Quality Improvement of Finite Element Mesh Models Modified by Mesh Deformation (original) (raw)
Related papers
Modeling of quality parameter values for improving meshes
Japan Journal of Industrial and Applied Mathematics, 2007
A novel quasi-statistical approach to improve the quality of triangular meshes is presented. The present method is based on modeling of an event of the mesh improvement. This event is modeled via modeling of a discrete random variable. The random variable is modeled in a tangent plane of each local domain of the mesh. One domain collects several elements with a common point. Values of random variable are calculated by modeling formula according to the initial sampling data of the projected elements with respect to all neighbors of the domain. Geometrical equivalent called potential form is constructed for each element of the domain with a mesh quality parameter value equal to the modeled numerical value. Such potential forms create potential centers of the domain. Averaging the coordinates of potential centers of the domain gives a new central point position. After geometrical realization over the entire mesh, the shapes of triangular elements are changed according to the normal distribution. It is shown experimentally that the mean of the final mesh is better than the initial one in most cases, so the event of the mesh improvement is likely occurred. Moreover, projection onto a local tangent plane included in the algorithm allows preservation of the model volume enclosed by the surface mesh. The implementation results are presented to demonstrate the functionality of the method. Our approach can provide a flexible tool for the development of mesh improvement algorithms, creating better-input parameters for the triangular meshes and other kinds of meshes intended to be applied in finite element analysis or computer graphics.
Smoothing and local refinement techniques for improving tetrahedral mesh quality
Computers & Structures, 2005
The improvement in the mesh quality without changing its connectivity is bounded. This bound is associated with the topology of the mesh and with the constraints imposed by the boundary of the domain. To solve this problem, we propose in this work to combine the tetrahedral mesh optimization technique introduced in [1,2] with the local mesh refinement algorithm presented in . The main idea consists in increasing the node number, and thus, the degrees of freedom, in the neighbourhood of the regions where the elements have poor quality. Then, we refine all the elements whose quality are below to a certain threshold. Once it is done, we initiate another stage of optimization until the quality of the mesh reaches a limit.
A comparison of tetrahedral mesh improvement techniques
1996
Automatic mesh generation and adaptive re nement methods for complex three-dimensional domains have proven to be very successful tools for the e cient solution of complex applications problems. These methods can, however, produce poorly shaped elements that cause the numerical solution to be less accurate and more di cult to compute. Fortunately, the shape of the elements can be improved through several mechanisms, including face-swapping techniques that change local connectivity and optimizationbased mesh smoothing methods that adjust grid point location. We consider several criteria for each of these two methods and compare the quality of several meshes obtained by using di erent combinations of swapping and smoothing. Computational experiments show that swapping is critical to the improvement of general mesh quality and that optimization-based smoothing is highly e ective in eliminating very small and very large angles. The highest quality meshes are obtained by using a combination of swapping and smoothing techniques.
Approximate Shape Quality Mesh Generation
Engineering With Computers, 2001
We present two techniques for simplifying the list processing required in standard iterative refinement approaches to shape quality mesh generation. The goal of these techniques is to gain simplicity of programming, efficiency in execution, and robustness of termination. 'Shape quality' for a mesh generation method usually means that, under suitable conditions, a mesh with all angles exceeding a prescribed tolerance is generated. The methods introduced in this paper are truncated versions of such methods. They depend on the shape improvement properties of the terminaledge LEPP-Delaunay refinement technique; we refer to them as approximate shape quality methods. They are intended for geometry-based preconditioning of coarse initial meshes for subsequent refinement to meet data representation needs. One technique is an algorithm re-organization to avoid maintaining a global list of triangles to be refined. The reorganization uses a recursive triangle processing strategy. Truncating the recursion depth results in an approximate method. Based on this, we argue that the refinement process can be carried out using a static list of the triangles to be refined that can be identified in the initial mesh. Comparisons of approximate to full shape quality meshes are provided.
Quality meshing with weighted Delaunay refinement
Proceedings of the thirteenth annual ACM- …, 2002
Delaunay meshes with bounded circumradius to shortest edge length ratio have been proposed in the past for quality meshing. The only poor quality tetrahedra called slivers that can occur in such a mesh can be eliminated by the sliver exudation method. This method has been shown to work for periodic point sets, but not with boundaries. Recently a randomized point-placement strategy has been proposed to remove slivers while conforming to a given boundary. In this paper we present a deterministic algorithm for generating a weighted Delaunay mesh which respects the input boundary and has no poor quality tetrahedron including slivers. This success is achieved by combining the weight pumping method for sliver exudation and the Delaunay refinement method for boundary conformation. We show that an incremental weight pumping can be mixed seamlessly with vertex insertions in our weighted Delaunay refinement paradigm.
An Approach to Improving Triangular Surface Mesh
JSME International Journal Series C, 2005
Our method is based on an implementation of quasi-statistical modeling for improving meshes by producing mesh elements with modeled values of different mesh quality parameters. In this paper we implement this approach to triangular surface mesh. Considering the initial distribution of the mesh quality parameter values, we assume that after improvement the distribution of elements of the mesh varies from a rather random distribution to a smoother one, such as a normal distribution. The preliminary choice of the desirable distribution affects the new parameter values modeled by the formula presented here. Uncertainty of the smoothed vertex positions of the mesh element affords to use a statistical approach in sense of random variable modeling to connect quasi-statistical modeling and mesh improvement techniques. The so-called "kernel" method allows creating different applicable to a mesh processing algorithms, which can be interpreted as a kind of smoothing technique to determine vertex direction movement with the distribution control of the shape of mesh elements. An aspect ratio is mainly used in present research as a mesh quality parameter. The geometry of the initial mesh surface is preserved by local mesh improving such that the new positions of the interior nodes of the mesh remain on the original discrete surface. Our method can be interpreted as a kind of smoothing technique with using the distribution control of the mesh quality parameter values. This method is comparable with optimization-based approach for avoiding the invalid elements of the mesh by producing a mesh with a rather homogeneous distribution of the mesh elements. Experimental results are included to demonstrate the functionality of our method. This method can be used at a pre-process stage for subsequent studies (finite element analysis, computer graphics, etc.) by providing the better-input parameters for these processes.
Post Refinement Element Shape Improvement For Quadrilateral Meshes
Schneiders and Debye (1995) present two algorithms for quadrilateral mesh refinement. These algorithms refine quadrilateral meshes while maintaining mesh conformity. The first algorithm maintains conformity by introducing triangles. The second algorithm maintains conformity without triangles, but requires a larger degree of refinement. Both algorithms introduce nodes with non-optimal valences. Non-optimal valences create acute and obtuse angles, decreasing element quality. This paper presents techniques for improving the quality of quadrilateral meshes after Schneiders' refinement. Improvement techniques use topology and node valence optimization rather than shape metrics; hence, improvement is computationally inexpensive. Meshes refined and subsequently topologically improved contain no triangles, even though triangles are initially introduced by Schneiders' refinement. Triangle elimination is especially important for linear elements since linear triangles perform poorly. I...
International Journal for Numerical Methods in Engineering, 2004
key words: Finite element method, mesh refinement, octasection, tetrahedron, hierarchical adaptive approximation SUMMARY Adaptive refinement of finite element approximations on tetrahedral meshes is generally considered to be a non-trivial task. (We wish to stress that this paper deals with mesh refinement as opposed to remeshing.) The splitting individual finite elements needs to be done with much care to prevent significant deterioration of the shape quality of the elements of the refined meshes. Considerable complexity thus results, which makes it difficult to design (and even more importantly, to later maintain) adaptive tetrahedra-based simulation codes. An adaptive refinement methodology, dubbed CHARMS (Conforming Hierarchical Adaptive Refinement MethodS), had recently been proposed by Krysl, Grinspun, and Schröder. The methodology streamlines and simplifies mesh refinement, since conforming (compatible) meshes always result by construction. The present work capitalizes on these conceptual developments to build a mesh refinement technique for tetrahedra. Shape quality is guaranteed for an arbitrary number of refinement levels due to our use of element octasection based on the Kuhn triangulation of the cube. Algorithms and design issues related to the inclusion of the present technique in a CHARMS-based object oriented software framework (http://hogwarts.ucsd.edu/\~pkrysl/CHARMS) are described.
Applied Sciences, 2022
Triangular meshes play critical roles in many applications, such as numerical simulation and additive manufacturing. However, the triangular meshes transformed from computer-aided design models using common algorithms may have many undesirable narrow triangles, which tends to affect the downstream applications. In this paper, we proposed two algorithms for Delaunay mesh construction and simplification to improve the quality of the triangular meshes. Two improved mesh operations of inserting vertices and collapsing vertices based on the principle of minimum volume destruction were designed. The improved vertex inserting operation is able to modify the local mesh so that it will conform to the local Delaunay property. The improved vertex collapsing operation can realize the simplification of the original mesh while maintaining the local Delaunay property. The results of visualized rendering and thermal diffusion simulations verified the improvement of the proposed algorithms in the as...
Tetrahedral mesh improvement via optimization of the element condition number
International Journal for Numerical Methods in Engineering, 2002
We present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, we formulate two optimization objective functions that are di erentiated by their goal: the ÿrst seeks to improve the average quality of the tetrahedral mesh; the second aims to improve the worst-quality element in the mesh. We review the optimization techniques used with each objective function and present experimental results that demonstrate the e ectiveness of the mesh improvement methods. We show that a combined optimization approach that uses both objective functions obtains the best-quality meshes for several complex geometries.