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 the information necessary for random access, we suggest 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. Furthermore, we prove that the maximum number of face-connected components in any segment of this curve is bounded by twice the refinement level plus one (minus one in 2d) and that the number of corner-connected components is bounded by two. We conclude with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.