Mesh Generation for Finite Element Analysis of Electric Machines

This paper describes two modified methods for triangular and quadrilateral meshing for finite element analysis of 2D electric machines. One is coupling the classic Delaunay method and advancing front method to generate optimal triangulation; the other is coupling the classic paving and Delaunay triangulation for optimal quadrilateral meshing. Various electric machine models are meshed successfully to demonstrate the robustness and effectiveness of the methods.

A fast and practical method to pack spheres for mesh generation

Sphere packing is an attractive way to generate high quality mesh. Several algorithms have been proposed in this topic, however these algorithms are not sufficiently fast for large scale problems. The paper presents an efficient sphere packing algorithm which is much faster and appears to be the most practical among all sphere packing methods presented so far for mesh generation. The algorithm packs spheres inside a domain using advancing front method. High efficiency has resulted from a concept of 4R measure, which localizes all the computations involved in the whole sphere packing process.

Mesh Generation and Dynamic Mesh Management for KIVA-3V

To improve mesh quality for KIVA-3V a method has been developed for rapid mesh generation and dynamic mesh management with moving valves for internal combustion engines. Two phases are included in rapid mesh generation： the initial mesh generation and the mesh pre-treatment. In the second step （pre-treatment）, the connectivity of those cells is generated by a new algorithm added to the KIVA-3V code after the initial mesh generated. In dynamic mesh management phase, a new rezoning algorithm is developed and the basic principle is that the rezoning starts from the moving part. The movement of the adjustment is treated as an ＂earth quake wave＂ propagating to the surrounding vertexes. The amount of coordinate adjustment of the surrounding vertexes is determined by the movement of the epicenter and the distance between the vertexes and the ＂epicenter＂. Finally, a real IC engine mesh is generated and managed aceording to the new method. It gives a new theory and a new method for creating and managing the mesh in IC engine.

Mesh generation and optimization from digital rock fractures based on neural style transfer

The complex geometric features of subsurface fractures at different scales makes mesh generation challenging and/or expensive.In this paper,we make use of neural style transfer(NST),a machine learning technique,to generate mesh from rock fracture images.In this new approach,we use digital rock fractures at multiple scales that represent’content’and define uniformly shaped and sized triangles to represent’style’.The 19-layer convolutional neural network(CNN)learns the content from the rock image,including lower-level features(such as edges and corners)and higher-level features(such as rock,fractures,or other mineral fillings),and learns the style from the triangular grids.By optimizing the cost function to achieve approximation to represent both the content and the style,numerical meshes can be generated and optimized.We utilize the NST to generate meshes for rough fractures with asperities formed in rock,a network of fractures embedded in rock,and a sand aggregate with multiple grains.Based on the examples,we show that this new NST technique can make mesh generation and optimization much more efficient by achieving a good balance between the density of the mesh and the presentation of the geometric features.Finally,we discuss future applications of this approach and perspectives of applying machine learning to bridge the gaps between numerical modeling and experiments.

Study on boundary search method for DFM mesh generation

The boundary mesh of the casting model was determined by direct calculation on the triangular facets extracted from the STL file of the 3D model. Then the inner and outer grids of the model were identified by the algorithm in which we named Inner Seed Grid Method. Finally, a program to automatically generate a 3D FDM mesh was compiled. In the paper, a method named Triangle Contraction Search Method (TCSM) was put forward to ensure not losing the boundary grids; while an algorithm to search inner seed grids to identify inner/outer grids of the casting model was also brought forward. Our algorithm was simple, clear and easy to construct program. Three examples for the casting mesh generation testified the validity of the program.

METHOD FOR ADAPTIVE MESH GENERATION BASED ON GEOMETRICAL FEATURES OF 3D SOLID

In order to provide a guidance to specify the element size dynamically during adaptive finite element mesh generation, adaptive criteria are firstly defined according to the relationships between the geometrical features and the elements of 3D solid. Various modes based on different datum geometrical elements, such as vertex, curve, surface, and so on, are then designed for generating local refined mesh. With the guidance of the defmed criteria, different modes are automatically selected to apply on the appropriate datum objects to program the element size in the local special areas. As a result, the control information of element size is successfully programmed covering the entire domain based on the geometrical features of 3D solid. A new algorithm based on Delatmay triangulation is then developed for generating 3D adaptive finite element mesh, in which the element size is dynamically specified to catch the geometrical features and suitable tetrahedron facets are selected to locate interior nodes continuously. As a result, adaptive mesh with good-quality elements is generated. Examples show that the proposed method can be successfully applied to adaptive finite element mesh automatic generation based on the geometrical features of 3D solid.

Mesh Generation from Dense 3D Scattered Data Using Neural Network

An improved self-organizing feature map (SOFM) neural network is presented to generate rectangular and hexagonal lattic with normal vector attached to each vertex. After the neural network was trained, the whole scattered data were divided into sub-regions where classified core were represented by the weight vectors of neurons at the output layer of neural network. The weight vectors of the neurons were used to approximate the dense 3-D scattered points, so the dense scattered points could be reduced to a reasonable scale, while the topological feature of the whole scattered points were remained.

Energy-Minimizing Curve Fitting for High-Order Surface Mesh Generation

We investigate different techniques for fitting Bézier curves to surfaces in context of high-order curvilinear mesh generation. Starting from distance-based least-squares fitting we develop an incremental algorithm, which incorporates approximations of stretch and bending energy. In the process, the algorithm reduces the energy weight in favor of accuracy, leading to an optimized set of sampling points. This energy-minimizing fitting strategy is applied to analytically defined as well as triangulated surfaces. The results confirm that the proposed method straightens and shortens the curves efficiently. Moreover the method preserves the accuracy and convergence behavior of distance-based fitting. Preliminary application to surface mesh generation shows a remarkable improvement of patch quality in high curvature regions.

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation

Two-dimensional finite element mesh generation algorithm for electromagnetic field calculation is proposed in this paper to improve the efficiency and accuracy of electromagnetic calculation. An image boundary extraction algorithm is developed to map the image on the geometric domain. Identification algorithm for the location of nodes in polygon area is proposed to determine the state of the node. To promote the average quality of the mesh and the efficiency of mesh generation, a novel force-based mesh smoothing algorithm is proposed. One test case and a typical electromagnetic calculation are used to testify the effectiveness and efficiency of the proposed algorithm. The results demonstrate that the proposed algorithm can produce a high-quality mesh with less iteration.

Mapping-Based 3D Hexahedral Finite Element Mesh Generation Method

Mapping mesh generation is widely applied in pre-processes of Finite Element Method （FEM）. In this study, the basic 3D mapping equations by Lagrange interpolating function are founded. Based these equations, a mapping pattern library, which maps essential configurations e.g. line, circle, rotary body, sphere etc. to hexahedral FEM mesh, has been built. Then available FEM mesh will be generated by clipping and assembling the mapped essential objects. Study case illustrates that the proposed method is simple and efficient to generate valid FEM mesh for complex 3D engineering structure.

Frontiers in biomolecular mesh generation and molecular visualization systems

With the development of biomolecular modeling and simulation,especially implicit solvent modeling,higher requirements are set for the stability,efficiency and mesh quality of molecular mesh generation software.In this review,we summarize the recent works in biomolecular mesh generation and molecular visualization.First,we introduce various definitions of molecular surface and corresponding meshing software.Second,as the mesh quality significantly influences biomolecular simulation,we investigate some remeshing methods in the fields of computer graphics and molecular modeling.Then,we show the application of biomolecular mesh in the boundary element method(BEM)and the finite element method(FEM).Finally,to conveniently visualize the numerical results based on the mesh,we present two types of molecular visualization systems.

THREE-DIMENSIONAL FINITE ELEMENT DELAUNAY MESH GENERATION BY A PERFECTED NODE CONNECTION METHOD

How to automatically generate three-dimensional finite element Delaunay mesh by a peifected node connection method is introduced, where nodes are generated based on existing elements, instead of independence of node creation and elements generation in traditional node connection method. Therefore, Ihe the difficulty about how to automatically create nodes in the traditional method is overcome.

Surface Modelling and Mesh Generation for Simulating Superplastic Forming

This paper presents an approach which enables surface modelling, mesh generation and the Finite Element (FE) analysis to be integrated together to simulate superplastic forming process for complex shaped components. Techniques have been developed to generate an FE mesh over non-four-sided surface areas, the boundaries of which are Bezier curves of arbitrary degree, using a consistent expression. Theoretical evidence is given to determine the number of Bezier triangular patches required for accurately re-constructing die surfaces within a commercial FE solver. The developed techniques have been successfully used in determining the process parameters for forming a 3D rectangular box.

A Modified Paving Approach and Automatic Mesh Grading Method to Quadrilateral Mesh Generation

A modified paving technique for automatic generation of all-quadrilateral mesh fromarbitrary 2-D geometry is presented. The generated mesh elementS are nearly square andperpendicular to boundaries. Aner the nodes and elementS formation is completed. a fully automaticgrading method is applied to increase the accuracy and reliability of engineering analysis. In thispaper, we mainly describe the theory of mathematical algorithm and present some examples ofautomatically generated mesh.

A New Approach to Fully Automatic Mesh Generation

Automatic mesh generation is one of the most important parts in CIMS (Computer Integrated Manufacturing System). A method based on mesh grad-ing propagation which automatically produces a triangular mesh in a multiply connected planar region is presented in this paper. The method decomposes the planar region into convex subregions, using algorithms which run in linear time. For every subregion, an algorithm is used to generate shrinking polygons according to boundary gradings and form Delaunay triangulation between two adjacent shrinking polygons, both in linear time. It automatically propagates boundary gradings into the interior of the region and produces satisfactory quasi-uniform mesh.

Automatic Mesh Generation on a Regular Background Grid

This paper presents an automatic mesh generation procedure on a 2D domain based on a regular background grid. The idea is to devise a robust mesh generation scheme with equal emphasis on quality and efficiency. Instead of using a traditional regular rectangular grid, a mesh of equilateral triangles is employed to ensure triangular element of the best quality will be preserved in the interior of the domain. As for the boundary, it is to be generated by a node/segment insertion process. Nodes are inserted into the background mesh one by one following the sequence of the domain boundary. The local structure of the mesh is modified based on the Delaunay criterion with the introduction of each node. Those boundary segments, which are not produced in the phase of node insertion, will be recovered through a systematic element swap process. Two theorems will be presented and proved to set up the theoretical basic of the boundary recovery part. Examples will be presented to demonstrate the robustness and the quality of the mesh generated by the proposed technique.

Fast advancing layer method for viscous mesh generation

An efficient Advancing Layer Method(ALM)is presented to create semi-structured prisms on viscous walls,in which a procedure that checks possible front intersections is essential to its efficiency.This paper develops various novel schemes to improve the algorithm’s efficiency precisely while not sacrificing its robustness and the resulting mesh quality.First,it employs a set of new techniques,and data structures are developed to improve the efficiency of the frontcheck procedure.Then,within each octant,a new filter is developed to reduce the intersection computations in the searching process.In addition,data structures are well designed to store the contiguously accessed data in each computing-intensive loop in a contiguous space for a potentially better cache hit ratio.We built a geometry model library formed by examples of industrial complexity to demonstrate the practicability of the algorithm.All the efforts mentioned above enable us to reduce the percentage of computing time taken by intersection check to an acceptable level(approximately 26%),which make it no longer be the most time-consuming part.

Prismatic mesh generation based on anisotropic volume harmonic field

In this paper,we present an effective prismatic mesh generation method for viscous flow simulations.To address the prismatic mesh collisions in recessed cavities or slit areas,we exploit 3D tensors controlled anisotropic volume harmonic field to generate prismatic meshes.Specially,a well-fitting tetrahedral mesh is first constructed to serve as the discrete computation domain of volume harmonic fields.Then,3D tensors are exploited to control the volume harmonic field that better fits the shape geometry.From the topological perspective,the generation of the prismatic mesh can be treated as a topology-preserved morphing of the viscous wall.Therefore,iso-surfaces in the volume harmonic field should be homeomorphic to the viscous wall while fitting its shapes.Finally,a full prismatic mesh can be induced by estimating the forward directions and visible regions in the volume harmonic field.Moreover,to be compatible with different simulation situations,the thickness of prismatic meshes should be variable.Our approach provides local adjustable thickness of prismatic meshes,which can be achieved by controlling local 3D tensors.The proposed anisotropic volume harmonic field based prismatic meshes are efficient and robust,and a full prismatic mesh can be guaranteed without low quality collisions.Various experiments have shown that our proposed prismatic meshes have obvious advantages in terms of efficiency and effectiveness.

An accelerated scheme with high quality mesh based on Lloyd iteration

High quality mesh plays an important role for finite element methods in science computation and numerical simulation.Whether the mesh quality is good or not,to some extent,it determines the calculation results of the accuracy and efficiency.Different from classic Lloyd iteration algorithm which is convergent slowly,a novel accelerated scheme was presented,which consists of two core parts:mesh points replacement and local edges Delaunay swapping.By using it,almost all the equilateral triangular meshes can be generated based on centroidal Voronoi tessellation(CVT).Numerical tests show that it is significantly effective with time consuming decreasing by 40%.Compared with other two types of regular mesh generation methods,CVT mesh demonstrates that higher geometric average quality increases over 0.99.

Hybrid Surface Mesh Adaptation for Climate Modeling

Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.