Publications

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This paper explores potential methods for characterizing the meshing complexity of solid geometry. While numerous metrics exist to measure the quality of the finite element, there are currently no metrics that measure the quality of a solid with respect to its meshing complexity. The meshing complexity of a solid is defined by how difficult it is to generate a valid finite element mesh for a given solid. There are many variables that affect meshing complexity. This paper seeks to discuss methods that are decoupled from more subjective variables such as user expertise and software maturity, and it will focus on methods that describe the topological and geometric aspects of a solid. It will present techniques based on: medial axis transformation, wavelets, curvature, proximity, intersection, heuristic topology search, and the measurement of space (volume/area/length) and will analyze their suitability as meshing complexity metrics.

The cybersecurity consortium, which was established by DOE/NNSA’s Minority Serving Institutions Partnerships Program (MSIPP), allows students from any of the partner schools (13 HBCUs, two national laboratories, and a public school district) to have all consortia options available to them, to create career paths and to open doors to DOE sites and facilities to student members of the consortium. As a part of this year consortium activities, Sandia National Laboratories and the University of Virgin Islands conducted a week long cyber workshop that consisted of three courses; Digital Forensics and Malware Analysis, Python Programming, and ThunderBird Cup. These courses are designed to enhance cyber defense skills and promote learning within STEM related fields.

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This paper proposes a method for predicting the complexity of meshing computer aided design (CAD) geometries with unstructured, hexahedral, finite elements. Meshing complexity refers to the relative level of effort required to generate a valid finite element mesh on a given CAD geometry. A function is proposed to approximate the meshing complexity for single part CAD models. The function is dependent on a user defined element size as well as on data extracted from the geometry and topology of the CAD part. Several geometry and topology measures are proposed, which both characterize the shape of the CAD part and detect configurations that complicate mesh generation. Based on a test suite of CAD models, the function is demonstrated to be accurate within a certain range of error. The solution proposed here is intended to provide managers and users of meshing software a method of predicting the difficulty in meshing a CAD model. This will enable them to make decisions about model simplification and analysis approaches prior to mesh generation.

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Sweeping has become the workhorse algorithm for creating conforming hexahedral meshes of complex models. This paper describes progress on the automatic, robust generation of MultiSwept meshes in CUBIT. MultiSweeping extends the class of volumes that may be swept to include those with multiple source and multiple target surfaces. While not yet perfect, CUBIT's MultiSweeping has recently become more reliable, and been extended to assemblies of volumes. Sweep Forging automates the process of making a volume (multi) sweepable: Sweep Verification takes the given source and target surfaces, and automatically classifies curve and vertex types so that sweep layers are well formed and progress from sources to targets.

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.

A new method for lessening skew in mapped meshes is presented. This new method involves progressive subdivision of a surface into loops consisting of four sides. Using these loops, constraints can then be set on the curves of the surface, which will propagate interval assignments across the surface, allowing a mesh with a better skew metric to be generated.