Automatic Mesh Generation Method Research Articles

A Simple Automatic Hexahedron Mesh Generation and Polyhedral Smoothed Finite Element Method for Mechanics Problems

A new fully automatic pure hexahedron mesh, called lotus mesh, generation technique of an arbitrary 2D/3D geometric domain and polyhedral smoothed finite element method (PSFEM) for efficient numerical simulation are presented. The lotus mesh algorithm is mainly based on the signed distance function (SDF) and the density function to generate nodes and control node density, respectively. We improved the generality of the SDF-based mesh method, realizing the meshing of 2D arbitrary polygons and 3D complex structures, and propose geometry-based adaptive meshing methods. In addition, to improve the stability and accuracy of lotus mesh, PSFEM based on smoothed finite method (SFEM) is proposed. Unlike the existing SFEM, this paper adopts an indirect way to calculate the stiffness matrix, which first calculates the transition matrix on the smoothed domain, and then maps it back to the real stiffness matrix through the transformation matrix, to address stiffness integral operation of the 3D complex polyhedron. Several demonstration examples are presented to verify the lotus mesh and its accuracy. • A fully automatic pure hexahedron mesh, lotus mesh, is proposed, whose algorithm structure is simple and easy to implement. • Mesh generation method based on signed distance function is improved to realize the meshing of 2D arbitrary polygons and 3D complex structures with geometry-based adaptivity. • Polyhedral smoothed finite element method is proposed, which has higher accuracy using lotus mesh than conventional finite element method.

Automatic Delaunay mesh generation method and physically-based mesh optimization method on two-dimensional regions

Delaunay mesh generation method is a common method for unstructured mesh (or unstructured grid) generation. Delaunay mesh generation method can conveniently add new points to the existing mesh without remeshing the whole domain. However, the quality of the generated mesh is not high enough if compared with some mesh generation methods. To obtain high-quality mesh, this paper developed an automatic Delaunay mesh generation method and a physically-based mesh optimization method on two-dimensional regions. For the Delaunay mesh generation method, boundary-conforming problem was ensured by create nodes at centroid of mesh elements. The definition of node bubbles and element bubbles was provided to control local mesh coarseness and fineness automatically. For the physically-based mesh optimization method, the positions of boundary node bubbles are predefined, the positions of interior node bubbles are adjusted according to interbubble forces. Size of interior node bubbles is further adjusted according to the size of adjacent node bubbles. Several examples show that high-quality meshes are obtained after mesh optimization.

Parallel and automatic isotropic tetrahedral mesh generation of misaligned assemblies

Mesh generation is a challenge for high-performance numerical simulation, one reason is the complex geometry representing solution domain makes pre-processing difficult, especially for those assembly model containing hundreds and thousands of components involving misaligned interfaces between neighboring parts, and no state-of-art meshing tools could provide automatic functions for processing such complex model, another reason is hundreds of millions or even billions meshes should be generated quickly, which also exceeds the capabilities of available tools. In this paper, a novel parallel and automatic mesh generation method is proposed. Firstly, a surface imprinting algorithm based on the hybrid representation of discrete and continuous surfaces is proposed to process misaligned assembly model automatically. Then, the repaired assembly model is used as an input for a carefully designed mesh generation pipeline which connects the procedures of mesh sizing control, and three-level parallel tetrahedral mesh generation in order. This proposed method could produce hundreds of millions consistent mesh qualified for high-performance numerical simulation based on thousands of geometry components. Numerical experiments on a giant dam model and an integrated circuit board model demonstrates the effectiveness of this method.

Rapid Aerodynamic Calculation Method for Hypersonic Gliding Vehicle

The accuracy and efficiency are always conflict in the process of aerodynamic shape design, especially for hypersonic gliding vehicle (HGV). In this work, a rapid aerodynamic calculation method for hypersonic gliding vehicle is conducted, including shape parametric modelling, automatic mesh generation and rapid computational fluid dynamics (CFD) method. In details, the aerodynamic shapes of HGV are modelled by multi-section solids, which parameterized by class function/shape function transformation (CST) method and exponential function. Then, the computational meshes are generated automatically in two steps: one is generating surface mesh by Delaunay method, and another is generating volume mesh by adaptive Cartesian method. In order to minor the computational cost, the hypersonic aerodynamic are analysed by combining the Euler equation and the viscosity force. We have tested the accuracy and efficiency of this rapid aerodynamic calculation method in two flight states for a typical HGV. Compared with Navier Stokes (NS) equations, the results shown the errors of axial aerodynamic force are all less than 6%, but time costs are reduced in hundreds of times.

Triangular mesh generation on free-form surfaces based on bubble dynamics simulation

Purpose Modern CAD systems facilitate the creation of any surface geometry imaginable, and complex surfaces for free-form grid shells are often represented by a set of Non-Uniform Rational B-Splines surface patches. But it remains an intractable issue how to generate high-quality grids on complex surfaces efficiently. To solve this issue, an automatic triangular mesh generation method is presented, based on bubble dynamics simulation and a modified Delaunay method. Design/methodology/approach A moderate amount of points are first distributed on a given surface. Next, by regarding the points as elastic bubbles with the same size and introducing the forces acting on bubbles, the motion control equations of bubbles are established. The equilibrium state of the bubble system is found by Verlet algorithm. Then, the Voronoi diagram on the surface is obtained by calculating the intersection between the surface and the three-dimensional (3D) Voronoi diagram of the centers of bubbles. Finally, a triangular mesh, Delaunay triangulation on the surface, is determined based on the dual change of the Voronoi diagram. Findings This method generates meshes on the surface directly, unlike mapping-based methods, avoiding the mapping distortion. Examples are given to demonstrate the successful execution of this method. The result also illustrates that this method is applicable to various surfaces in high automation level and resultant meshes are highly uniform and well-shaped. Originality/value Thus, this method provides the convenience for the geometry design of complex free-form grid structure.

An algorithm for decomposition of sub-domains and quadrilateral mesh generation with line constraints

The technique for quadrilateral mesh generation on arbitrary 2-D domain has been quite mature; however, the existing methods and software can not directly deal with mesh generation with internal line constraints. In flood analysis and other analysis, the analysis models often contain a large number of constraint lines. In mesh generation, the sides of elements besides constraint lines must be attached to constraint lines, so that boundary conditions can be defined on these constraint lines. In this paper, a general method for automatic quadrilateral mesh generation with internal line constraints is presented. The mesh generation process is mainly divided into two stages, i.e. the automatic decomposition of sub-domains and quadrilateral mesh generation in each sub-domain. The sub-domains enclosed by constraint lines and boundaries are determined automatically with the proposal algorithm in this paper. Then nodes are generated on each edge of sub-domains based on mesh size requirements. By solving an integer linear programming problem, the number of nodes on each edge is adjusted automatically, so that the total number of boundary nodes in each sub-domain is even, satisfying the necessary condition for generating all-quadrilateral mesh. For free constraint lines in each sub-domain, the method of regarding constraint lines as holes with zero area is proposed, so that constraint lines can be treated as internal boundaries. The merging method of constraint lines and outer boundary is given, which can deal with all possible distribution of constraint lines and has generality. The examples of mesh generation with a large number of constraint lines are given to demonstrate the reliability of proposed method.

Proposal on automatic triangular mesh generation method considering stress singularity near interface edge of bonded structure

Proposal on automatic triangular mesh generation method considering stress singularity near interface edge of bonded structure

쉘 구조물의 용접 변형량 예측을 위한 요소망 생성 방법

In shipbuilding, hull assemblies are manufactured by welding. The thermal deformation caused by the welding produces shape deformation. Counter-deformed design methods have been used in shipyards to cope with the weld-induced deformation of ship assembles. Finite element methods(FEMs) are frequently used to estimate welding distortion in the counter-deformed design. For the estimation of welding distortion, producing uniform rectangular elements is required to enter thermal loads on the welding line and obtain accurate analysis results. In this paper, a new automatic mesh generation method is proposed for prediction of welding deformation in FEM. Meshes are constructed for test cases to demonstrate the feasibility of the proposed mesh generation method.

An automatic adaptive mesh generation method for weight window in Monte Carlo particle transport

The variance reduction technique of mesh-based weight window was widely used in reactor shielding calculation. However, there are disadvantages in the traditional calculation procedure with weight window method based manual operation. It is time consuming to perform iterative calculations to get an effective weight window. Even for experts, they can only give an approximate division range of mesh parameters. Iteratively mesh plotting is needed for the under-bias or over-bias of particles. To solve the problem, an automatic adaptive mesh generation method was proposed for weight window based on the characteristics of particle’s transport. The method involved coarse and fine meshing. Coarse mesh boundary parameters can be automatically generated based on the division of the interested area. Fine mesh boundary parameters can be produced by the automatic process of the mean free paths at the current energy of the particle. Coarse meshing and fine meshing were combined to generate the final meshing scheme. The fusion shielding benchmark and the ITER T426 benchmark were selected as the benchmark cases. The accuracy and efficiency of the proposed method were demonstrated.

BARAM: 전산유체 해석을 위한 가상풍동 시스템

BARAM system that means 'wind' in Korean has been established as a virtual wind tunnel system for aircraft design. Its aim is to provide researchers with easy-to-use, production-level environment for all stages of CFD simulation. To cope with this goal an integrated environment with a set of CFD solvers is developed and coupled with an highly-efficient visualization software. BARAM has three improvements comparing with previous CFD simulation environments. First, it provides a new automatic mesh generation method for structured and unstructured grid. Second, it also provides real-time visualization for massive CFD data set. Third, it includes more high-fidelity CFD solvers than commercial solvers.

Parallel AFMPB solver with automatic surface meshing for calculation of molecular solvation free energy

We present PAFMPB, an updated and parallel version of the AFMPB software package for fast calculation of molecular solvation-free energy. The new version has the following new features: (1) The adaptive fast multipole method and the boundary element methods are parallelized; (2) A tool is embedded for automatic molecular VDW/SAS surface mesh generation, leaving the requirement for a mesh file at input optional; (3) The package provides fast calculation of the total solvation-free energy, including the PB electrostatic and nonpolar interaction contributions. PAFMPB is implemented in C and Fortran programming languages, with the Cilk Plus extension to harness the computing power of both multicore and vector processing. Computational experiments demonstrate the successful application of PAFMPB to the calculation of the PB potential on a dengue virus system with more than one million atoms and a mesh with approximately 20 million triangles. Program summaryProgram title: Parallel AFMPBCatalogue identifier: AEGB_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEGB_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: GNU General Public License, version 2No. of lines in distributed program, including test data, etc.: 40558No. of bytes in distributed program, including test data, etc.: 2349976Distribution format: tar.gzProgramming language: Mixed C and Fortran, Compiler: Intel or GNU with Cilk Plus enabled.Computer: Any, but the code is mainly designed for multicore architectures.Operating system: Linux.RAM: Depends on the size of the discretized biomolecular system.Classification: 3.Catalogue identifier of previous version: AEGB_v1_1Journal reference of previous version: Comput. Phys. Comm. 184 (2013) 2618External routines: Users are allowed to use external routines/libraries (e.g., MSMS [6] and TMSMesh [4]) to generate compatible surface mesh input data if they choose not to use the embedded automatic mesh generation tool in the package. Post-processing tools such as VCMM [5] and VMD [3] can also be used for visualization and analyzing results.The package uses two subprograms: (1) The iterative Krylov subspace solver, SPARSKIT, from Yousef Saad [2]; and (2) Cilk-based parallel fast multipole methods from FMMSuite [1].Does the new version supersede the previous version? YesNature of problem: Numerical solution of the linearized Poisson–Boltzmann equation that describes electrostatic interactions of molecular systems in ionic solutions.Solution method: The linearized Poisson–Boltzmann equation is reformulated as a boundary integral equation and is subsequently discretized using the node-patch scheme. The resulting linear system is solved using Krylov subspace solvers iteratively. The reformulation of the equation provides an upper bound for the number of iterations. Within each iteration, the matrix–vector multiplication is accelerated using the adaptive plane-wave expansion based fast multipole methods. The majority of the codes are parallelized using the Cilk runtime.Reasons for new version: New functions are added and a few old functions like force calculations are removed. The algorithm is parallelized and most parts of the code are rewritten.Summary of revisions: The computation is parallelized and an automatic mesh generation method for BEM is added.Restrictions: The program has only been tested on machines running Linux operating system.Additional comments: The Cilk runtime used in the development and testing is from the Intel compiler Suite. The GNU Cilk Plus and Cilk Plus/LLVM branches have not been tested.Running time: The running time depends on the number of discretized elements (N) and their distribution. It also depends on the number of cores used in the computation.

Acceleration of Dynamic Bubble Mesh Generation for Large-Scale Model

An automatic mesh generation method employing a dynamic bubble system can provide a high-quality mesh for electromagnetic finite element analysis. However, it takes a very long time to compute bubbles' movement when a mesh with a large number of elements is generated. The bubbles move according to a force among them, such as the van der Waals force. However, the force received from bubbles of very far distance can be ignored. Therefore, it is unnecessary to calculate the force from all the bubbles. In this paper, we propose a subdivided dynamic bubble system in order to shorten the computation time. The proposed method considers the analysis region to be divided into some tetrahedral subdivisions, and then the bubbles move independently in the tetrahedral subdivisions. As a result, acceleration of the computation time is achieved.

해상 풍력 타워에 관한 자동요소 생성법

The more accurate numerical analysis is needed, The more important to arrange nodes and elements properly on the structures wanted to be analyzed. In this study, automatic mesh generation method is developed for triangular mesh modeling in wind tower and substructure formed in circular sections especially, which have structural and economical benefits in shallow water area. It can consider variety conditions by inputting the detail data such as height and types. Also, this study includes the comparison and verification with the mesh generation by Delaunay triangular technique on 3 dimensional space and the examples of mesh generation for proposed tower and substructure. The result of this study will be widely applied to analyze the existing and proposed models for wind turbines.

The Parallelized Automatic Mesh Generation Using Dynamic Bubble System With GPGPU

An automatic mesh generation method employing a dynamic bubble system can provide a high-quality mesh for electromagnetic finite-element analysis. However, there is a problem in that it takes a very long time to compute the bubbles' movement when a mesh with a large number of elements is produced. It is possible to independently and simultaneously compute the bubbles' movement; therefore, the computation of the bubbles' movement is suitable for parallel computing. In order to shorten the computation time, the computation of the bubbles' movement is parallelized with the graphics-processing unit (GPU). We propose a dynamic bubble system parallelized with GPU. As a result, a reduction in computation time was achieved.

Application of strand meshes to complex aerodynamic flow fields

We explore a new approach for viscous computational fluid dynamics calculations for external aerodynamics around geometrically complex bodies that incorporates nearly automatic mesh generation and efficient flow solution methods. A prismatic-like grid using “strands” is grown a short distance from the body surface to capture the viscous boundary layer, and adaptive Cartesian grids are used throughout the rest of the domain. The approach presents several advantages over established methods: nearly automatic grid generation from triangular or quadrilateral surface tessellations, very low memory overhead, automatic mesh adaptivity for time-dependent problems, and fast and efficient solvers from structured data in both the strand and Cartesian grids.The approach is evaluated for complex geometries and flow fields. We investigate the effects of strand length and strand vector smoothing to understand the effects on computed solutions. Results of three applications using the strand-adaptive Cartesian approach are given, including a NACA wing, isolated V-22 (TRAM) rotor in hover, and the DLR-F6 wing-body transport. The results from these cases show that the strand approach can successfully resolve near-body and off-body features as well as or better than established methods.

Hybrid Grid Generation Method for Complex Geometries

A hybrid mesh generation method is described to discretize complex geometries. The idea behind this hybrid method is to combine the orthogonality and directionality of a structured grid, the efficiency and simplicity of a Cartesian grid, and the flexibility and ease of an unstructured grid in an attempt to develop an automatic, robust, and fast hybrid mesh generation method for configurations of engineering interest. A semistructured quadrilateral grid is first generated on the wetted surfaces. A background Cartesian grid, covering the domain of interest, is then constructed using a Quadtree-based Cartesian Method. Those Cartesian cells overlapping with the semistructured grids or locating outside of computational domain are then removed using an Alternating Digital Tree method. Finally, an unstructured grid generation method is used to generate unstructured triangular cells to fill all empty regions in the domain as a result of the trimming process. The automatic placement of sources at the geometrical irregularities is developed to render these regions isotropic, thus effectively overcoming the difficulty of generating highly stretched good-quality elements in these regions. The self-dividing of the exposed semistructured elements with high aspect ratio and the adaptation of the background mesh using the cell size information from the exposed semistructured elements for generating Cartesian cells are introduced to improve the quality of unstructured triangular elements and guarantee the success of the unstructured grid generation in the void regions. The developed hybrid grid generation method is used to generate a hybrid grid for a number of test cases, demonstrating its ability and robustness to mesh complex configurations.

An automatic 3D mesh generation method for domains with multiple materials

This paper describes an automatic and efficient approach to construct unstructured tetrahedral and hexahedral meshes for a composite domain made up of heterogeneous materials. The boundaries of these material regions form non-manifold surfaces. In earlier papers, we developed an octree-based isocontouring method to construct unstructured 3D meshes for a single material (homogeneous) domain with manifold boundary. In this paper, we introduce the notion of a material change edge and use it to identify the interface between two or several different materials. A novel method to calculate the minimizer point for a cell shared by more than two materials is provided, which forms a non-manifold node on the boundary. We then mesh all the material regions simultaneously and automatically while conforming to their boundaries directly from volumetric data. Both material change edges and interior edges are analyzed to construct tetrahedral meshes, and interior grid points are analyzed for proper hexahedral mesh construction. Finally, edge-contraction and smoothing methods are used to improve the quality of tetrahedral meshes, and a combination of pillowing, geometric flow and optimization techniques is used for hexahedral mesh quality improvement. The shrink set of pillowing schemes is defined automatically as the boundary of each material region. Several application results of our multi-material mesh generation method are also provided.

Three-dimensional automatic mesh generation for hybrid electromagnetic simulations

Hybrid mesh generation is required for finite-difference time-domain/finite-element time-domain (FDTD/FETD) hybrid simulations. A combined approach is presented to automatically generate Cartesian/tetrahedral hybrid meshes for open and closed structures. This approach first generates a buffer zone that surrounds a target with specified tightness. The advancing-front technique with ldquosweep-and-retryrdquo is subsequently applied to generate an initial tetrahedral mesh that fills the buffer zone. Finally, the tetrahedral mesh undergoes a combined quality improvement procedure. Due to the low profile of the resulting tetrahedral mesh, the sparse Cholesky decomposition can be applied effectively to solve the resulting FETD matrix. Several examples are provided to demonstrate the main features and the performance of the proposed automatic mesh-generation method.

Optimization of arches using genetic algorithm

An optimization procedure is presented for the minimum weight and strain energy optimization for arch structures subjected to constraints on stress, displacement and weight responses. Both thickness and shape variables defining the natural line of the arch are considered. The computer program which is developed in this study can be used to optimize thick, thin and variable thickness curved beams/arches. An automated optimization procedure is adopted which integrates finite element analysis, parametric cubic spline geometry definition, automatic mesh generation and genetic algorithm methods. Several examples are presented to illustrate optimal arch structures with smooth shapes and thickness variations. The changes in the relative contributions of the bending, membrane and shear strain energies are monitored during the whole process of optimization.

3D anisotropic unstructured grid generation

AbstractThis paper describes a fully automatic 3D anisotropic mesh generation method for domains of arbitrary shape. The spacing of the boundary mesh is computed by the analysis of the principal curvatures and directions of the boundary surfaces. The spacing in the domain is obtained by interpolation of the spacing at the boundaries on a suitably constructed background mesh. Examples which illustrate the performance of the proposed methodology are presented. Copyright © 2005 John Wiley & Sons, Ltd.