Matthew L. Staten

Unconstrained Paving & Plastering: A New Idea for All Hexahedral Mesh Generation

Unconstrained Plastering is a new algorithm with the goal of generating a conformal all-hexahedral mesh on any solid geometry assembly. Paving[1] has proven reliable for quadrilateral meshing on arbitrary surfaces. However, the 3D corollary, Plastering [2][3][4][5], is unable to resolve the unmeshed center voids due to being over-constrained by a pre-existing boundary mesh. Unconstrained Plastering attempts to leverage the benefits of Paving and Plastering, without the over-constrained nature of Plastering. Unconstrained Plastering uses advancing fronts to inwardly project unconstrained hexahedral layers from an unmeshed boundary. Only when three layers cross, is a hex element formed. Resolving the final voids is easier since closely spaced, randomly oriented quadrilaterals do not over-constrain the problem. Implementation has begun on Unconstrained Plastering, however, proof of its reliability is still forthcoming.

Unconstrained Paving and Plastering: Progress Update

Modeling and simulation has become an essential step in the engineering design process. Modeling and simulation can be used during either the original design phases, or on assessment of existing designs. In either case, the end result is increased confidence in the design, faster time to market, and reduced engineering cost. An essential step in modeling and simulation is the creation of a finite element mesh which accurately models the geometric features of the model being analyzed. Meshes generated for three-dimensional models are typically composed of either all-tetrahedral or all-hexahedral elements. Some methods exist for the generation and analysis of hybrid meshes

A Comparison of Mesh Morphing Methods for 3D Shape Optimization

The ability to automatically morph an existing mesh to conform to geometry modifications is a necessary capability to enable rapid prototyping of design variations. This paper compares six methods for morphing hexahedral and tetrahedral meshes, including the previously published FEMWARP and LBWARP methods as well as four new methods. Element quality and performance results show that different methods are superior on different models. We recommend that designers of applications that use mesh morphing consider both the FEMWARP and a linear simplex based method.

A Selective Approach to Conformal Refinement of Unstructured Hexahedral Finite Element Meshes

Hexahedral refinement increases the density of an all-hexahedral mesh in a specified region, improving numerical accuracy. Previous research using solely sheet refinement theory made the implementation computationally expensive and unable to effectively handle concave refinement regions and self-intersecting hex sheets. The Selective Approach method is a new procedure that combines two diverse methodologies to create an efficient and robust algorithm able to handle the above stated problems. These two refinement methods are: 1) element by element refinement and 2) directional refinement. In element by element refinement, the three inherent directions of a Hex are refined in one step using one of seven templates. Because of its computational superiority over directional refinement, but its inability to handle concavities, element by element refinement is used in all areas of the specified region except regions local to concavities. The directional refinement scheme refines the three inherent directions of a hexahedron separately on a hex by hex basis. This differs from sheet refinement which refines hexahedra using hex sheets. Directional refinement is able to correctly handle concave refinement regions. A ranking system and propagation scheme allow directional refinement to work within the confines of the Selective Approach Algorithm.

Localized coarsening of conforming all-hexahedral meshes

Finite element mesh adaptation methods can be used to improve the efficiency and accuracy of solutions to computational modeling problems. In many applications involving hexahedral meshes, localized modifications which preserve a conforming all-hexahedral mesh are desired. Effective hexahedral refinement methods that satisfy these criteria have recently become available; however, due to hexahedral mesh topology constraints, little progress has been made in the area of hexahedral coarsening. This paper presents a new method to locally coarsen conforming all-hexahedral meshes. The method works on both structured and unstructured meshes and is not based on undoing previous refinement. Building upon recent developments in quadrilateral coarsening, the method utilizes hexahedral sheet and column operations, including pillowing, column collapsing, and sheet extraction. A general algorithm for automated coarsening is presented and examples of models that have been coarsened with this new algorithm are shown. While results are promising, further work is needed to improve the automated process.

A methodology for quadrilateral finite element mesh coarsening

High fidelity finite element modeling of continuum mechanics problems often requires using all quadrilateral or all hexahedral meshes. The efficiency of such models is often dependent upon the ability to adapt a mesh to the physics of the phenomena. Adapting a mesh requires the ability to both refine and/or coarsen the mesh. The algorithms available to refine and coarsen triangular and tetrahedral meshes are very robust and efficient. However, the ability to locally and conformally refine or coarsen all quadrilateral and all hexahedral meshes presents many difficulties. Some research has been done on localized conformal refinement of quadrilateral and hexahedral meshes. However, little work has been done on localized conformal coarsening of quadrilateral and hexahedral meshes. A general method which provides both localized conformal coarsening and refinement for quadrilateral meshes is presented in this paper. This method is based on restructuring the mesh with simplex manipulations to the dual of the mesh. In addition, this method appears to be extensible to hexahedral meshes in three dimensions.

Parallel Hex Meshing from Volume Fractions

In this work, we introduce a new method for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to Eulerian-based codes that generate volume fraction data on a Cartesian grid. A step-by-step procedure for generating an all-hexahedral mesh is presented. We focus specifically on the challenges of developing a parallel implementation using the message passing interface (MPI) to ensure a continuous, conformal and good quality hex mesh.

Fun sheet matching: towards automatic block decomposition for hexahedral meshes

Depending upon the numerical approximation method that may be implemented, hexahedral meshes are frequently preferred to tetrahedral meshes. Because of the layered structure of hexahedral meshes, the automatic generation of hexahedral meshes for arbitrary geometries is still an open problem. This layered structure usually requires topological modifications to propagate globally, thus preventing the general development of meshing algorithms such as Delaunay’s algorithm for tetrahedral meshes or the advancing-front algorithm based on local decisions. To automatically produce an acceptable hexahedral mesh, we claim that both global geometric and global topological information must be taken into account in the mesh generation process. In this work, we propose a theoretical classification of the layers or sheets participating in the geometry capture procedure. These sheets are called fundamental, or fun-sheets for short, and make the connection between the global layered structure of hexahedral meshes and the geometric surfaces that are captured during the meshing process. Moreover, we propose a first generation algorithm based on fun-sheets to deal with 3D geometries having 3- and 4-valent vertices.

Parallel hexahedral meshing from volume fractions

In this work, we introduce a new method for generating Lagrangian computational meshes from Eulerian-based data. We focus specifically on shock physics problems that are relevant to Eulerian-based codes that generate volume fraction data on a Cartesian grid. A step-by-step procedure for generating an all-hexahedral mesh is presented. We focus specifically on the challenges of developing a parallel implementation using the message passing interface to ensure a continuous, conformal and good quality hex mesh.

A Constraint-Based System to Ensure the Preservation of Sharp Geometric Features in Hexahedral Meshes

Generating a full hexahedral mesh for any 3D geometric domain is still a challenging problem. Among the different attempts, the octree-based methods are the most efficient from an engineering point of view. But the main drawback of such methods is the lack of control near the boundary. In this work, we propose an a posteriori technique based on the notion of the fundamental mesh in order to improve the mesh quality near the boundary. This approach is based on the resolution of a constraint problem defined on the topology of the CAD model that we have to discretize.