2 (2011): 33–38. http://dx.doi.org/10.20870/ijvr.2011.10.2.2809.

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Modeling the deformation of 3D plant is a challenge in computer graphics. This paper presents a simulation method for physically simulating interactive deformation of 3D plant models. This method creates a tetrahedral mesh from the initial triangular plant model, the tetrahedral mesh is then used for dynamic response calculation of collision or interaction, the original triangular mesh is deformed along with the tetrahedral mesh. A capsule-based method and a spatial hashing based method are used for efficient and accurate collision detection. Smooth deformation effects and real-time simulation on 3D plant models demonstrate the effectiveness of our method. The main contribution of this paper is the proposed method can handle the geometric complexity of various plants by a simple model.

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16

Xu, Kai, Zhi-Quan Cheng, Yanzhen Wang, Yueshan Xiong, and Hao Zhang. "Quality encoding for tetrahedral mesh optimization." Computers & Graphics 33, no. 3 (2009): 250–61. http://dx.doi.org/10.1016/j.cag.2009.03.020.

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17

Zhang, Wenjing, Yuewen Ma, Jianmin Zheng, and William J. Allen. "Tetrahedral mesh deformation with positional constraints." Computer Aided Geometric Design 81 (August 2020): 101909. http://dx.doi.org/10.1016/j.cagd.2020.101909.

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18

Jensen, Kristian Ejlebjerg, and Gerard Gorman. "Details of tetrahedral anisotropic mesh adaptation." Computer Physics Communications 201 (April 2016): 135–43. http://dx.doi.org/10.1016/j.cpc.2015.12.002.

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19

Kettunen, Lauri, and Kimmo Forsman. "Tetrahedral mesh generation in convex primitives." International Journal for Numerical Methods in Engineering 38, no. 1 (1995): 99–117. http://dx.doi.org/10.1002/nme.1620380107.

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20

Chen, Jianjun, Jianjing Zheng, Yao Zheng, Zhoufang Xiao, Hang Si, and Yufeng Yao. "Tetrahedral mesh improvement by shell transformation." Engineering with Computers 33, no. 3 (2016): 393–414. http://dx.doi.org/10.1007/s00366-016-0480-z.

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21

Song, Songhe, Min Wan, Shengxi Wang, Desheng Wang, and Zhengping Zou. "Robust and Quality Boundary Constrained Tetrahedral Mesh Generation." Communications in Computational Physics 14, no. 5 (2013): 1304–21. http://dx.doi.org/10.4208/cicp.030612.010313a.

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AbstractA novel method for boundary constrained tetrahedral mesh generation is proposed based on Advancing Front Technique (AFT) and conforming Delaunay triangulation. Given a triangulated surface mesh, AFT is firstly applied to mesh several layers of elements adjacent to the boundary. The rest of the domain is then meshed by the conforming Delaunay triangulation. The non-conformal interface between two parts of meshes are adjusted. Mesh refinement and mesh optimization are then preformed to obtain a more reasonable-sized mesh with better quality. Robustness and quality of the proposed method is shown. Convergence proof of each stage as well as the whole algorithm is provided. Various numerical examples are included as well as the quality of the meshes.

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22

Yang, Caiyun, Yutaka Ohtake, and Hiromasa Suzuki. "Sealed Decomposition of a Triangular Mesh with Tetrahedral Mesh Segmentation." Computer-Aided Design and Applications 8, no. 3 (2011): 421–33. http://dx.doi.org/10.3722/cadaps.2011.421-433.

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23

Waluyo, S. "Minimizing Artificial Stiffness in Linear Tetrahedral Element Using Virtual Mesh Refinement." Journal of Mechanics 34, no. 3 (2016): 291–97. http://dx.doi.org/10.1017/jmech.2016.113.

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AbstractThis work presents a new method to minimize artificial stiffness in linear tetrahedral element using virtual mesh refinement (VRM) method. The basic idea behind this work is to give additional degree of freedom by using internal mesh over the linear tetrahedral element. This local internal mesh and its corresponding equilibrium condition under particular boundary condition are invisible to users or virtual. Using specialized displacement test vectors, strain energy is obtained and used to calculate reduction factor for artificial stiffness. Numerical experiments are performed at the end to briefly qualitatively show performance of our proposed method.

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BERZINS, MARTIN. "SOLUTION-BASED MESH QUALITY INDICATORS FOR TRIANGULAR AND TETRAHEDRAL MESHES." International Journal of Computational Geometry & Applications 10, no. 03 (2000): 333–46. http://dx.doi.org/10.1142/s021819590000019x.

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A new mesh quality measure for triangular and tetrahedral meshes is presented. This mesh quality measure is based both on geometrical and solution information and is derived by considering the error when linear triangular and tetrahedral elements are used to approximate a quadratic function. The new measure is shown to be related to existing measures of mesh quality but with the advantage that local solution information in the form of scaled derivatives along edges is taken into account. This advantage is demonstrated by a comparison with a geometrical indicator on a parameterized problem.

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25

Mohamad Lutfi Samsudin and Hasril Hasini. "Application of Polyhedral Mesh for Vortex Formation Study for Simple Single Pump Sump." CFD Letters 13, no. 9 (2021): 13–27. http://dx.doi.org/10.37934/cfdl.13.9.1327.

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Meshing of domain in CFD is an important step to ensure accuracy of the solution. In the past, hexahedral or tetrahedral mesh systems were commonly used, and both have their merits and demerits. For large and complex geometry, polyhedral is another option but its accuracy is claimed to be lacking. In this paper, the use of polyhedral mesh system by past researchers are reviewed. Evaluation on the application of polyhedral mesh system for the study of the vortex formation with a simple single pump sump model is made. Validation was made through the comparison of the results from hexahedral, tetrahedral and polyhedral mesh sizes and the experimental data from published data. The polyhedral mesh system was found to perform satisfactorily and was able to match the results from the hexahedral mesh system as well as the experimental data.

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Xi, Ning, Yinjie Sun, Lei Xiao, and Gang Mei. "Designing Parallel Adaptive Laplacian Smoothing for Improving Tetrahedral Mesh Quality on the GPU." Applied Sciences 11, no. 12 (2021): 5543. http://dx.doi.org/10.3390/app11125543.

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Mesh quality is a critical issue in numerical computing because it directly impacts both computational efficiency and accuracy. Tetrahedral meshes are widely used in various engineering and science applications. However, in large-scale and complicated application scenarios, there are a large number of tetrahedrons, and in this case, the improvement of mesh quality is computationally expensive. Laplacian mesh smoothing is a simple mesh optimization method that improves mesh quality by changing the locations of nodes. In this paper, by exploiting the parallelism features of the modern graphics processing unit (GPU), we specifically designed a parallel adaptive Laplacian smoothing algorithm for improving the quality of large-scale tetrahedral meshes. In the proposed adaptive algorithm, we defined the aspect ratio as a metric to judge the mesh quality after each iteration to ensure that every smoothing improves the mesh quality. The adaptive algorithm avoids the shortcoming of the ordinary Laplacian algorithm to create potential invalid elements in the concave area. We conducted 5 groups of comparative experimental tests to evaluate the performance of the proposed parallel algorithm. The results demonstrated that the proposed adaptive algorithm is up to 23 times faster than the serial algorithms; and the accuracy of the tetrahedral mesh is satisfactorily improved after adaptive Laplacian mesh smoothing. Compared with the ordinary Laplacian algorithm, the proposed adaptive Laplacian algorithm is more applicable, and can effectively deal with those tetrahedrons with extremely poor quality. This indicates that the proposed parallel algorithm can be applied to improve the mesh quality in large-scale and complicated application scenarios.

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27

Schneider, Teseo, Yixin Hu, Xifeng Gao, Jérémie Dumas, Denis Zorin, and Daniele Panozzo. "A Large-Scale Comparison of Tetrahedral and Hexahedral Elements for Solving Elliptic PDEs with the Finite Element Method." ACM Transactions on Graphics 41, no. 3 (2022): 1–14. http://dx.doi.org/10.1145/3508372.

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The Finite Element Method (FEM) is widely used to solve discrete Partial Differential Equations (PDEs) in engineering and graphics applications. The popularity of FEM led to the development of a large family of variants, most of which require a tetrahedral or hexahedral mesh to construct the basis. While the theoretical properties of FEM basis (such as convergence rate, stability, etc.) are well understood under specific assumptions on the mesh quality, their practical performance, influenced both by the choice of the basis construction and quality of mesh generation, have not been systematically documented for large collections of automatically meshed 3D geometries. We introduce a set of benchmark problems involving most commonly solved elliptic PDEs, starting from simple cases with an analytical solution, moving to commonly used test problem setups, and using manufactured solutions for thousands of real-world, automatically meshed geometries. For all these cases, we use state-of-the-art meshing tools to create both tetrahedral and hexahedral meshes, and compare the performance of different element types for common elliptic PDEs. The goal of this benchmark is to enable comparison of complete FEM pipelines, from mesh generation to algebraic solver, and exploration of relative impact of different factors on the overall system performance. As a specific application of our geometry and benchmark dataset, we explore the question of relative advantages of unstructured (triangular/ tetrahedral) and structured (quadrilateral/hexahedral) discretizations. We observe that for Lagrange-type elements, while linear tetrahedral elements perform poorly, quadratic tetrahedral elements perform equally well or outperform hexahedral elements for our set of problems and currently available mesh generation algorithms. This observation suggests that for common problems in structural analysis, thermal analysis, and low Reynolds number flows, high-quality results can be obtained with unstructured tetrahedral meshes, which can be created robustly and automatically. We release the description of the benchmark problems, meshes, and reference implementation of our testing infrastructure to enable statistically significant comparisons between different FE methods, which we hope will be helpful in the development of new meshing and FEA techniques.

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28

Keranen, J., J. Kangas, A. Ahola, and L. Kettunen. "Implicit Yee-like scheme on tetrahedral mesh." IEEE Transactions on Magnetics 38, no. 2 (2002): 717–20. http://dx.doi.org/10.1109/20.996186.

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29

Si, Hang. "Constrained Delaunay tetrahedral mesh generation and refinement." Finite Elements in Analysis and Design 46, no. 1-2 (2010): 33–46. http://dx.doi.org/10.1016/j.finel.2009.06.017.

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30

Ibanez, D. A., E. Love, T. E. Voth, J. R. Overfelt, N. V. Roberts, and G. A. Hansen. "Tetrahedral mesh adaptation for Lagrangian shock hydrodynamics." Computers & Mathematics with Applications 78, no. 2 (2019): 402–16. http://dx.doi.org/10.1016/j.camwa.2018.06.013.

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31

Freitag, Lori A., and Carl Ollivier-Gooch. "Tetrahedral mesh improvement using swapping and smoothing." International Journal for Numerical Methods in Engineering 40, no. 21 (1997): 3979–4002. http://dx.doi.org/10.1002/(sici)1097-0207(19971115)40:21<3979::aid-nme251>3.0.co;2-9.

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32

Marshall, J. S., J. R. Grant, A. A. Gossler, and S. A. Huyer. "Vorticity Transport on a Lagrangian Tetrahedral Mesh." Journal of Computational Physics 161, no. 1 (2000): 85–113. http://dx.doi.org/10.1006/jcph.2000.6490.

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33

Shephard, Mark S. "Update to: Approaches to the Automatic Generation and Control of Finite Element Meshes." Applied Mechanics Reviews 49, no. 10S (1996): S5—S14. http://dx.doi.org/10.1115/1.3101978.

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This paper updates the status of efforts on the development of automatic mesh generation techniques for general three-dimensional domains. The technical areas reviewed include: (i) issues associated with automatic mesh generation of CAD geometric models, (ii) local mesh modification procedures for improving mesh quality, (iii) advances in tetrahedral mesh generators, (iv) generation of anisotropic meshes, (v) hexahedral mesh generators, and (vi) implementation of automatic mesh generators on parallel computers.

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34

Dassi, Franco, Lennard Kamenski, and Hang Si. "Tetrahedral Mesh Improvement Using Moving Mesh Smoothing and Lazy Searching Flips." Procedia Engineering 163 (2016): 302–14. http://dx.doi.org/10.1016/j.proeng.2016.11.065.

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35

BLANDFORD, DANIEL K., GUY E. BLELLOCH, DAVID E. CARDOZE, and CLEMENS KADOW. "COMPACT REPRESENTATIONS OF SIMPLICIAL MESHES IN TWO AND THREE DIMENSIONS." International Journal of Computational Geometry & Applications 15, no. 01 (2005): 3–24. http://dx.doi.org/10.1142/s0218195905001580.

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We describe data structures for representing simplicial meshes compactly while supporting online queries and updates efficiently. Our data structure requires about a factor of five less memory than the most efficient standard data structures for triangular or tetrahedral meshes, while efficiently supporting traversal among simplices, storing data on simplices, and insertion and deletion of simplices. Our implementation of the data structures uses about 5 bytes/triangle in two dimensions (2D) and 7.5 bytes/tetrahedron in three dimensions (3D). We use the data structures to implement 2D and 3D incremental algorithms for generating a Delaunay mesh. The 3D algorithm can generate 100 Million tetrahedra with 1 Gbyte of memory, including the space for the coordinates and all data used by the algorithm. The runtime of the algorithm is as fast as Shewchuk's Pyramid code, the most efficient we know of, and uses a factor of 3.5 less memory overall.

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36

Zhao, Jing, Zhongyu Mao, Wenming Zhou, and Yongguo Feng. "Stability impact on wind turbine blades trailing edge from bonding zone modelling methods." Journal of Physics: Conference Series 2854, no. 1 (2024): 012105. http://dx.doi.org/10.1088/1742-6596/2854/1/012105.

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Abstract The trailing edge of wind turbine blade will undergo a large deformation under the action of load, resulting in a higher risk of damage and failure. The finite element analysis modeling method directly affects the simulation result, furthermore impacts the result of blade structure design. Therefore, it is necessary to find out a modeling method, which is capable to reflect the stability of bonding regions more accurately. This paper aims to discuss the influences of different finite element modeling methods on the buckling stability of blade trailing edge. The influences of shell element, tetrahedron element and hexahedron element on the blade stiffness are considered. The bonding region were simulated separately by combining shell element with bonding web, shell element with tetrahedron element and shell element with hexahedron. The influences of different bonding region modeling methods on the trailing edge buckling factor were analyzed by using the eigenvalue buckling analysis method of finite element. The simulation results provided data support for the future validation of the blade trailing edge bonding area modeling method. The results show that, the tetrahedral mesh provides a higher stiffness, followed by the hexahedral mesh, and the adhesive web form has the smallest stiffness. In order to simulate the more realistic stiffness of the adhesive area at the trailing edge of the blade, adhesive web plates can be built in the flange area of the blade root and the core material area of the trial adhesive mold; The direct bonding area can be simulated employing the hexahedron mesh; The tetrahedral mesh has high stiffness and is not suitable for modeling the adhesive area at the trailing edge. Blade simulation modeling can flexibly use different adhesive forms according to actual situations, ensuring the reliability of the simulation model.

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Okada, Hiroshi, Hiroshi Kawai, Kousuke Araki, and Tsubasa Miyazaki. "Three-Dimensional Crack Propagation Analysis Based on VCCM (Virtual Crack Closure-Integral Method) for Tetrahedral Finite Element." Advanced Materials Research 33-37 (March 2008): 901–6. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.901.

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This paper describes the development of a software to perform three-dimensional crack propagation analyses. The software is based on the conventional finite element method with second order tetrahedral element and an automatic mesh generation software. Hexahedral finite elements have historically been used in fracture analyses and methodologies to compute the crack parameters have been developed for the hexahedral elements. In present research, the authors have developed a VCCM (virtual crack closure-integral method) for the second order tetrahedral finite element. Use of the tetrahedral element allows us to utilize an automatic mesh generation software. The direction and rate of crack propagation are predicted based on the stress intensity factors and the shape of crack is updated. Hence, a software package containing the modules for mesh generation, for finite element analysis, for stress intensity factor evaluation, for predicting the rate and the direction of crack propagation and for updating crack configuration, can be developed.

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38

Vasilev, Eugene, Dmitry Lachinov, Anton Grishin, and Vadim Turlapov. "Fast tetrahedral mesh generation and segmentation of an atlas-based heart model using a periodic uniform grid." Russian Journal of Numerical Analysis and Mathematical Modelling 33, no. 5 (2018): 315–23. http://dx.doi.org/10.1515/rnam-2018-0026.

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Abstract A fast procedure for generation of regular tetrahedral finite element mesh for objects with complex shape cavities is proposed. The procedure like LBIE-Mesher can generate tetrahedral meshes for the volume interior to a polygonal surface, or for an interval volume between two surfaces having a complex shape and defined in STL-format. This procedure consists of several stages: generation of a regular tetrahedral mesh that fills the volume of the required object; generation of clipping for the uniform grid parts by a boundary surface; shifting vertices of the boundary layer to align onto the surface.We present a sequential and parallel implementation of the algorithm and compare their performance with existing generators of tetrahedral grids such as TetGen, NETGEN, and CGAL. The current version of the algorithm using the mobile GPU is about 5 times faster than NETGEN. The source code of the developed software is available on GitHub.

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Li, Wang, and Wang. "A Fast Particle-Locating Method for the Arbitrary Polyhedral Mesh." Algorithms 12, no. 9 (2019): 179. http://dx.doi.org/10.3390/a12090179.

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A fast particle-locating method is proposed for the hybrid Euler–Lagrangian models on the arbitrary polyhedral mesh, which is of essential importance to improve the computational efficiency by searching the host cells for the tracked particles very efficiently. A background grid, i.e., a uniform Cartesian grid with a grid spacing much smaller than computational mesh, is constructed over the whole computational domain. The many-to-many mapping relation between the computational mesh and the background grid is then specified through a recursive tetrahedron neighbor searching procedure, after the tetrahedral decomposition of computational cells and a mapping inverse operation. Finally, the host cell is straightforwardly identified by the point-in-cell test among the optional elements determined based on the mapping relation. The proposed method is checked on three meshes with different types of the cells and compared with the existing methods in the literatures. The results reveal that the present method is highly efficient and easy to implement on the arbitrary polyhedral mesh.

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Febrianto, Pramudya, M. Ghulam Muzakki, and Azhari Sastranegara. "Studi Komparatif Mesh Hexahedral dan Tetrahedral pada Analisis Statis Crane Hook dengan ANSYS." Jurnal Teknik Mesin Sinergi 22, no. 1 (2024): 63. http://dx.doi.org/10.31963/sinergi.v22i1.4834.

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Dalam proses pemindahan barang, hook crane diperlukan sebagai pengait beban berat. Untuk memastikan integritas struktural dan keamanan hook crane, diperlukan desain dan analisis yang melibatkan perhitungan serta simulasi rumit guna memprediksi perilakunya dalam menangani beban tertentu dan kondisi terbatas. Penelitian ini bertujuan untuk mengetahui keefektifan mesh hexahedral dan tetrahedral dalam analisis statis hook crane menggunakan software ANSYS. Proses analisis melibatkan pembuatan model hook crane dan penerapan teknik meshing yang berbeda. Hasil analisis dibandingkan untuk menilai keakuratan dan efisiensi waktu komputasi dari masing-masing teknik meshing. Temuan penelitian ini akan memberikan kontribusi penting dalam pengembangan metode yang lebih akurat dan efisien untuk menganalisis hook crane, meningkatkan keamanan dan kinerja komponen penting ini dalam berbagai aplikasi industri. Penelitian ini menggunakan berbagai jenis mesh, baik orde rendah maupun orde tinggi, dan menunjukkan kemampuan yang berbeda dalam menangkap distribusi tegangan pada struktur geometri hook crane. Mesh tetrahedral orde rendah dan tinggi memberikan hasil yang serupa dengan efisiensi komputasi yang baik dibandingkan dengan mesh hexahedral orde rendah. Meskipun mesh hexahedral orde tinggi menghasilkan distribusi tegangan yang lebih linear, penggunaannya memerlukan waktu komputasi yang lebih lama. Selain itu, penelitian ini menunjukkan bahwa pemilihan jenis mesh harus didasarkan pada kriteria spesifik dari kasus yang sedang dianalisis, dengan mempertimbangkan trade-off antara kepresisian hasil dan efisiensi komputasi.Dalam proses pemindahan barang, hook crane diperlukan sebagai pengait beban berat. Untuk memastikan integritas struktural dan keamanan hook crane, diperlukan desain dan analisis yang melibatkan perhitungan serta simulasi rumit guna memprediksi perilakunya dalam menangani beban tertentu dan kondisi terbatas. Penelitian ini bertujuan untuk mengetahui keefektifan mesh hexahedral dan tetrahedral dalam analisis statis hook crane menggunakan software ANSYS. Proses analisis melibatkan pembuatan model hook crane dan penerapan teknik meshing yang berbeda. Hasil analisis dibandingkan untuk menilai keakuratan dan efisiensi waktu komputasi dari masing-masing teknik meshing. Temuan penelitian ini akan memberikan kontribusi penting dalam pengembangan metode yang lebih akurat dan efisien untuk menganalisis hook crane, meningkatkan keamanan dan kinerja komponen penting ini dalam berbagai aplikasi industri. Penelitian ini menggunakan berbagai jenis mesh, baik orde rendah maupun orde tinggi, dan menunjukkan kemampuan yang berbeda dalam menangkap distribusi tegangan pada struktur geometri hook crane. Mesh tetrahedral orde rendah dan tinggi memberikan hasil yang serupa dengan efisiensi komputasi yang baik dibandingkan dengan mesh hexahedral orde rendah. Meskipun mesh hexahedral orde tinggi menghasilkan distribusi tegangan yang lebih linear, penggunaannya memerlukan waktu komputasi yang lebih lama. Selain itu, penelitian ini menunjukkan bahwa pemilihan jenis mesh harus didasarkan pada kriteria spesifik dari kasus yang sedang dianalisis, dengan mempertimbangkan trade-off antara kepresisian hasil dan efisiensi komputasi.[PF1] [PF1]Sudah diperbaiki, mohon tinjauannya.

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Chen, Longbao, and Ding Zhou. "Analysis of Numerical Instability Factors and Geometric Reconstruction in 3D SIMP-Based Topology Optimization Towards Enhanced Manufacturability." Applied Sciences 15, no. 11 (2025): 6195. https://doi.org/10.3390/app15116195.

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The advancement of topology optimization (TO) and additive manufacturing (AM) has significantly enhanced structural design flexibility and the potential for lightweight structures. However, challenges such as intermediate density, mesh dependency, checkerboard patterns, and local extrema in TO can lead to suboptimal performance. Moreover, existing AM technologies confront geometric constraints that limit their application. This study investigates minimum compliance as the objective function and volume as the constraint, employing the solid isotropic material with penalization method, density filtering, and the method of moving asymptotes. It examines how factors like mesh type, mesh size, volume fraction, material properties, initial density, filter radius, and penalty factor influence the TO results for a metallic gooseneck chain. The findings suggest that material properties primarily affect numerical variations along the TO path, with minimal impact on structural configuration. For both hexahedral and tetrahedral mesh types, a recommended mesh size is identified where the results show less than a 1% difference across varying mesh sizes. An initial density of 0.5 is advised, with a filter radius of approximately 2.3 to 2.5 times the average unit edge length for hexahedral meshes and 1.3 to 1.5 times for tetrahedral meshes. The suggested penalty factor ranges of 3–4 for hexahedral meshes and 2.5–3.5 for tetrahedral meshes. The optimal geometric reconstruction model achieves weight reductions of 23.46% and 22.22% compared to the original model while satisfying static loading requirements. This work contributes significantly to the integration of TO and AM in engineering, laying a robust foundation for future design endeavors.

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Kuprat, Andrew, Denise George, Eldon Linnebur, Harold Trease, and R. Kent Smith. "Moving Adaptive Unstructured 3-D Meshes in Semiconductor Process Modeling Applications." VLSI Design 6, no. 1-4 (1998): 373–78. http://dx.doi.org/10.1155/1998/15828.

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The next generation of semiconductor process and device modeling codes will require 3-D mesh capabilities including moving volume and surface grids, adaptive mesh refinement and adaptive mesh smoothing. To illustrate the value of these techniques, a time dependent process simulation model was constructed using analytic functions to return time dependent dopant concentration and time dependent SiO2 volume and surface velocities. Adaptive mesh refinement and adaptive mesh smoothing techniques were used to resolve the moving boron dopant diffusion front in the Si substrate. The adaptive mesh smoothing technique involves minimizing the L2 norm of the gradient of the error between the true dopant concentration and the piecewise linear approximation over the tetrahedral mesh thus assuring that the mesh is optimal for representing evolving solution gradients. Also implemented is constrained boundary smoothing, wherein the moving SiO2/Si interface is represented by moving nodes that correctly track the interface motion, and which use their remaining degrees of freedom to minimize the aforementioned error norm. Thus, optimal tetrahedral shape and alignment is obtained even in the neighborhood of a moving boundary. If desired, a topological “reconnection” step maintains a Delaunay mesh at all times. The combination of adaptive refinement, adaptive smoothing, and mesh reconnection gives excellent front tracking, feature resolution, and grid quality for finite volume/finite element computation.

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Li, Guang Jun, Wen Jing Wang, Li An, and Ze Jin Zhang. "Research on Hexahedral and Tetrahedral Mesh Applied to Strength Analysis of Bogie Frame." Applied Mechanics and Materials 477-478 (December 2013): 150–54. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.150.

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The structure of bogie frame is meshed by hexahedral and tetrahedral elements respectively. FE analysis is taken based on the loads defined by JIS E 4207 standard and the stress distributions of two separate models are obtained. To clarify the accuracy of two kinds of finite element models, the bench test of the bogie frame is carried out. It shows that both the hexahedral and tetrahedral models are valid according to the comparison between FE results and experimental values when the structural model is regular. However, for complex structure model 10-node tetrahedral model takes precedence.

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Huang, C., J. Zhang, L. Liu, and G. Li. "A quality and efficient tetrahedral mesh generation method." Australian Journal of Mechanical Engineering 11, no. 2 (2013): 121–30. http://dx.doi.org/10.7158/m12-021.2013.11.2.

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Zhao, Jianjun. "STABLE TETRAHEDRAL MESH GENERATION ALGORITHM WITH BOUNDARY CONSISTENCY." Chinese Journal of Mechanical Engineering 40, no. 06 (2004): 100. http://dx.doi.org/10.3901/jme.2004.06.100.

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Usui, Yoshiya, Takafumi Kasaya, Yasuo Ogawa, and Hisanori Iwamoto. "Marine magnetotelluric inversion with an unstructured tetrahedral mesh." Geophysical Journal International 214, no. 2 (2018): 952–74. http://dx.doi.org/10.1093/gji/ggy171.

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Ohtake, Yutaka, Hiroshi Kawaharada, and Masaki Moriguchi. "9D-09 Tetrahedral Mesh Generation from Segmented Volume." Proceedings of the Bioengineering Conference Annual Meeting of BED/JSME 2010.23 (2011): 369–70. http://dx.doi.org/10.1299/jsmebio.2010.23.369.

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Si, Hang. "TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator." ACM Transactions on Mathematical Software 41, no. 2 (2015): 1–36. http://dx.doi.org/10.1145/2629697.

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You, Y. H., X. Y. Kou, and S. T. Tan. "Adaptive Tetrahedral Mesh Generation of 3D Heterogeneous Objects." Computer-Aided Design and Applications 12, no. 5 (2015): 580–88. http://dx.doi.org/10.1080/16864360.2015.1014736.

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Biswas, Rupak, and Roger C. Strawn. "Tetrahedral and hexahedral mesh adaptation for CFD problems." Applied Numerical Mathematics 26, no. 1-2 (1998): 135–51. http://dx.doi.org/10.1016/s0168-9274(97)00092-5.

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