Data Partitioning Strategies for Stencil Computations on NUMA Systems

Many scientific problems rely on the efficient execution of stencil computations, which are usually memory-bound. In this paper, stencils on two-dimensional data are executed on NUMA architectures. Each node of a NUMA system processes a distinct partition of the input data independent from other nodes. However, processors may need access to the memory of other nodes at the edges of the partitions. This paper demonstrates two techniques based on machine learning for identifying partitioning strategies that reduce the occurrence of remote memory access. One approach is generally applicable and is based on an uninformed search. The second approach caps the search space by employing geometric decomposition. The partitioning strategies obtained with these techniques are analyzed theoretically. Finally, an evaluation on a real NUMA machine is conducted, which demonstrates that the expected reduction of the remote memory accesses can be achieved.