A Constraint-Based System to Ensure the Preservation of Sharp Geometric Features in Hexahedral Meshes (original) (raw)
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Topologic and geometric constraint-based hexahedral mesh generation
2007
Hexahedral finite element meshes have historically offered some mathematical benefit over tetrahedral finite element meshes in terms of reduced error and smaller element counts, especially with respect to finite element analyses within highly elastic, and plastic, structural domains. However, because hexahedral finite element mesh generation often requires significant geometric decomposition, generating hexahedral meshes can be extremely difficult to perform and automate and the process often takes several orders of magnitude longer in time to complete than current methods for generating tetrahedral meshes. In this dissertation, we focus on delineating known constraints associated with hexahedral meshes and formulating these constraints utilizing the dual of the hexahedral mesh. Utilizing these constraints, we show that hexahedral mesh generation can be viewed as an optimization problem. We review existing hexahedral algorithms and describe how these algorithms operate to satisfy the hexahedral mesh generation constraints. The concept of a fundamental hexahedral mesh will be introduced and it will be shown how the fundamental mesh relates to a minimal hexahedral mesh for a given geometry. We will demonstrate conversion of existing hexahedral meshes to fundamental hexahedral meshes using hexahedral flipping operations to convert boundary sheets to fundamental sheets. Building on existing algorithms for generating hexahedral meshes from volumetric image data, we will show significant improvement in hexahedral mesh quality through the introduction of a single fundamental sheet into hexahedral meshes generated from isosurfacing techniques. We will outline a method for constructing hexahedral meshes where all hexahedra are convex and have positive volume utilizing triangle meshes of manifold surfaces to guide the placement of fundamental sheets into an existing hexahedral mesh. Finally, we demonstrate construction of hexahedral meshes for multi-surface geometric solids by introducing multiple fundamental sheets to satisfy the hexahedral mesh generation constraints for the geometric solid.
Octree-based reasonable-quality hexahedral mesh generation using a new set of refinement templates
International Journal for Numerical Methods in Engineering, 2009
An octree-based mesh generation method is proposed to create reasonable-quality, geometry-adapted unstructured hexahedral meshes automatically from triangulated surface models without any sharp geometrical features. A new, easy-to-implement, easy-to-understand set of refinement templates is developed to perform local mesh refinement efficiently even for concave refinement domains without creating hanging nodes. A buffer layer is inserted on an octree core mesh to improve the mesh quality significantly. Laplacian-like smoothing, angle-based smoothing and local optimization-based untangling methods are used with certain restrictions to further improve the mesh quality. Several examples are shown to demonstrate the capability of our hexahedral mesh generation method for complex geometries.
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:
Quality Improvement and Feature Capture in Hexahedral Meshes
Building high-quality quadrilateral/hexahedral meshes directly from volumetric data is hard. Existing algorithms for generating meshes from volumetric data are based on primal and dual isocontouring algorithms, and current research focuses on improving the quality of such meshes. Most techniques are based on isocontouring techniques, and work by generating a grid of hexahedra on the interior/exterior of an isosurface, and then adjusting the elements that lie on the boundary of the grid to fit the surface. As a result of the element adjustment, many of these elements lose their convexity, as measured by the scaled Jacobian metric. Recovering the convexity of these elements is difficult since the position of boundary vertices is restricted to the domain of the isosurface.
A constructive approach to constrained hexahedral mesh generation
Engineering with Computers, 2010
S. Mitchell proved that a necessary and sufficient condition for the existence of a topological hexahedral mesh constrained to a quadrilateral mesh on the sphere is that the constraining quadrilateral mesh contains an even number of elements. S. Mitchell's proof depends on S. Smale's theorem on the regularity of curves on compact manifolds.
Conforming hexahedral mesh generation via geometric capture methods
Proceedings of the 18th International Meshing …, 2009
An algorithm is introduced for converting a non-conforming hexahedral mesh that is topologically equivalent and geometrically similar to a given geometry into a conforming mesh for the geometry. The procedure involves embedding geometric topology information into the given non-conforming base mesh and then converting the mesh to a fundamental hexahedral mesh. The procedure is extensible to multi-volume meshes with minor modification, and can also be utilized in a geometry-tolerant form (i.e., unwanted features within a solid geometry can be ignored with minor penalty). Utilizing an octree-type algorithm for producing the base mesh, it may be possible to show asymptotic convergence to a guaranteed closure state for meshes within the geometry, and because of the prevalence of these types of algorithms in parallel systems, the algorithm should be extensible to a parallel version with minor modification.
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,
International Journal for Numerical Methods in Engineering, 1997
A method is presented for subdividing a large class of solid objects into topologically simple subregions suitable for automatic finite element meshing with hexahedral elements. The technique uses a geometric property of a solid, its medial surface, to define the necessary subregions. The subregions are defined explicitly to be one of only 13 possible types. The subdividing cuts are between parts of the object in geometric proximity and produce good quality meshes of hexahedral elements. The method as introduced here is applicable to solids with convex edges and vertices, but the extension to complete generality is feasible.
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...
Hexahedral mesh generation constraints
Engineering with Computers, 2008
Hexahedral finite element meshes have historically offered some mathematical benefit over tetrahedral finite element meshes in terms of reduced error, smaller element counts, and improved reliability, especially with respect to finite element analyses within highly elastic, and plastic, structural domains. However, hexahedral finite element mesh generation continues to be extremely difficult to perform and automate, with hexahedral mesh generation taking several orders of magnitude longer in time to complete over current tetrahedral mesh generators. In this paper, I focus on delineating the known constraints associated with hexahedral meshes, formulating these constraints utilizing the dual of the hexahedral mesh. Utilizing these constraints, it will be possible to highlight areas where better knowledge and incorporation of these constraints can augment existing algorithms, predict failure of specific methods, and suggest some additional methods for extending the class of geometries which can be hexahedrally meshed.