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Type: Text × search.filters.applied.f.series: Procedia engineering 163 (2016) × WGL Institute: WIAS ×

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Now showing 1 - 4 of 4
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    Preface
    (Amsterdam [u.a.] : Elsevier, 2016) Canann, Scott; Owen, Steven; Si, Hang
    [No abstract available]
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    Tetrahedral Mesh Improvement Using Moving Mesh Smoothing and Lazy Searching Flips
    (Amsterdam [u.a.] : Elsevier, 2016) Dassi, Franco; Kamenski, Lennard; Si, Hang
    We combine the new moving mesh smoothing, based on the integration of an ordinary differential equation coming from a given functional, with the new lazy flip technique, a reversible edge removal algorithm for local mesh quality improvement. These strategies already provide good mesh improvement on themselves, but their combination achieves astonishing results not reported so far. Provided numerical comparison with some publicly available mesh improving software show that we can obtain final tetrahedral meshes with dihedral angles between 40° and 123°.
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    On Tetrahedralisations of Reduced Chazelle Polyhedra with Interior Steiner Points
    (Amsterdam [u.a.] : Elsevier, 2016) Si, Hang; Goerigk, Nadja
    The non-convex polyhedron constructed by Chazelle, known as the Chazelle polyhedron [4], establishes a quadratic lower bound on the minimum number of convex pieces for the 3d polyhedron partitioning problem. In this paper, we study the problem of tetrahedralising the Chazelle polyhedron without modifying its exterior boundary. It is motivated by a crucial step in tetrahedral mesh generation in which a set of arbitrary constraints (edges or faces) need to be entirely preserved. The goal of this study is to gain more knowledge about the family of 3d indecomposable polyhedra which needs additional points, so-called Steiner points, to be tetrahedralised. The requirement of only using interior Steiner points for the Chazelle polyhedron is extremely challenging. We first “cut off” the volume of the Chazelle polyhedron by removing the regions that are tetrahedralisable. This leads to a 3d non-convex polyhedron whose vertices are all in the two slightly shifted saddle surfaces which are used to construct the Chazelle polyhedron. We call it the reduced Chazelle polyhedron. It is an indecomposable polyhedron. We then give a set of (N + 1)2 interior Steiner points that ensures the existence of a tetrahedralisation of the reduced Chazelle polyhedron with 4(N + 1) vertices. The proof is done by transforming a 3d tetrahedralisation problem into a 2d edge flip problem. In particular, we design an edge splitting and flipping algorithm and prove that it gives to a tetrahedralisation of the reduced Chazelle polyhedron.
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    An Anisoptropic Surface Remeshing Strategy Combining Higher Dimensional Embedding with Radial Basis Functions
    (Amsterdam [u.a.] : Elsevier, 2016) Dassi, Franco; Farrell, Patricio; Si, Hang
    Many applications heavily rely on piecewise triangular meshes to describe complex surface geometries. High-quality meshes significantly improve numerical simulations. In practice, however, one often has to deal with several challenges. Some regions in the initial mesh may be overrefined, others too coarse. Additionally, the triangles may be too thin or not properly oriented. We present a novel mesh adaptation procedure which greatly improves the problematic input mesh and overcomes all of these drawbacks. By coupling surface reconstruction via radial basis functions with the higher dimensional embedding surface remeshing technique, we can automatically generate anisotropic meshes. Moreover, we are not only able to fill or coarsen certain mesh regions but also align the triangles according to the curvature of the reconstructed surface. This yields an acceptable trade-off between computational complexity and accuracy.