3D Mesh Generation Research Articles

Measurement and interpretation of long-term deformation of a rock slope at the Ikura limestone quarry, Japan

More than 10 years of displacement measurements at the Ikura limestone quarry in Japan have clarified aspects of rock slope deformation arising from excavation in the quarry. Although the cause of most deformations can be explained theoretically, those occurring in a rock slope just behind the Tarumi working face proved perplexing. Contraction continued to occur on the rock slope although excavation of limestone had ceased at this face. The cause of this continuous deformation was evaluated through numerical analysis employed to assess the stability of the rock slope. An automatic 3D mesh generation technique was used to model the complex topography of the quarry resulting from the excavation and a finite element mesh model was rendered for each of the successive excavation stages. Elastic analysis then allowed the resulting rock slope deformation to be predicted. The calculated results reveal that the rock slope continued to deform elastically after excavation had ceased on the Tarumi face and that the on-going excavation at the Kawamukai working face, located 400 m away from the rock slope, was the probable cause. The calculated results using appropriate elastic moduli were in good agreement with measured results. The rock slopes are assessed as stable and the continuous deformation is believed to be elastic.

Accurate numerical models for simulation of radiation events in nano-scale semiconductor devices

Space and ground-level electronic equipment with devices of nanometer scale and extremely high densities may be strongly affected by ionizing radiation. Accurate numerical models are necessary for better analysis of radiation effects and design of radiation tolerant devices. Numerical models and adaptive dynamic 3D mesh generation presented in this paper enable efficient simulations of transient semiconductor device response to realistic multi-branched track, produced by ionizing particle and nuclear reactions. A description of the numerical models, adaptive 3D meshing approach, and efficient solution method for large 3D problems using unstructured meshes is provided. The developed approach efficiently uses computer resources, which makes possible solution of transient 3D multi-branched ion strike problems with 100,000 mesh nodes within 512MB computer memory.

An extended advancing front technique for closed surfaces mesh generation

AbstractAn extended advancing front technique (AFT) with shift operations and Riemann metric named as shifting‐AFT is presented for finite element mesh generation on 3D surfaces, especially 3D closed surfaces. Riemann metric is used to govern the size and shape of the triangles in the parametric space. The shift operators are employed to insert a floating space between real space and parametric space during the 2D parametric space mesh generation. In the previous work of closed surface mesh generation, the virtual boundaries are adopted when mapping the closed surfaces into 2D open parametric domains. However, it may cause the mesh quality‐worsening problem. In order to overcome this problem, the AFT kernel is combined with the shift operator in this paper. The shifting‐AFT can generate high‐quality meshes and guarantee convergence in both open and closed surfaces. For the shifting‐AFT, it is not necessary to introduce virtual boundaries while meshing a closed surface; hence, the boundary discretization procedure is largely simplified, and moreover, better‐shaped triangles will be generated because there are no additional interior constraints yielded by virtual boundaries. Comparing with direct methods, the shifting‐AFT avoids costly and unstable 3D geometrical computations in the real space. Some examples presented in this paper have demonstrated the advantages of shift‐AFT in 3D surface mesh generation, especially for the closed surfaces. Copyright © 2007 John Wiley & Sons, Ltd.

Westinghouse AP1000 internals heating rate distribution calculation using a 3D deterministic transport method

Cost reduction and reliability increase are systematically pursued systems and components; this requires, amongst other, the availability of sophisticated computer programs and detailed analysis models. As an example, the core shroud, the structure having the function to maintain the core centered on its axis, is being designed in the Westinghouse AP1000, differently from previous plants, as a highly heterogeneous structure. Its thermal-mechanical sizing must take into due account accuarately determined internal heat generation rates. The latter, if determined by combining 2D and 1D neutron and γ-ray calculations which imply the separation of spatial variables and are mainly applicable for fluxes in the reactor beltline region, may include overly conservative margins. On the other hand, Monte Carlo methods do not allow an easy quantification of the uncertainties related to overall calculation. Three-dimensional deterministic models, based on the discrete ordinate transport theory, have the potential to provide accuarate design data; they can be also effective provided that the well-known difficulty to create and tune a complex geometrical model in a reasonable time is overcome and adequate computer resources are available to perform the calculation (until few years ago [Botta et al., 1996. Three-Dimensional Reactor Pressure Vessel Fast Neutron Fluence Calculations for the AP600 Using TORT, 3-D Deterministic Radiation Transport Computer Programs: Features, Applications and Perspectives, NEA/NSC/DOC, OECD/NEA. Paris, France], massive parallel computers (i.e. Cray Computers) available only to large national laboratories and selected industrieshad to be used). ANSALDO is acting as Westinghouse subcontractor and it supported Westinghouse in all AP1000 Licensing Process to NRC from 1999 to nowdays for the internal heating rate generation rate and RPV fluence calculations. As computer power growths up ANSALDO refined its calculation methodology in order to improve the design itself. The recent development, by ENEA Bologna, of a pre-post processor based on the combinatorial geometry (the computer program BOT3P, [ORSI, 2002. BOT3P: Bologna Transport Analysis Pre-Post-processors Version 1.0, Nuclear Science and Engineering, no. 142. American Nuclear Society, USA, pp. 349–354; ORSI, 2004. BOT3P: Bologna Transport Analysis Pre-Post-processors Version 3.0, Nuclear Science and Engineering, no. 146. American Nuclear Society, USA. pp. 248–255; ORSI, 2005. BOT3P: Bologna Radiation Transport Analysis Pre-Post-Processors Version 4.0, Nuclear Science and Engineering, no. 150. American Nuclear Society, USA, pp. 368–373; ORSI, 2003. BOT3P: A Mesh Generation Software Package for the Transport Analysis Codes DORT, TORT, TWODANT, THREEDANT and MCNP, International Conference on Supercomputing in Nuclear Applications SNA’2003. Paris, France; ORSI, 2004. NEA-1678/05 BOT3P4.1. BOT3P4.1 3D Mesh Generator and Graphical Display of Geometry for Radiation Transport Codes, Display of Results”, OECD/NEA Data Bank. Issy-les-Moulineaux, France]) and the ongoing increment of computer power make the three-dimensional deterministic program TORT (part of the DOORS 3.2 Package, [RSICC Computer Code Collection DOORS-3.2, 1998, Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA]) an attractive choice to perform the determination of the core shroud heating rate distribution as a 3D continue functions. This paper illustrates the computational approach followed by ANSALDO Nucleare to determine the heating rate distribution into the W AP1000 Core Shroud (see Fig. 1). The calculation has been performed at 67 energy groups (47 neutrons plus 20 gammas) in P3 or in P5 Legendre approximation and 2,000,000 meshes have been used. The computational power required is massive: 2 GB of RAM and up to 50 GB of swap files peak storage for each run with an S8 full-symmetric angular quadrature and 120 GB of swap files peak storage with an S16 full-symmetric angular quadrature. By using a latest generation workstation based on an INTEL P-IV 3.2 GHz processor under LINUX operating system (both SUSE 9.2 or Red Hat 9.1 and better are suitable), each run requires less than a week of full computer time with the P3 Legendre approximation with an S8 full-symmetric angular quadrature. The code BOT3P has been used both for the preparation of the geometrical model and as post processor of the TORT program outputs. BOT3P permitted to cut the model development time by a significant factor and to retrieve efficiently large amount of data from the TORT binary files, allowing a graphical review of the input and output data and, finally, resulting in a unique tool for Quality Control for complex 3D models. This computational experience can be considered a good working example for the 3D deterministic transport method revival by considering that this method is widely accepted by licensing authorities.

Parallel decoupled terminal-edge bisection method for 3D mesh generation

We present a practical and stable algorithm for the parallel refinement of tetrahedral meshes. The algorithm is based on the refinement of terminal-edges and associated terminal stars. A terminal-edge is a special edge in the mesh which is the longest edge of every element that shares such an edge, while the elements that share a terminal-edge form a terminal star. We prove that the algorithm is inherently decoupled and thus scalable. Our experimental data show that we have a stable implementation able to deal with hundreds of millions of tetrahedra and whose speed is in between one and two order of magnitude higher from the method and implementation we presented (Rivara et al., Proceedings 13th international meshing roundtable, 2004).

3D finite element mesh generation of complicated tooth model based on CT slices

An interactive three-dimensional finite element generation method is presented for modelling a multi-connected teeth and mandible structure. The tetrahedron is chosen as the basic element type due to its rigorous adaptability to structures with geometric complexities. The mesh generation is implemented by allocating two quadrangles in adjacent CT image slices to form a set of tetrahedrons. By examining all the possible allocations and their degradations, an algorithm is developed for interactive mesh generation, resulting in a series of tetrahedrons consistent with all the others without overlapping and spacing. The developed system was applied to a tooth-mandibular structure, generating a complicated 3D FEM model consisting of 4762 nodes and 18,534 tetrahedral elements with nine different materials. This 3D model was successfully used to evaluate different tooth restoration strategies, which proved the viability and effectiveness of the proposed method.

Computational Mesh Generation for Vascular Structures with Deformable Surfaces

Computational blood flow and vessel wall mechanics simulations for vascular structures are becoming an important research tool for patient-specific surgical planning and intervention. An important step in the modelling process for patient-specific simulations is the creation of the computational mesh based on the segmented geometry. Most known solutions either require a large amount of manual processing or lead to a substantial difference between the segmented object and the actual computational domain. We have developed a chain of algorithms that lead to a closely related implementation of image segmentation with deformable models and 3D mesh generation. The resulting processing chain is very robust and leads both to an accurate geometrical representation of the vascular structure as well as high quality computational meshes. The chain of algorithms has been tested on a wide variety of shapes. A benchmark comparison of our mesh generation application with five other available meshing applications clearly indicates that the new approach outperforms the existing methods in the majority of cases.

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress- or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.

3D hybrid mesh generation for reservoir simulation

AbstractA great challenge for flow simulators of new generation is to gain more accuracy at well proximity within complex geological structures. For this purpose, a new approach based on hybrid mesh modelling was proposed in 2D by Balaven et al. (Proceedings of the 7th International Conference on Numerical Grid Generation in Computational Field Simulations, Whistler, Canada, 2000; 407–416). In this hybrid mesh, the reservoir is described by a structured quadrilateral mesh and drainage areas around wells are represented by radial circular meshes. In order to generate a global conforming mesh, unstructured transition meshes constituted by convex polygonal elements satisfying finite volume properties are used to connect these two structured meshes. The hybrid mesh allows us to take full advantage of the simplicity and practical aspects of structured meshes, while complexity inherent to unstructured meshes is introduced only where strictly needed. This paper presents the 3D extension of the generation of such a hybrid mesh (ECCOMAS, Jyväskylä, Finland, 2004). The proposed method uses 3D power diagrams to generate the transition mesh. Due to the round‐off errors, this mesh is modified in order to ensure the conformity with the structured meshes. In addition, some criteria are introduced to measure the mesh quality, as well as an optimization procedure to remove or to expand small edges of the transition mesh under finite volume properties constraints. Numerical results are given to show the efficiency of the approach. Copyright © 2005 John Wiley & Sons, Ltd.

Generation of 3D mixed element meshes using a flexible refinement approach

This paper describes and discusses the main characteristics and implementation issues of a 3D mixed element mesh generator based on a generalization of the modified octree approach. This mesh generator uses primitive elements of different type as internal nodes, a flexible refinement approach as refinement strategy (primitive elements are not always bisected), and bricks, pyramids, prisms and tetrahedra as final elements. The mesh generation process is divided in several steps: the generation of the initial mesh composed of primitive elements, the refinement of primitive elements until the point density requirements are fulfilled, the generation of a graded mesh between dense and coarse regions, and finally, the recognition of the final elements. The main algorithms and data structures are described in detail for each step of the mesh generation process. As result, examples of meshes that satisfy the Delaunay condition and that can be used with the control volume method are shown.

MRI Guided 3D Mesh Generation and Registration for Biological Modeling

An accurate three-dimensional (3D) mesh of biological models is fundamental for analysis and treatment simulations. Generally noninvasive magnetic resonance image (MRI) data are taken as the input for the simulation. The topologic relationship of anatomy is extracted from MR images through segmentation processes. To accelerate the biological modeling phase, template surface and volume meshes are generated based on MR images and∕or anatomical atlases (e.g., brain atlas, etc.). The boundary surfaces are extracted from segmented regions on the image slices, which are used as the input for 3D volume mesh generation. An intuitive graphic user interface was developed for biomedical applications. It integrated MRI data manipulation with surface mesh and volume mesh generators. Image volume and mesh geometries are registered in the MRI working space. As the core component of the system, a robust 3D mesh generation approach is presented. It is capable of describing irregular geometries exhibiting concave and convex surfaces. It uses deltahedral building blocks for volume mesh generation and creates high-quality, regular-shaped tetrahedral mesh elements. The approach supports multiple levels of localized refinement without reducing the overall mesh quality. The validity of this new mesh generation strategy and implementation is demonstrated via the medical applications in brain vasculature modeling, multimodality imaging for breast cancer detection, and numerous anatomically accurate models presented. Multiple material boundaries are preserved in each mesh with fidelity.

Photorealistic 3D reconstruction from handheld cameras

One of the major challenges in the fields of computer vision and computer graphics is the construction and representation of life-like virtual 3D scenarios within a computer. The VISIRE project attempts to reconstruct photo-realistic 3D models of large scenarios using as input multiple freehand video sequences, while rendering the technology accessible to the non-expert. VISIRE is application oriented and hence must deal with multiple issues of practical relevance that were commonly overlooked in past experiences. The paper presents both an innovative approach for the integration of previously unrelated experiences, as well as a number of novel contributions, such as: an innovative algorithm to enforce closedness of the trajectories, a new approach to 3D mesh generation from sparse data, novel techniques dealing with partial occlusions and a method for using photo-consistency and visibility constrains to refine the 3D mesh.

3D tetrahedral, unstructured and anisotropic mesh generation with adaptation to natural and multidomain metric

In this paper we present a 3D tetrahedral, unstructured and anisotropic mesh generator that is not based on the Delaunay, frontal or octree method. Instead, it proceeds by local optimizations and uses an anisotropic shape criterion to fit a metric field. Then, we introduce a new 3D metric field that tightens the mesh around interfaces when the calculation domain is divided in several subdomains, and a 3D metric field that places enough elements through each subdomain thickness, without introducing too many nodes in the other directions. Finally, we show some applications for material forming geometries.

Advances in tetrahedral mesh generation for modelling of three‐dimensional regions with complex, curvilinear crack shapes

AbstractAdvances in tetrahedral mesh generation for general, three‐dimensional domains with and without cracks are described and validated through extensive studies using a wide range of global geometries and local crack shapes. Automated methods are described for (a) implementing geometrical measures in the vicinity of the crack to identify irregularities and to improve mesh quality and (b) robust node selection on crack surfaces to ensure optimal meshing both locally and globally. The resulting numerical algorithms identify both node coincidence and also local crack surface penetration due to discretization of curved crack surfaces, providing a proven approach for removing inconsistencies. Numerical examples using the resulting 3D mesh generation program to mesh complex 3D domains containing a range of crack shapes and sizes are presented. Quantitative measures of mesh quality clearly show that the element shape and size distributions are excellent, including in regions surrounding crack fronts. Copyright © 2005 John Wiley & Sons, Ltd.

535 テンプレートを用いたハイブリッドフロント法による3次元メッシュの自動生成(S06-1 メッシュ生成 (1),S06 メッシュ生成)

535 テンプレートを用いたハイブリッドフロント法による3次元メッシュの自動生成(S06-1 メッシュ生成 (1),S06 メッシュ生成)

Balanced Octree for Tetrahedral Mesh Generation

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.

Semi-formal design of reliable mesh generation systems

A reliable mesh generation infrastructure is designed based on software engineering principles. Formal methods, software design documents and clear modular decomposition criteria are introduced to improve the quality of mesh generation software. The design document for a simple 2D mesh generation data structure is presented using a semi-formal specification. The proposed semi-formal documentation system avoids any ambiguity during the software design process and will help in driving the software test cases. Using the proposed software, design techniques result in a consistent software design that is easy to extend and modify.

A Method for Adaptive Mesh Generation Taking into Account the Continuity Requirements of Magnetic Field

This paper proposes a method to generate adaptively 2D and 3D finite element meshes taking into account the continuity requirements of the magnetic field at the interface between two neighboring elements. First, this paper proposes a new error estimator that includes the Zienkiewicz and Zhu error norm estimator and the boundary rules in the electromagnetic field. Using a 2D simple model, this paper decides two parameters of the proposed estimator. Next, this paper presents a 3D mesh generation method based on the Voronoi-Delaunay theory, which ensures that the bounding surface of the domain is contained in the triangulation. The method has the capability to decrease the amount of information on the connectivity of boundary nodes by generating nodes not only in the interior of the domain but also on its surface. Two simple magnetostatic field problems are provided to illustrate the usefulness of the proposed method.

118 3 次元自動メッシュシステムを用いた筋-ヒフ連成表情解析

118 3 次元自動メッシュシステムを用いた筋-ヒフ連成表情解析

A fully 3D adaptive finite element simulation and prototype for gas flow in a porous media

This paper presents a three-dimensional (3D) adaptive finite element solution for gas flow in a porous media. The solution obtained is truly 3D and employs a dynamic h-adaptive refinement technique for efficiency. The adaptive procedure uses a new node-based storage mechanism [Wang GH, Tyler JM, Weltman JS, Callahan JD. Advances in Engineering Software including Computing Systems in Engineering 1999;30:31–41]. This node-based structure substantially reduces the memory necessary to store the finite element mesh. A prototype simulator, written in C++, has been implemented for Eugene Island block 305, a multi-well condensate reservoir off the coast of Louisiana to demonstrate the use of this adaptive procedure. Results, presented in this paper, show dramatic agreement with the actual production data. This prototype simulator uses Windows workstations to support a fully dynamic 3D mesh plus mesh generation.