A memory efficient algorithm for adaptive multidimensional integration with multiple GPUs

We present a memory-efficient algorithm and its implementation for solving multidimensional numerical integration on a cluster of compute nodes with multiple GPU devices per node. The effective use of shared memory is important for improving the performance on GPUs, because of the bandwidth limitation of the global memory. The best known sequential algorithm for multidimensional numerical integration CUHRE uses a large dynamic heap data structure which is accessed frequently. Devising a GPU algorithm that caches a part of this data structure in the shared memory so as to minimizes global memory access is a challenging task. The algorithm presented here addresses this problem. Furthermore we propose a technique to scale this algorithm to multiple GPU devices. The algorithm was implemented on a cluster of Intel^® Xeon^® CPU X5650 compute nodes with 4 Tesla M2090 GPU devices per node. We observed a speedup of up to 240 on a single GPU device as compared to a speedup of 70 when memory optimization was not used. On a cluster of 6 nodes (24 GPU devices) we were able to obtain a speedup of up to 3250. All speedups here are with reference to the sequential implementation running on the compute node.