Publications

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Grid-based mesh generation methods have been available for many years and can provide a reliable method for meshing arbitrary geometries with hexahedral elements. The principal use for these methods has mostly been limited to biological-type models where topology that may incorporate sharp edges and curve definitions are not critical. While these applications have been effective, robust generation of hexahedral meshes on mechanical models, where the topology is typically of prime importance, impose difficulties that existing grid-based methods have not yet effectively addressed. This work introduces a set of procedures that can be used in resolving the features of a geometric model for grid-based hexahedral mesh generation for mechanical or topology-rich models.

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.

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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.

Sweeping algorithms have become very mature and can create a semi-structured mesh on a large set of solids. However, these algorithms require that all linking surfaces be mappable or submappable. This restriction excludes solids with imprints or protrusions on the linking surfaces. The grafting algorithm allows these solids to be swept. It then locally modifies the position and connectivity of the nodes on the linking surfaces to align with the graft surfaces. Once a high-quality surface mesh is formed on the graft surface, it is swept along the branch creating a 2 3/4-D mesh.

This paper presents a new technique for automatically detecting interval constraints for swept volumes with holes. The technique finds true volume constraints that are not necessarily imposed by the surfaces of the volume. A graphing algorithm finds independent, parallel paths of edges from source surfaces to target surfaces. The number of intervals on two paths between a given source and target surface must be equal; in general, the collection of paths determine a set of linear constraints. Linear programming techniques solve the interval assignment problem for the surface and volume constraints simultaneously.