Adapting irregular computations to large CPU-GPU clusters in the MADNESS framework

Graphics Processing Units (GPUs) are becoming the workhorse of scalable computations. MADNESS is a scientific framework used especially for computational chemistry. Most MADNESS applications use operators that involve many small tensor computations, resulting in a less regular organization of computations on GPUs. A single GPU kernel may have to multiply by hundreds of small square matrices (with fixed dimension ranging from 10 to 28). We demonstrate a scalable CPU-GPU implementation of the MADNESS framework over a 500-node partition on the Titan supercomputer. For this hybrid CPU-GPU implementation, we observe up to a 2.3-times speedup compared to an equivalent CPU-only implementation with 16 cores per node. For smaller matrices, we demonstrate a speedup of 2.2-times by using a custom CUDA kernel rather than a cuBLAS-based kernel.