Lawrence Berkeley National Laboratory

Achieving high performance and performance portability for large-scale scientific applications is a major challenge on heterogeneous computing systems such as many-core CPUs and accelerators like GPUs. In this work, we implement a widely used block eigensolver, Locally Optimal Block Preconditioned Conjugate Gradient (LOBPCG), using two popular directive based programming models (OpenMP and OpenACC) for GPU-accelerated systems. Our work differs from existing work in that it adopts a holistic approach that optimizes the full solver performance rather than narrowing the problem into small kernels (e.g., SpMM, SpMV). Our LOPBCG GPU implementation achieves a 2.8$${\times }$$–4.3$${\times }$$ speedup over an optimized CPU implementation when tested with four different input matrices. The evaluated configuration compared one Skylake CPU to one Skylake CPU and one NVIDIA V100 GPU. Our OpenMP and OpenACC LOBPCG GPU implementations gave nearly identical performance. We also consider how to create an efficient LOBPCG solver that can solve problems larger than GPU memory capacity. To this end, we create microbenchmarks representing the two dominant kernels (inner product and SpMM kernel) in LOBPCG and then evaluate performance when using two different programming approaches: tiling the kernels, and using Unified Memory with the original kernels. Our tiled SpMM implementation achieves a 2.9$${\times }$$ and 48.2$${\times }$$ speedup over the Unified Memory implementation on supercomputers with PCIe Gen3 and NVLink 2.0 CPU to GPU interconnects, respectively.