Bounds on the cost of compatible refinement of simplex decomposition trees in arbitrary dimensions

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 functi...

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Bibliographic Details
Published in:Computational geometry : theory and applications 2019-02, Vol.79, p.14-29
Main Authors: Atalay, F. Betul, Mount, David M.
Format: Article
Language:English
Subjects:
Compatible meshes
Hierarchical simplicial meshes
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Summary: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.
ISSN:0925-7721
DOI:10.1016/j.comgeo.2019.01.004