All-hexahedral element meshing by generating the dual mesh (original) (raw)

All-hexahedral element meshing: automatic elimination of self-intersecting dual lines

International Journal for Numerical Methods in Engineering, 2002

There has been some degree of success in all-hexahedral meshing. Standard methods start with the object geometry deÿned by means of an all-quadrilateral mesh, followed by the use of the combinatorial dual to the mesh in order to deÿne the internal connectivities among elements. For all of the known methods using the dual concept, it is necessary to ÿrst prevent or eliminate self-intersecting (SI) dual lines of the given quadrilateral mesh. The relevant features of SI lines are studied, giving a method to remove them, which avoids deforming the original geometry. Some examples of resulting meshes are shown where the current meshing method has been successfully applied.

A grid-based algorithm for the generation of hexahedral element meshes

Engineering With Computers - EWC, 1996

An algorithm for the generation of hexahedraIelement meshes is presented. The algorithm works in two steps. first the interior of the volume is filled with a regular grid; then the boundary region is meshed by using basically twodimensional operations. The algorithm was designed for use in the fern-simulation of metal forming processes where a remeshing mus~ be done very often. In principle, it can be used for meshing any geomewy with hexahedral elements and examples of meshes for geometries arising from various applications are given. The algorithm is checked against the criteria proposed by Sabin [1] (Advances in Engineering Software, 13. 220-225).

Unstructured and Semi-Structured Hexahedral Mesh Generation Methods

Computational Technology Reviews, 2014

Discretization techniques such the finite element method, the finite volume method or the discontinuous Galerkin method are the most used simulation techniques in applied sciences and technology. These methods rely on a spatial discretization adapted to the geometry and to the prescribed distribution of element size. Several fast and robust algorithms have been developed to generate triangular and tetrahedral meshes. In these methods local connectivity modifications are a crucial step. Nevertheless, in hexahedral meshes the connectivity modifications propagate through the mesh. In this sense, hexahedral meshes are more constrained and therefore, more difficult to generate. However, in many applications such as boundary layers in computational fluid dynamics or composite material in structural analysis hexahedral meshes are preferred. In this work we present a survey of developed methods for generating structured and unstructured hexahedral meshes.

Topology and Geometry of Hexahedral Complex: Combined Approach for Hexahedral Meshing

Journal of Computational Science and Technology, 2009

In present paper a new approach for hexahedral mesh generation is suggested. The process of hexahedral mesh generation for an arbitrary volume is an open subject. Two main stages exist: determining topological connectivity of the mesh and its geometrical embedding. There are many interesting solutions proposed in various methods, which mostly rely on topological validity of the mesh. Nevertheless, the final quality of the mesh strongly depends on the step of mesh embedding, which has direct connection with geometry of the mesh and shapes of the elements. In order to generate hexahedral meshes topologically valid and geometrically qualitative, we propose a new guide for hexahedral meshing that combines both geometrical and topological aspects of hexahedral complex, which is to be generated. This guide includes topological construction of the spine of three-manifold and encoding with a matrix of incidence based on curvature information.

Algorithms for Quadrilateral and Hexahedral Mesh Generation

2012

This lecture reviews the state of the art in quadrilateral and hexahedral mesh generation. Three lines of development – block decomposition, superposition and the dual method – are described. The refinement problem is discussed, and methods for octree-based meshing are presented. 1

An interior surface generation method for all-hexahedral meshing

Engineering With Computers, 2010

This paper describes an all-hexahedral generation method focusing on how to create interior surfaces. It is well known that a solid homeomorphic to a ball with even number of bounding quadrilaterals can be partitioned into a compatible hexahedral mesh where each associated hexahedron corresponds to the intersection of three interior surfaces that are dual to the original hexahedral mesh. However,

Octree-based generation of hexahedral element meshes

1996

We present a new algorithm for the generation of hexahedral element meshes. The algorithm starts with an octree discretization of the interior of the input object which is converted to a conforming hexahedral element mesh. Then the isomorphism technique 9] is used to adapt the mesh to the object boundary. keywords. hexahedra, mesh generation, octree 1 Introduction The last decades have seen immense progress in the development of numerical algorithms for the simulation of technical and physical processes. Finite element, nite di erence and nite volume methods are now routinely used in engineering. Therefore interest has grown in reducing simulation turnaround time, and the development of powerful, easy-to-use mesh generation programs has become an important issue. Much work has been done on algorithms for the generation of triangular, quadrilateral and tetrahedral element meshes. The state of the art is reviewed in 1], online information can be found in 2] and 3]. Mesh generators of this type have been integrated in many commercial programs. Unfortunately, the situation is worse in the eld of hex meshing. Most existing programs use mapped-meshing and multiblock techniques which require much user interaction and are therefore very time-consuming. Algorithms for the automatic generation of hexahedral element meshes have come up only recently, in essence the following techniques are used:

Research on the Algorithm for Grid-Based Hexahedral Mesh Generation of CAD Assembly Models

According to the geometric sharp features of CAD assembly models, an algorithm for the automated generation of grid-based full hexahedral element meshes was developed. This method involves six steps: geometric feature identification, cubic grid structure generation, jagged core mesh generation, surface matching, topological optimization and node smoothing. In the grid-based hexahedral mesh, the quality of the inner mesh is fine, the quality and the topological connections are very bad. Considering the specialty of the grid-based, this paper focused on the research for the surface matching and the topological optimization techniques in the grid-based hexahedral mesh generation. Among the surface matching process in this paper, a new matching algorithm combining the embedding technique was proposed, establishing the corresponding the boundary element relation between solid models and core grid, to make the hexahedral mesh accurately describe the geometric features of multiple-component assemblies. Among the topological optimization process, a new optimization technique was proposed, building the hexahedral shrink sets for the every geometry body and geometry surface, and then eliminating the hexahedral elements with bad topological connection by adding a layer of hexahedral elements on the boundary of the corresponding shrink set. Numerical examples show that the hexahedral mesh generated by the algorithm proposed in this paper described accurately the geometric features of the numerical models, and eliminated the poor hexahedral elements.

A frontal approach to hex-dominant mesh generation

Advanced Modeling and Simulation in Engineering Sciences, 2014

Background: Indirect quad mesh generation methods rely on an initial triangular mesh. So called triangle-merge techniques are then used to recombine the triangles of the initial mesh into quadrilaterals. This way, high-quality full-quad meshes suitable for finite element calculations can be generated for arbitrary two-dimensional geometries. Methods: In this paper, a similar indirect approach is applied to the three-dimensional case, i.e., a method to recombine tetrahedra into hexahedra. Contrary to the 2D case, a 100% recombination rate is seldom attained in 3D. Instead, part of the remaining tetrahedra are combined into prisms and pyramids, eventually yielding a mixed mesh. We show that the percentage of recombined hexahedra strongly depends on the location of the vertices in the initial 3D mesh. If the vertices are placed at random, less than 50% of the tetrahedra will be combined into hexahedra. In order to reach larger ratios, the vertices of the initial mesh need to be anticipatively organized into a lattice-like structure. This can be achieved with a frontal algorithm, which is applicable to both the two-and three-dimensional cases. The quality of the vertex alignment inside the volumes relies on the quality of the alignment on the surfaces. Once the vertex placement process is completed, the region is tetrahedralized with a Delaunay kernel. A maximum number of tetrahedra are then merged into hexahedra using the algorithm of Yamakawa-Shimada. Results: Non-uniform mixed meshes obtained following our approach show a volumic percentage of hexahedra that usually exceeds 80%. Conclusions: The execution times are reasonable. However, non-conformal quadrilateral faces adjacent to triangular faces are present in the final meshes.

Hexahedral Meshing: Mind the Gap!

2017

This article introduces a method to generate a hex-dominant mesh from an input tet mesh. We first compute a global parameterization, then we isolate the ``void'' (also called ``gap'' or ``cavity''), that is the zone where the global parameterization is singular or too much distorted. Once properly isolated, the void can be meshed with different algorithms. Thus, our main technical contribution is an algorithm that computes the boundary of the void and makes it compatible with both the hexahedra generated in the regular part of the parameterization and the input boundary. We tested our method on a large collection of objects (200+) with different settings. In most cases, we obtained very good quality results compared to the state-of-the-art solutions. In addition to improving the state-of-the-art in hex-dominant meshing, a second contribution of this work is to introduce a pipeline architecture, which can be used to compare present and future algorithms involv...