稠密对称和厄米特特征值问题ELPA2分布式特征值求解器的GPU加速
GPU-Acceleration of the ELPA2 Distributed Eigensolver for Dense Symmetric and Hermitian Eigenproblems
摘要：
本征值问题的求解通常是一个关键的计算瓶颈，它限制了数值算法的易处理系统规模，其中包括化学和凝聚态物理中的电子结构理论。大型特征值问题很容易超过单个计算节点的计算能力，因此必须在分布式存储并行计算机上求解。在这里，我们提出了面向GPU优化的ELPA两阶段三对角化特征值求解器（ELPA 2）。在基于cubLAS的GPU卸载之上，我们添加了一个CUDA内核来加速特征向量的反变换，这可能是两阶段三对角化算法中计算成本最高的部分。我们在两种混合CPU-GPU架构上对该GPU加速的特征值求解器的性能进行了基准测试，即基于Intel Xeon Gold CPU和NVIDIA Volta GPU的计算集群，以及基于IBM POWER 9 CPU和NVIDIA Volta GPU的Summit超级计算机。与以前的基准测试CPU的架构，GPU加速的两阶段求解器表现出优于一个阶段的对应并行性能。最后，我们展示了性能的GPU加速本征求解器在这项工作中开发的常规半本地KS-DFT计算，包括数千个原子。
英文摘要：
The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. We benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU-GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.
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