Evaluation of hierarchical mesh reorderings

Irregular and sparse scientific computing programs frequently experience performance losses due to inefficient use of the memory system in most machines. Previous work has shown that, for a graph model, performing a partitioning and then reordering within each partition improves performance. More recent work has shown that reordering heuristics based on a hypergraph model result in better reorderings than those based on a graph model. This paper studies the effects of hierarchical reordering strategies within the hypergraph model. In our experiments, the reorderings are applied to the nodes and elements of tetrahedral meshes, which are inputs to a mesh optimization application. We show that cache performance degrades over time with consecutive packing, but not with breadth-first ordering, and that hierarchical reorderings involving hypergraph partitioning followed by consecutive packing or breadth-first orderings in each partition improve overall execution time.