Adaptive tetrahedral mesh generation by constrained centroidal voronoi-delaunay tessellations for finite element methods

2013 ◽  
Vol 30 (5) ◽  
pp. 1633-1653 ◽  
Author(s):  
Jie Chen ◽  
Yunqing Huang ◽  
Desheng Wang ◽  
Xiaoping Xie
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Delaunay Tessellations ◽  
Tetrahedral Mesh Generation

Balanced Octree for Tetrahedral Mesh Generation

2004 ◽  
Vol 471-472 ◽  
pp. 608-612 ◽  
Author(s):  
Kin Man Au ◽  
Kai Ming Yu
Keyword(s):  
Finite Element ◽  
Mesh Generation ◽  
Real Life ◽  
Tetrahedral Mesh ◽  
Generation Process ◽  
Major Step ◽  
Element Analysis ◽  
Molded Parts ◽  
Tetrahedral Mesh Generation ◽  
As Stress

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.

An Evaluation of Tetrahedral Mesh Generation for Nonrigid Registration of Brain MRI

2011 ◽  
pp. 131-142 ◽  
Author(s):  
Panagiotis A. Foteinos ◽  
Yixun Liu ◽  
Andrey N. Chernikov ◽  
Nikos P. Chrisochoides
Keyword(s):  
Mesh Generation ◽  
Brain Mri ◽  
Tetrahedral Mesh ◽  
Nonrigid Registration ◽  
Tetrahedral Mesh Generation

scholarly journals Survey of meshless and generalized finite element methods: A unified approach

Acta Numerica ◽  
2003 ◽  
Vol 12 ◽  
pp. 1-125 ◽  
Author(s):  
Ivo Babuška ◽  
Uday Banerjee ◽  
John E. Osborn
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Mesh Generation ◽  
Variational Principles ◽  
Meshless Methods ◽  
Nonlinear Pdes ◽  
Time Step ◽  
Complicated Geometry ◽  
Generalized Finite Element ◽  
Selection Of

In the past few years meshless methods for numerically solving partial differential equations have come into the focus of interest, especially in the engineering community. This class of methods was essentially stimulated by difficulties related to mesh generation. Mesh generation is delicate in many situations, for instance, when the domain has complicated geometry; when the mesh changes with time, as in crack propagation, and remeshing is required at each time step; when a Lagrangian formulation is employed, especially with nonlinear PDEs. In addition, the need for flexibility in the selection of approximating functions (e.g., the flexibility to use non-polynomial approximating functions), has played a significant role in the development of meshless methods. There are many recent papers, and two books, on meshless methods; most of them are of an engineering character, without any mathematical analysis.In this paper we address meshless methods and the closely related generalized finite element methods for solving linear elliptic equations, using variational principles. We give a unified mathematical theory with proofs, briefly address implementational aspects, present illustrative numerical examples, and provide a list of references to the current literature.The aim of the paper is to provide a survey of a part of this new field, with emphasis on mathematics. We present proofs of essential theorems because we feel these proofs are essential for the understanding of the mathematical aspects of meshless methods, which has approximation theory as a major ingredient. As always, any new field is stimulated by and related to older ideas. This will be visible in our paper.

Parallel and automatic isotropic tetrahedral mesh generation of misaligned assemblies

2020 ◽  
Vol 2 (2) ◽  
pp. 149-163
Author(s):  
Peng Zheng ◽  
Yang Yang ◽  
Zhiwei Liu ◽  
Quan Xu ◽  
Junji Wang ◽  
...  
Keyword(s):  
Mesh Generation ◽  
Tetrahedral Mesh ◽  
Tetrahedral Mesh Generation
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