A tetrahedral space-filling curve for non-conforming adaptive meshes

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 1...

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Bibliographic Details
Published in:arXiv.org 2017-04
Main Authors: Burstedde, Carsten, Holke, Johannes
Format: Article
Language:English
Subjects:
Algorithms
Boundary element method
Distributed memory
Random access
Tetrahedra
Triangles
Online Access:Get full text
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Summary:We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.
ISSN:2331-8422
DOI:10.48550/arxiv.1509.04627