Soji Yamakawa

HEXHOOP: Modular Templates for Converting a Hex-Dominant Mesh to an ALL-Hex Mesh

Abstract.This paper presents a new mesh conversion template called HEXHOOP, which fully automates a con-version from a hex-dominant mesh to an all-hex mesh. A HEXHOOP template subdivides a hex/prism/pyramid element into a set of smaller hex elements while main-taining the topological conformity with neighboring elements. A HEXHOOP template is constructed by assembling sub-templates, cores and caps. A dicing template for a hex and a prism is constructed by choosing the appropriate combination of a core and caps. A template that dices a pyramid without losing conformity to the adjacent element is derived from a HEXHOOP template. Some experimental results show that the HEXHOOP templates successfully convert a hex-dominant mesh into an all-hex mesh.

Polygon crawling: feature edge extraction from a general polygonal surface for mesh generation

This article describes a method for extracting feature edges of a polygonal surface for mesh generation. This method can extract feature edges from a polygonal surface typically created by a CAD facet generator in which typical feature edge extraction methods fail due to severe nonuniformity and anisotropy. The method is based on the technique called “polygon crawling,” which samples a sequence of points on the polygonal surface by moving a point along the polygonal surface. Extracting appropriate feature edges is important for creating a coarse mesh without yielding self-intersections. Extensive tests have been performed with various CAD-generated facet models, and this technique has shown good performance in extracting feature edges.

Hex-dominant mesh generation with directionality control via packing rectangular solid cells

A new computational method that creates a hex-dominant mesh of an arbitrary 3D geometric domain is presented. The proposed method generates a high-quality hex-dominant mesh by: (1) controlling the directionality of the output hex-dominant mesh; and (2) avoiding ill-shaped elements induced by nodes located too closely to each other. The proposed method takes a 3D geometric domain as input and creates a hex-dominant mesh that consists of mostly hexahedral elements with additional prism elements and tetrahedral elements. The proposed method packs rectangular solid cells on the boundary of and inside the input domain to obtain ideal node locations for a hex-dominant mesh. Each cell has a potential energy field that mimics a body centered cubic (BCC) structure, and the cells are moved to stable positions by a physically-based simulation. The simulation mimics the formation of a crystal pattern so that the centers of the cells give ideal node locations for a hex-dominant mesh. The domain is then meshed into a tetrahedral mesh by the advancing front method, and finally the tetrahedral mesh is converted to a hex-dominant mesh by merging some tetrahedrons.

Triangular/quadrilateral remeshing of an arbitrary polygonal surface via packing bubbles

This paper describes a new computational method for creating a triangular and quadrilateral mesh of an arbitrary polygonal surface while controlling the anisotropy and directionality of the mesh. The input polygonal surface may include non-manifold edges and holes, and it can be either a closed polyhedron or an open polygonal surface. The method creates a mesh in two steps. In the first step, volumetric cells are packed - ellipsoidal bubbles for a triangular mesh or rectangular solid bubbles for a quadrilateral mesh - on the input polygonal surface, then vertices are created at the centers of the bubbles and superimposed onto the input polygonal surface. In the second step, the original vertices of the input polygonal surface are deleted. The method is tolerant to the noise typically introduced by the measurement error of a laser range scanner, it can control element size and anisotropy precisely, and it creates high quality mesh elements. Applications of the proposed scheme include: reducing the number of elements of a mesh created by a laser range scanner, CT scanner, or MRI scanner; creating a surface mesh that can be a starting mesh for a tetrahedral or a hexahedral finite element mesh; and solution-adaptive anisotropic remeshing for finite element analysis.

QUAD-LAYER: LAYERED QUADRILATERAL MESHING OF NARROW TWO-DIMENSIONAL DOMAINS BY BUBBLE PACKING AND CHORDAL AXIS TRANSFORMATION ◊

This paper presents a computational method for quadrilateral meshing of a thin, or narrow, two-dimensional domain for finite element analysis. The proposed method creates a well-shaped single-layered, multi-layered, or partially multi-layered quadrilateral mesh. Element sizes can be uniform or graded. A high quality, layered quadrilateral mesh is often required for finite element analysis of a narrow two-dimensional domain with a large deformation such as in the analysis of rubber deformation or sheet metal forming. Fully automated quadrilateral meshing is performed in two stages: (1) extraction of the skeleton of a given domain by discrete chordal axis transformation, and (2) discretization of the chordal axis into a set of line segments and conversion of each of the line segments to a single quadrilateral element or multiple layers of quadrilateral elements. In each step a physically-based computational method called bubble packing is applied to discretize a curve into a set of line segments of specified sizes. Experiments show that the accuracy of a large-deformation FEM analysis can be significantly improved by using a well-shaped quadrilateral mesh created by the proposed method.

Removing Self Intersections of a Triangular Mesh by Edge Swapping, Edge Hammering, and Face Lifting

This paper describes a computational method for removing self intersections of a triangular mesh. A self intersection is a situation where a part of a surface mesh collides with another part of itself, i.e., two mesh elements intersect each other. It destroys the integrity of the mesh and makes the mesh unusable for certain applications. A mesh generator often creates a self intersection when a relatively large element size is specified over a region with a narrow clearance. There has been no automated method that automatically removes self intersections, and such self intersections needed to be corrected by manually editing the mesh. The proposed method automatically resolves a self intersection by re-connecting edges and adjusting node locations. This technique removes a typical self intersection and recovers the integrity of the triangular mesh. Experimental results show the effectiveness of the proposed method.

Subdivision templates for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without pyramid elements

This paper presents a computational method for converting a non-conformal hex-dominant mesh to a conformal hex-dominant mesh without help of pyramid elements. During the conversion, the proposed method subdivides a non-conformal element by applying a subdivision template and conformal elements by a conventional subdivision scheme. Although many finite element solvers accept mixed elements, some of them require a mesh to be conformal without a pyramid element. None of the published automated methods could create a conformal hex-dominant mesh without help of pyramid elements, and therefore the applicability of the hex-dominant mesh has been significantly limited. The proposed method takes a non-conformal hex-dominant mesh as an input and converts it to a conformal hex-dominant mesh that consists only of hex, tet, and prism elements. No pyramid element will be introduced. The conversion thus considerably increases the applicability of the hex-dominant mesh in many finite element solvers.

Converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for FEM accuracy and efficiency

This paper presents a computational method for converting a tetrahedral mesh to a prism-tetrahedral hybrid mesh for improved solution accuracy and computational efficiency of finite element analysis. The proposed method inserts layers of prism elements and deletes tetrahedral elements in sweepable sub-domains, in which cross-sections remain topologically identical and geometrically similar along a certain sweeping path. The total number of finite elements is reduced because roughly three tetrahedral elements are converted to one prism element. The solution accuracy of the finite element analysis improves since a prism element yields a more accurate solution than a tetrahedral element. Only previously known method for creating such a prism-tetrahedral mesh was to manually decompose a target volume into sweepable and non-sweepable sub-volumes and mesh each sub-volume separately. The proposed method starts from a cross-section of a tetrahedral mesh and replaces the tetrahedral elements with layers of prism elements until prescribed quality criteria can no longer be satisfied. The method applies a sequence of edge-collapse, local-transformation, and smoothing operations to remove or displace nodes located within the volume to be replaced with a layer of prism elements. Series of computational fluid dynamics simulations and structural analyses have been conducted, and the results verified a better performance of prismtetrahedral hybrid mesh in finite element simulations.

Layered tetrahedral meshing of thin-walled solids for plastic injection molding FEM

This paper describes a method for creating a well-shaped, layered tetrahedral mesh of a thin-walled solid by adapting the surface triangle sizes to the estimated wall thickness. The primary target application of the method is the finite element analysis of plastic injection molding, in which a layered mesh improves the accuracy of the solution. The edge lengths of the surface triangles must be proportional to the thickness of the domain to create well-shaped tetrahedrons; when the edge lengths are too short or too long, the shape of the tetrahedron tends to become thin or flat. The proposed method creates such a layered tetrahedral mesh in three steps: (1) create a preliminary tetrahedral mesh of the target geometric domain and estimate thickness distribution over the domain; (2) create a non-uniform surface triangular mesh with edge length adapted to the estimated thickness, then create a single-layer tetrahedral mesh using the surface triangular mesh; and (3) subdivide tetrahedrons of the single-layer mesh into multiple layers by applying a subdivision template. The effectiveness of the layered tetrahedral mesh is verified by running some experimental finite element analyses of plastic injection molding.

Improving Element-Boundary Alignment in All-Hex Meshes of Thin-Walled Solids by Side-Face Identification

This paper presents a new computational method for identifying side faces of thin-walled solids that can be excluded from the first step of conformal transformation from a tet mesh to an all-hex mesh. By excluding such side faces, all-hex meshes created by the conformal transformation method better align with the boundary of the side faces and tend to exhibit better scaled Jacobian quality. The proposed method first finds seeds of the candidate faces that may belong to the side faces. Then the candidate faces are grown across edges that have a low dihedral angle. Finally the candidate faces are retracted until no edge between a candidate face and non-candidate face has a low dihedral angle. Experimental results demonstrate clearly improvement of the element-boundary alignment and scaled Jacobian quality.