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.

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.

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.

A Brief Summary of Finite Element Method Applications to Nonlinear Wave-structure Interactions

We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.

AUTOMATIC FINIT EELEMENT MODELING OF A WING

This paper is concerned about the automatic finite element modeling of a wing structure. The row and column method is used to identify the structure parts(ribs, spars, skins and pillars). A customization module of PCL(PATRAN Command Language under PATRAN 6.0) code from constructing airfoil curves to creating the entire wing FEM model is designed and developed. The geome tric, mesh density, material, load and boundary parameters can be easily and correctly input with the friendly interactive interface. A VFW614 wing is analyzed from creating airfoil curves to the show of stresses calculated by using NASTRAN 68 as an example. The results show that this customization module is very effective and efficient.

Study on Mesh-Control Device for the Mesh Generator Based on Tree Structures

In this paper, a process of the quadtree mesh generation is described, then a mesh control device of the tree based mesh generators is analyzed in detail. Some examples are given to demonstrate that the mesh control device allows for efficient a priori and a posteriori mesh refinements.

Discrete Maximum Principle and a Delaunay-Type Mesh Condition for Linear Finite Element Approximations of Two-Dimensional Anisotropic Diffusion Problems

A Delaunay-type mesh condition is developed for a linear finite element approximation of two-dimensional anisotropic diffusion problems to satisfy a discrete maximum principle.The condition is weaker than the existing anisotropic non-obtuse angle condition and reduces to the well known Delaunay condition for the special case with the identity diffusion matrix.Numerical results are presented to verify the theoretical findings.

基于IGES文件的舰船航行性能数值仿真模型

模型的主要目标是基于IGES文件利用OpenGL和有限元网格分别实现船体的智能建模和网格划分,并且针对大量数据样本的情况提出基于分类错误率的决策树方法,提取有效的数据实现高效率的网格计算,以便更高效地建立舰船航行性能数值仿真模型。

有限元网格划分技术

本文试图提供有限元网格划分领域的一个清晰的概貌。本文对已发表的有限元网格划分方法进行了综述，并对其进行了分类和优缺点分析。此外，本文还讨论了有限元网格划分的研究前沿。

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.

有限元网格Delaunay剖分的拓扑不相容问题研究

Delaunay三角剖分将产生网格拓扑不相容问题. 本文详细研究了利用网格元素的自下而上/自上而下的拓扑分类分式， 代替传统的、 花费时间的、 不准确的 “内/外” 几何检查， 初步解决了Delaunay三角剖分中存在的各种不相容问题， 节约了计算时间， 提高了计算效率.

Polygonal finite element-based content-aware image warping

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes.This enables simple and efficient implementation,but in turn,restricts the representation capability of the deformation,often leading to unsatisfactory warping results.We present a novel,flexible polygonal finite element(poly-FEM)method for content-aware image warping.Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image.This allows highly adaptive meshes and smoother warping with fewer degrees of freedom,thus significantly extending the flexibility and capability of the warping representation.Benefiting from the continuous formulation of image deformation,our polyFEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations.We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-ofthe-art methods.

THE COMPACTION OF TIME-DEPENDENT VISCOUS GRANULAR MATERIALS CONSIDERING INERTIAL FORCES

In the present paper, compactions of time-dependent viscous granular materials are simulated step by step using the automatic adaptive mesh generation schemes. Inertial forces of the viscous incompressible aggregates axe taken into account. The corresponding conservation equations, the weighted-integral formulations, and penalty finite element model are investigated. The fully discrete finite element equations for the simulation are derived. Polygonal particles of aggregates are simplified as mixed three-node and four-node elements. The automatic adaptive mesh generation schemes include contact detection algorithms, and mesh upgrade schemes. Solu- tions of the numerical simulation axe in good agreement with some results from literatures. With minor modification, the proposed numerical model can be applied in several industries, including the pharmaceutical, ceramic, food, and household product manufacturing.

Recent Progress in Numerical Methods for the Poisson-Boltzmann Equation in Biophysical Applications

Efficiency and accuracy are two major concerns in numerical solutions of the Poisson-Boltzmann equation for applications in chemistry and biophysics.Recent developments in boundary element methods,interface methods,adaptive methods,finite element methods,and other approaches for the Poisson-Boltzmann equation as well as related mesh generation techniques are reviewed.We also discussed the challenging problems and possible future work,in particular,for the aim of biophysical applications.

The Geometry Behind Numerical Solvers of the Poisson-Boltzmann Equation

Electrostatics interactions play a major role in the stabilization of biomolecules:as such,they remain a major focus of theoretical and computational studies in biophysics.Electrostatics in solution is strongly dependent on the nature of the solvent and on the ions it contains.While methods that treat the solvent and ions explicitly provide an accurate estimate of these interactions,they are usually computationally too demanding to study large macromolecular systems.Implicit solvent methods provide a viable alternative,especially those based on Poisson theory.The Poisson-Boltzmann equation(PBE)treats the system in a mean field approximation,providing reasonable estimates of electrostatics interactions in a solvent treated as continuum.In the first part of this paper,we review the theory behind the PBE,including recent improvement in which ions size and dipolar features of solvent molecules are taken into account explicitly.The PBE is a non linear second order differential equation with discontinuous coefficients,for which no analytical solution is available for large molecular systems.Many numerical solvers have been developed that solve a discretized version of the PBE on a mesh,either using finite difference,finite element,or boundary element methods.The accuracy of the solutions provided by these solvers highly depend on the geometry of their underlying meshes,as well as on the method used to embed the physical system on the mesh.In the second part of the paper,we describe a new geometric approach for generating unstructured tetrahedral meshes as well as simplifications of these meshes that are well fitted for solving the PBE equation using multigrid approaches.