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arXiv · 1509.04627

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

Carsten Burstedde·Johannes Holke
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Abstract

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.

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Carsten Burstedde, Johannes Holke. 2015-09-15. A tetrahedral space-filling curve for non-conforming adaptive meshes. https://doi.org/10.1137/15m1040049

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