Ted D. Blacker

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.

Seams and Wedges in Plastering : A 3-D Hexahedral Mesh Generation Algorithm

This paper describes mesh correction techniques necessary for meshing an arbitrary volume with a completely hexahedral mesh. Specifically, it describes seams and wedges, mechanisms that overcome major hurdles encountered in the preliminary work on the plastering algorithm. The plastering algorithm iteratively projects layers of elements inward from a quadrilateral discretization of the volumes bounding faces. Seams and wedges resolve incompatibilities in the mesh and in the progressing boundary, thus ensuring the correct formation of a hexahedral mesh from the plastering algorithm.

Optismoothing: an optimization-driven approach to mesh smoothing

Abstract This paper presents a mesh smoothing technique that uses optimization principles to minimize a distortion metric throughout a mesh. A comparison is made with laplacian and isoparametric smoothing techniques.

Finite element derivative recovery by moving least square interpolants

Abstract A simple, accurate technique for recovery of displcements and derivatives, such as strains is presented. The technique is based on local interpolation of nodal displacements using a moving least square method. The strains are then recovered by taking appropriate derivatives of this interpolant. Numerical experiments in linear elasticity and heat conduction on the convergence and accuracy of the recovered derivatives show very good results and superconvergence for strains in many cases; the technique is also effective for displacement interpolation for projection methods.

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.

The spatial twist continuum: a connectivity based method for representing all-hexahedral finite element meshes

Abstract This paper introduces the spatial twist continuum (STC), a powerful extension of the dual of a hexahedral mesh. The STC captures the global connectivity constraints inherent in hexahedral meshing. We begin by describing the two-dimensional analog of the representation for quadrilateral meshes: The STC of a quadrilateral mesh is an arrangement of curves called chords. Chords pass through opposite quadrilateral edges and intersect at quadrilateral centroids. The power of the STC is displayed in the three-dimensional representation, where continuous surfaces called twist planes pass through layers of hexahedra. Pairs of twist planes intersect to form chords that pass through opposite faces of hexahedra. Triples of twist planes orthogonally intersect at the centroids of hexahedra. The continuity of the twist planes and chords, and how twist planes and chords twist through space, are the basis of the spatial twist continuum.

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

Automated Conformal Hexahedral Meshing Constraints, Challenges and Opportunities

Abstract.Automated hexahedral element meshing has been the ‘Holy Grail’ of mesh generation research for years. The rigid connectivity and shape constraints of these meshes provide the challenge. The ever-present economic pressure for automating meshing of complex geometries, difficult transitions and large mesh sizes establishes the opportunity. This paper will systematically review the requirements of the hexahedral meshing challenge, the various approaches to the solution of the problem (along with their respective attributes), and some musings about future research opportunities.

Analysis automation with paving: A new quadrilateral meshing technique☆

Abstract This paper describes the impact of paving, a new automatic mesh generation algorithm, on the analysis portion of the design process. Paving generates an all-quadrilateral mesh in arbitrary 2D geometries. The paving technique significantly impacts the analysis process by drastically reducing the time and expertise requirements of traditional mesh generation. Paving produces a high quality mesh based on geometric boundary definitions and user specified element sizing constraints. In this paper we describe the paving algorithm, discuss varying aspects of the impact of the technique on design automation, and elaborate on current research into 3D all-hexahedral mesh generation.

Enhanced derivative recovery through least square residual penalty

Abstract L 2 projective techniques have proven very useful for postprocessing of derivatives, such as strains, in finite element solutions of elliptic problems. However, these projections often exhibit substantial errors near boundaries. It is shown here that adding the square of the residuals of selected governing equations to the least square form enhances the accuracy. Both global and local projection schemes are considered. Results are presented which show that these enhancements significantly increase the accuracy and convergence of recovered derivatives.