Timothy J. Tautges

THE WHISKER WEAVING ALGORITHM: A CONNECTIVITY‐BASED METHOD FOR CONSTRUCTING ALL‐HEXAHEDRAL FINITE ELEMENT MESHES

This paper introduces a new algorithm called whisker weaving for constructing unstructured, all-hexahedral finite element meshes. Whisker weaving is based on the Spatial Twist Continuum (STC), a global interpretation of the geometric dual of an all-hexahedral mesh. Whisker weaving begins with a closed, all-quadrilateral surface mesh bounding a solid geometry, then constructs hexahedral element connectivity advancing into the solid. The result of the whisker weaving algorithm is a complete representation of hex mesh connectivity only: Actual mesh node locations are determined afterwards. The basic step of whisker weaving is to form a hexahedral element by crossing or intersecting dual entities. This operation, combined with seaming or joining operations in dual space, is sufficient to mesh simple block problems. When meshing more complex geometries, certain other dual entities appear such as blind chords, merged sheets, and self-intersecting chords. Occasionally specific types of invalid connectivity arise. These are detected by a general method based on repeated STC edges. This leads into a strategy for resolving some cases of invalidities immediately. The whisker weaving implementation has so far been successful at generating meshes for simple block-type geometries and for some non-block geometries. Mesh sizes are currently limited to a few hundred elements. While the size and complexity of meshes generated by whisker weaving are currently limited, the algorithm shows promise for extension to much more general problems.

Feature based hex meshing methodology: feature recognition and volume decomposition ☆

Considerable progress has been made on automatic hexahedral mesh generation in recent years. A few automated meshing algorithms (e.g. mapping, submapping, sweeping) have proven to be very reliable on certain classes of geometry. While it is always worth pursuing general algorithms viable on arbitrary geometry, a combination of the well-established algorithms is ready to take on classes of complicated geometry. By partitioning the entire geometry into meshable pieces matched with appropriate meshing algorithms, the original geometry becomes meshable and may achieve better mesh quality. Each meshable portion is recognized as a meshing feature. This paper, which is a part of the feature based meshing methodology, presents the work on shape recognition and volume decomposition to automatically decompose a CAD model into hex meshable volumes. There are four phases in this approach: Feature Determination to extract decomposition features; Cutting Surfaces Generation to form the cutting surfaces; Body Decomposition to get the imprinted volumes; and Meshing Algorithm Assignment to match volumes decomposed with appropriate meshing algorithms. This paper focuses on describing feature determination and volume decomposition; the last part has been described in another paper. The feature determination procedure is based on the CLoop feature recognition algorithm that is extended to be more general. Some decomposition and meshing results are demonstrated in the final section.

Automatic scheme selection for toolkit hex meshing

Current hexahedral mesh generation techniques rely on a set of meshing tools, which when combined with geometry decomposition leads to an adequate mesh generation process. Of these tools, sweeping tends to be the workhorse algorithm, accounting for at least 50% of most meshing applications. Constraints which must be met for a volume to be sweepable are derived, and it is proven that these constraints are necessary but not sufficient conditions for sweepability. This paper also describes a new algorithm for detecting extruded or sweepable geometries. This algorithm, based on these constraints, uses topological and local geometric information, and is more robust than feature recognition-based algorithms. A method for computing sweep dependencies in volume assemblies is also given. The auto sweep detect and sweep grouping algorithms have been used to reduce interactive user time required to generate all-hexahedral meshes by filtering out non-sweepable volumes needing further decomposition and by allowing concurrent meshing of independent sweep groups. Parts of the auto sweep detect algorithm have also been used to identify independent sweep paths, for use in volume-based interval assignment.

CGM: A Geometry Interface for Mesh Generation, Analysis and Other Applications

Abstract.Geometry modeling has recently emerged as a commodity capability. Several geometry modeling engines are available which provide largely the same capability, ad most high-end CAD systems provide access to their geometry through APIs. However, subtle differences exist between these modelers, both at the syntax level and in the underlying topological models. A modeler-independent interface to geometry bridges these differences, allowing applications to be developed in a true modeler- independent manner. The Common Geometry Module, or CGM, provides such an interface to geometry. At the most basic level, CGM translates geometry function calls to access geometry in its native format. To smooth over topological differences between modelers, and to allow modeler-independent modification of topology, CGM maintains its own topology datastructure. CGM also provides functionality not found in most modelers, like support for non-manifold topology, and alternative representations, including facet-based and ‘virtual’ geometry. CGM is designed to be extensible, allowing applications to derive application-specific capabilities from topological entities defined in CGM. The CUBIT Mesh Generation Toolkit has been modified to work directly with CGM. CGM is also designed to simplify the implementation of other solid model-based or alternative representations of geometry. Ports to Solid Works and Pro/Engineer are underway. CGM is also being used as the foundation for parallel mesh generation and is being used for geometry support in several advanced finite element analysis codes.

Three-dimensional modeling of complex fusion devices using CAD-MCNPX interface

Abstract MCNPX’s geometric modeling capabilities are limited to Boolean combinations of primitive geometric shapes. These capabilities are not sufficient for simulating particle transport in stellerators, whose geometric models are quite complex. We describe a CAD based implementation of MCNPX, where a CAD geometry engine is used directly for solid model representation and evaluation. The application of this code, to calculating the neutron wall loading distribution (γ) in the Z and toroidal directions for the ARIES-CS[2] design, is described.

The TSTT Mesh Interface

PDE-based numerical simulation applications commonly use basic software infrastructure to manage mesh, geometry, and discretization data. The commonality of this infrastructure implies the software is theoretically amenable to re-use. However, the traditional reliance on library-based implementations of these functionalities hampers experimentation with different software instances that provide similar functionality. This is especially true for meshing and geometry libraries where applications often directly access the underlying data structures, which can be quite different from implementation to implementation. Thus, using different libraries interchangeably or interoperably for this functionality has proven difficult at best and has hampered the wide spread use of advanced meshing and geometry tools developed by the research community. To address these issues, the Terascale Simulation Tools and Technologies center is working to develop standard interfaces to enable the creation of interoperable and interchangeable simulation tools. In this paper, we focus on a languageand data-structure-independent interface supporting query and modification of mesh data conforming to a general abstract data model. We describe the model and interface, and provide programming “best practices” recommendations based on early experience implementing and using the interface.

Hexahedral mesh generation via the dual

Wereview the spatial twist continuum (STC), away of viewing the dual of a hexahedral (cubic) mesh as a simple non-degenerate arrangement of surfaces. Given a quadrilateral mesh of a closed surface, the STC gives insight into how the interior volume can be filled with hexahedra that respect the surface mesh. We review a hexahedral mesh generation heuristic called Whisker Weaving. Whisker Weaving incrementally builds the STC in an advancing front fashion. Although computational geometry has traditionally focussed on triangular and tetrahedral meshes, quadrilateral and hexahedral meshes are often considered to be more valuable for finite element analysis. The CUBIT environment being developed at Sandia National Laboratories is a suite of quadrilateral and hexahedral meshing tools. Whisker Weaving is one of these tools. CUBIT is used directly by practicing analysts, and is incorporated into a number of commercial mesh generation codes. 1 Spatial Twist Continuum We first describe the spatial twist continuum (STC) for a two-dimensional mesh and then generalize to three dimensions. It is possible to generalize to arbitrary dimensions. Consider the dual of a quadrilateral mesh. We use dual in the same sense as the Voronoi diagram is the dual of a Delaunay triangulation, except that here we concentrate on the graph properties of the dual and the geometric embedding is arbitrary. Each vertex of the dual has edge-degree four. As such, each vertex can be considered as the intersection of two curves as in Figure 1 left. Opposite edges at each vertex are identified as belonging to the same curve. In this way, the dual of the mesh can be considered as an arrangement of curves as in Figure 1 right. Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association of Computing Machinery,To copy otherwise, or to republish, requires a fee and/or specific permission. 11th Computational Geometry, Vancouver, B.C. Canada @ 1995 ACM 0-89791 -724 -3/95/0006 ...

One-to-one sweeping based on harmonic S-T mappings of facet meshes and their cages

3.50 Figure

Forming and resolving wedges in the spatial twist continuum

The sweeping algorithm is one of the most robust techniques to generate hexahedral meshes. During one-to-one sweeping, the most difficult thing is to map an all-quad source surface mesh onto its target surface. In this paper, a harmonic function is used to map meshes from a source surface to its target surface. The result shows that it can generate an all-quad mesh on the target surface with good mesh quality for the convex, concave or multiply-connected surface and thus avoid expensive smoothing algorithm (untangling). Meanwhile, the cage-based deformation method is used to locate interior nodes between the source and target surface during sweeping. Finally, examples are provided and the execution time for our proposed algorithm is discussed.

Interoperable geometry and mesh components for SciDAC applications

The spatial twist continuum (STC) is a powerful extension of the dual of a hexahedral mesh Murdochet al.,Int. J. Numer. Math. Engng (submitted). The STC captures the global connectivity constraints inherent in hexahedral meshing. Whisker wwaving is an advancing-front type of algorithm based on the STC[Tautges et al., Int. J. Numer. Math. Engng (submitted]. During the whisker weaving algorithm, certain types of degenerate elements calledwedges [Biacker; Myers (1993)Engng with Computers 9, 83–93 arise. This paper describedwedges and how they are formed, and presentscollapsing anddriving, two strategies for removing these degeneracies.