Hierarchical Partitioning Techniques for Structured Adaptive Mesh Refinement Applications

This paper presents the design and preliminary evaluation of hierarchical partitioning and load-balancing techniques for distributed structured adaptive mesh refinement (SAMR) applications. The overall goal of these techniques is to enable the load distribution to reflect the state of the adaptive grid hierarchy and exploit it to reduce synchronization requirements, improve load-balance, and enable concurrent communications and incremental redistribution. The hierarchical partitioning algorithm (HPA) partitions the computational domain into subdomains and assigns them to hierarchical processor groups. Two variants of HPA are presented in this paper. The static hierarchical partitioning algorithm (SHPA) assigns portions of overall load to processor groups. In SHPA, the group size and the number of processors in each group is setup during initialization and remains unchanged during application execution. It is experimentally shown that SHPA reduces communication costs as compared to the Non-HPA scheme, and reduces overall application execution time by up to 59%. The adaptive hierarchical partitioning algorithm (AHPA) dynamically partitions the processor pool into hierarchical groups that match the structure of the adaptive grid hierarchy. Initial evaluations of AHPA show that it can reduce communication costs by up to 70%.