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 runtime partitioning and load balancing of adaptive unstructured grids. 1 Introduction Advances in adaptive software and methodology notwithstanding, parallel computational strategies will be an essential ingredient in solving complex, real-life problems. However, parallel computers are easily programmed with regular data structures; so the development of efficient parallel adaptive algorithms for unstructured grids poses a serious challenge. An efficient parallelization of these unstructured adaptive..