. Whisker Weaving is an advancing front algorithm for all-hexahedral mesh generation. It uses global information derived from grouping the mesh dual into surfaces, the STC, to construct the connectivity of the mesh, then positions the nodes afterwards. Currently we are able to reliably generate hexahedral meshes for complicated geometries and surface meshes. However, the surface mesh must be modified locally. Also, in large, highlyunstructured meshes, there are usually isolated regions where hex quality is poor. Reliability has been achieved by using new, provable curve-contraction algorithms to sequence the advancing front process. We have also demonstrated that sheet moving can remove certain types of invalid connectivity. keywords. hexahedra, mesh generation, advancing front, topology, curve contraction 1. Introduction The finite element method (FEM) is effective for studying a wide variety of physics. Before a FEM analysis can be performed, however, a mesh of the model must be g...

We propose a new method for constructing all-hexahedral finite element meshes. The core of our method is to build up a compatible combinatorial cell complex of hexahedra for a solid body which is topologically a ball and for which a quadrilateral surface mesh of a certain structure is prescribed. The step-wise creation of the hex complex is guided by the cycle structure of the combinatorial dual of the surface mesh. Our method transforms the graph of the surface mesh iteratively by changing the dual cycle structure until we get the surface mesh of a single hexahedron. Starting with a single hexahedron and reversing the order of the graph transformations, each transformation step can be interpreted as adding one or more hexahedra to the so far created hex complex. Given an arbitrary solid body, we first decompose it into simpler subdomains equivalent to topological balls by adding virtual 2-manifolds. Second, we determine a compatible quadrilateral surface mesh for all created...

This paper describes an algorithm to extract adaptive and quality quadrilateral/hexahedral meshes directly from volumetric imaging data. First, a bottom-up surface topology preserving octree-based algorithm is applied to select a starting octree level. Then the dual contouring method is used to extract a preliminary uniform quad/hex mesh, which is decomposed into finer quads/hexes adaptively without introducing any hanging nodes. The positions of all boundary vertices are recalculated to approximate the boundary surface more accurately. Mesh adaptivity can be controlled by a feature sensitive error function, the regions that users are interested in, or finite element calculation results. Finally, the relaxation based technique is deployed to improve mesh quality. Several demonstration examples are provided from a wide variety of application domains. Some extracted meshes have been extensively used in finite element simulations.

. The 3D meshing process begins with the definition of the outer geometry. With a CAD system and a 2d quadrilateral mesh generator, a closed all-quadrilateral mesh is obtained, which is the start point for the process that this communication describes. Once imposed the outer quadrilateral mesh, the connectivity between the inner elements becomes strongly conditioned. Following the guidelines of the outer topology, the inner one is almost entirely defined. Several ways may be decided for certain configurations, some of them requiring special considerations in order to achieve a valid FEM mesh. The process is entirely performed by constructing the (graph theoretical) dual of the hexahedral mesh, this means no metric information is managed until the final (positioning and smoothing) steps. The essential steps of this scheme and several examples obtained are described on this communication. Nestor A. Calvo and Sergio R. Idelsohn. 2 1 INTRODUCTION At the present there are a few all...

. In this paper we present a recursive volume decomposition method for automatically decomposing complex shaped objects with both protrusions and depressions into simpler sub-objects for automatic hexahedral mesh generation. The sub-volumes after decomposition are classified into either convex or swept volumes. For a convex volume, it is mapped to a collection of hexahedral objects. On the other hand, for a swept volume, a hexahedral mesh can be created by generating a quadrilateral mesh on the sweeping face and then sweeping this quadrilateral mesh onto the swept volume. Moreover, in order to apply the current mesh generation approach to more general geometry we use the topological and geometric requirements to determine the generalized swept volumes. To separate volumes into sub-volumes, a recursive algorithm of volume decomposition is used until all the volumes are either convex or swept objects. 1. Introduction Finite element analysis (FEA) is used extensively in applications such...

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We describe an approach to construct hexahedral solid NURBS (Non-Uniform Rational B-Splines) meshes for patient-specific vascular geometric models from imaging data for use in isogeometric analysis. First, image processing techniques, such as contrast enhancement, filtering, classification, and segmentation, are used to improve the quality of the input imaging data. Then, luminal surfaces are extracted by isocontouring the preprocessed data, followed by the extraction of vascular skeleton via Voronoi and Delaunay diagrams. Next, the skeleton-based sweeping method is used to construct hexahedral control meshes. Templates are designed for various branching configurations to decompose the geometry into mapped meshable patches. Each patch is then meshed using one-to-one sweeping techniques, and boundary vertices are projected to the luminal surface. Finally, hexahedral solid NURBS are constructed and used in isogeometric analysis of blood flow. Piecewise linear hexahedral meshes can also be obtained using this approach. Examples of patient-specific arterial models are presented. Key words: Patient-specific vascular models, hexahedral mesh, skeleton-based sweeping, NURBS, isogeometric analysis, blood flow. 1

Sweep method is one of the most robust techniques to generate hexahedral meshes in extrusion volumes. One of the main issues to be dealt by any sweep algorithm is the projection of a source surface mesh onto the target surface. This paper presents a new algorithm to map a given mesh over the source surface onto the target surface. This projection is carried out by means of a least-squares approximation of an affine mapping defined between the parametric spaces of the surfaces. Once the new mesh is obtained on the parametric space of the target surface, it is mapped up according to the target surface parameterization. Therefore, the developed algorithm does not require to solve any root finding problem to ensure that the projected nodes are on the target surface. Afterwards, this projection algorithm is extended to three dimensional cases and it is used to generate the inner layers of elements in the physical space.

This paper proposes chordal surface transform for representation and discretization of thin section solids, such as automobile bodies, plastic injection mold components and sheet metal parts. A multiple-layered all-hex mesh with a high aspect ratio is a typical requirement for mold flow simulation of thin section objects. The chordal surface transform reduces the problem of 3D hex meshing to 2D quad meshing on the chordal surface. The chordal surface is generated by cutting a tet mesh of the input CAD model at its mid plane. Radius function and curvature of the chordal surface are used to provide sizing function for quad meshing. Two-way mapping between the chordal surface and the boundary is used to sweep the quad elements from the chordal surface onto the boundary, resulting in a layered all-hex mesh. The algorithm has been tested on industrial models, whose chordal surface is 2-manifold. The graphical results of the chordal surface and the multiple-layered all-hex mesh are presented along with the quality measures. The results show geometrically adaptive high aspect ratio all-hex mesh, whose average scaled Jacobean, is close to 1.0.

This paper presents a mesh quality metric for hexahedral and wedge elements. A series of studies was carried out to relate the proposed metric with the solution errors. During the studies, the metric was also compared with the aspect ratio, the warping factor and the control number. The results show that the metric can be used to identify invalid as well as potential poor quality elements, which may cause larger solution errors.