Publications

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Verdict is a collection of subroutines for evaluating the geometric qualities of triangles, quadrilaterals, tetrahedra, and hexahedra using a variety of functions. A quality is a real number assigned to one of these shapes depending on its particular vertex coordinates. These functions are used to evaluate the input to finite element, finite volume, boundary element, and other types of solvers that approximate the solution to partial differential equations defined over regions of space. This article describes the most recent version of Verdict and provides a summary of the main properties of the quality functions offered by the library. It finally demonstrates the versatility and applicability of Verdict by illustrating its use in several scientific applications that pertain to pre, post, and end-to-end processing.

This paper presents methods and applications of sheet insertion in a hexahedral mesh. A hexahedral sheet is dual to a layer of hexahedra in a hexahedral mesh. Because of symmetries within a hexahedral element, every hexahedral mesh can be viewed as a collection of these sheets. It is possible to insert new sheets into an existing mesh, and these new sheets can be used to define new mesh boundaries, refine the mesh, or in some cases can be used to improve quality in an existing mesh. Sheet insertion has a broad range of possible applications including mesh generation, boundary refinement, R-adaptivity and joining existing meshes. Examples of each of these applications are demonstrated.

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This paper presents a new method for handling non-conforming hexahedralto- hexahedral interfaces. One or both of the adjacent hexahedralmeshes are locally modified to create a one-to-onemapping between between themesh nodes and quadrilaterals at the interface allowing a conforming mesh to be created. In the finite element method, non-conforming interfaces are currently handled using constraint conditions such as gapelements, tied contacts, or multi-point constraints. By creating a conforming mesh, the need for constraint conditions is eliminated resulting in a smoother, more precise numerical solution. The method presented in this paper uses hexahedral dual operations, including pillowing, sheet extraction, dicing and column collapse operations, to affect the local mesh modifications. In addition, an extension to pillowing, called sheet inflation, is introduced to handle the insertion of self-intersecting and self-touching sheets. The quality of the resultant conforming hexahedral mesh is high and the increase in number of elements is moderate.

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We present Mark-It, a marking user interface that reduced the time to decompose a set of CAD models exhibiting a range of decomposition problems by as much as fifty percent. Instead of performing about 50 mesh decomposition operations using a conventional UI, Mark-It allows users to perform the same operations by drawing 2D marks in the context of the 3D model. The motivation for this study was to test the potential of a marking user interface for the decomposition aspect of the meshing process. To evaluate Mark-It, we designed a user study that consisted of a brief tutorial of both the non-marking and marking UIs, performing the steps to decompose four models contributed to us by experienced meshers at Sandia National Laboratories, and a post-study debriefing to rate the speed, preference, and overall learnability of the two interfaces. Our primary contributions are a practical user interface design for speeding-up mesh decomposition and an evaluation that helps characterize the pros and cons of the new user interface.

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.