Self-Avoiding Walks over Adaptive Unstructured Grids

In this paper, we present self-avoiding walks as a novel technique to “linearize” a triangular mesh. Unlike space-filling curves which are based on a geometric embedding, our algorithm is combinatorial since it uses the mesh connectivity only. We also show how the concept can be easily modified for adaptive grids that are generated in a hierarchical manner based on a set of simple rules, and made amenable for efficient parallelization. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.