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Title: Bounds on the cost of compatible refinement of simplex decomposition trees in arbitrary dimensions
Authors: Atalay, Fatma Betül
Mount, David M.
Keywords: Hierarchical simplicial meshes
compatible meshes
Issue Date: Feb-2019
Publisher: Elsevier B.V.
Source: Atalay, F. B., and Mount, D. M. (2019). Bounds on the cost of compatible refinement of simplex decomposition trees in arbitrary dimensions. Computational Geometry, 79, 14-29.
Abstract: A hierarchical simplicial mesh is a recursive decomposition of space into cells that are simplices. Such a mesh is compatible if pairs of neighboring cells meet along a single common face. Compatibility condition is important in many applications where the mesh serves as a discretization of a function. Enforcing compatibility involves refining the simplices further if they share split faces with their neighbors, thus generates a larger mesh. We prove a tight upper bound on the expansion factor for 2-dimensional meshes, and show that the size of a simplicial subdivision grows by no more than a constant factor when compatibly refined. We also prove upper bounds for d-dimensional meshes. (C) 2019 Elsevier B.V. All rights reserved.
ISSN: 9257721
Appears in Collections:Bilgisayar Mühendisliği Bölümü / Department of Computer Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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