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One of the most important and commonly used operations in many linear algebrafunctions is matrix-matrix multiplication (GEMM), which is also a key componentin obtaining high performance of many scientific codes. It is a computationallyintensive function requiring $O(n^3)$ operations, and its high computationalintensity makes it well-suited to be significantly accelerated with GPUs.Today, many research problems require solving a very large number of relativelysmall GEMM operations that cannot utilise the entire GPU. To overcome thisbottleneck, special functions have been developed that pack several GEMMoperations into one and then compute them simultaneously on a GPU, which iscalled a batch operation. In this research work, we have proposed a differentapproach based on linking multiple GEMM operations to MPI ranks and thenbinding multiple MPI ranks to a single GPU. To increase GPU utilisation, moreMPI ranks (i.e. GEMM operations) are added. We implement and test this approachin the field of theoretical physics to compute entanglement properties throughsimulated annealing Monte Carlo simulation of quantum spin chains. For thespecific use case, we were able to simulate a much larger spin system andachieve a speed-up of up to $35\times$ compared to the parallel CPU-onlyversion.

Batched matrix operations on distributed GPUs with application in theoretical physics