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.

Improving the Quality of Conforming Triangular Meshes by Topological Clean up and DSI

A new method as a post-processing step is presented to improve the shape quality of triangular meshes, which uses a topological clean up procedure and discrete smoothing interpolate (DSI) algorithm together. This method can improve the angle distribution of mesh element. while keeping the resulting meshes conform to the predefined constraints which are inputted as a PSLG.

A perceptual quality metric for 3D triangle meshes based on spatial pooling

In computer graphics, various processing operations are applied to 3D triangle meshes and these processes often involve distortions, which affect the visual quality of surface geometry. In this context, perceptual quality assessment of 3D triangle meshes has become a crucial issue. In this paper, we propose a new objective quality metric for assessing the visual difference between a reference mesh and a corresponding distorted mesh. Our analysis indicates that the overall quality of a distorted mesh is sensitive to the distortion distribution. The proposed metric is based on a spatial pooling strategy and statistical descriptors of the dis- tortion distribution. We generate a perceptual distortion map for vertices in the reference mesh while taking into account the visual masking effect of the human visual system. The proposed metric extracts statistical descriptors from the dis- tortion map as the feature vector to represent the overall mesh quality. With the feature vector as input, we adopt a support vector regression model to predict the mesh quality score. We validate the performance of our method with three publicly available databases, and the comparison with state-of-the-art metrics demonstrates the superiority of our method. Experimental results show that our proposed method achieves a high correlation between objective assessment and subjective scores.

Hybrid grid generation for viscous flow simulations in complex geometries

In this paper,we present a hybrid grid generation approach for viscous flow simulations by marching a surface triangulation on viscous walls along certain directions.Focuses are on the computing strategies used to determine the marching directions and distances since these strategies determine the quality of the resulting elements and the reliability of the meshing procedure to a large extent.With respect to marching directions,three strategies featured with different levels of efficiencies and robustness performance are combined to compute the initial normals at front nodes to balance the trade-off between efficiency and robustness.A novel weighted strategy is used in the normal smoothing scheme,which evidently reduces the possibility of early stop of front generation at complex corners.With respect to marching distances,the distance settings at concave and/or convex corners are locally adjusted to smooth the front shape at first;a further adjustment is then conducted for front nodes in the neighbourhood of gaps between opposite viscous boundaries.These efforts,plus other special treatments such as multi-normal generation and fast detection of local/global intersection,as a whole enable the setup of a hybrid mesher that could generate qualitied viscous grids for geometries with industry-level complexities.

Regular Posit ion-Oriented Method for Mesh Smoothing

Mesh smoothing is an essential technique for the improvement of mesh quality in finite element analysis,due to the fact that mesh quality has a large impact on the convergence of the computational scheme and the accuracy of the numerical results.A novel mesh smoothing method based on regular-position-guided operations is presented in this paper.The method introduced here contains two main stages:The first stage computes the regular position of each vertex based on the shape of the element and conducts regular-position-oriented-based element transformations independently;the second stage determines the finial position of each vertex according to its surrounding elements with an assembly strategy.This method is not limited to planar triangular mesh,but applicable to surface polygonal mesh.Numerical experiments on various mesh models demonstrate the effectiveness and potential of this method.

Mesh simplification algorithm based on edge curvature metrics and local optimization

Aiming at the problem that the mesh simplification algorithm loses the geometric features of the model in large-scale simplification,an improved half-edge collapse mesh simplification algorithm is proposed.The concept of approximate measurement of edge curvature is introduced,and the edge curvature is added to the error measure,so that the order of half-edge collapse of the mesh is changed,and the simplified details of the mesh model can be preserved accurately.At the same time,by analyzing the quality of simplified triangular mesh,optimizing triangular mesh locally,reducing the amount of narrow triangles,the quality of the simplified model is improved.The proposed algorithm was tested on Cow model,Car model and Bunny model,and compared with another three algorithms,one of them is a classical mesh simplification algorithm based on edge collapse,the other is an improved algorithm of the classical one.The experimental results show that the improved algorithm can better retain the detail features of the original model at the same reduction ratio,and has reasonable mesh allocation,fast execution speed and small error.

Mesh Motion Approach Based on Spring Analogy Method for Unstructured Meshes

Mesh motion strategy is one of the key points in many fluid-structure interaction problems. One popular technique used to solve this problem is known as the spring analogy method. In this paper a new mesh update approach based on the spring analogy method is presented for the effective treatment of mesh moving boundary problems. The proposed mesh update technique is developed to avoid the generation of squashed invalid elements and maintain mesh quality by considering each element shape and grid scale to the definition of the spring stiffness. The method is applied to several 2D and 3D boundary correction problems for fully unstructured meshes and evaluated by a mesh quality indicator. With these applications,it is demonstrated that the present method preserves mesh quality even under large motions of bodies. We highlight the advantages of this method with respect to robustness and mesh quality.