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

TL;DR

This paper presents a novel space-filling curve for triangular and tetrahedral meshes that enables efficient storage, traversal, and adaptive refinement, facilitating scalable mesh management on distributed systems.

Contribution

It introduces a new space-filling curve for non-conforming adaptive meshes with efficient algorithms for mesh operations and a low-memory encoding scheme.

Findings

Constant-time algorithms for mesh element operations

Low-memory encoding for random access

Scalability demonstrated on large distributed systems

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.