from GPU to CPU.

![image](fig/kernel.png){width="99.00000%"}

Performance and Scalability {#sec:results}
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The performance of the GPU-accelerated ELPA2 solver is benchmarked on the Talos cluster at Max Planck Computing and Data Facility and the Summit supercomputer at Oak Ridge National Laboratory. Each node of Talos has 2 Intel Xeon Gold 6148 CPUs (40 cores in total) and 2 NVIDIA Tesla Volta V100 (each has 32 GB high-bandwidth memory, double precision peak 7.0 TFLOP/s, PCIe 32 GB/s interconnect) GPUs. Benchmarks presented in Fig. \[fig:all\_talos\] are performed on Talos. The ELPA code is compiled with the Intel 19.0.5 compiler suite, Intel MPI 2019.5, Intel MKL 2019.5, and CUDA 10.1. Each node of Summit has 2 IBM POWER9 CPUs (44 cores in total, of which 42 are for running applications) and 6 NVIDIA Tesla Volta V100 (each has 16 GB high-bandwidth memory, double precision peak 7.8 TFLOP/s, NVLink 300 GB/s interconnect) GPUs. Benchmarks presented in Figs. \[fig:all\_summit\], \[fig:decomp3\_summit\], \[fig:decomp5\_summit\] are performed on Summit. The ELPA code is compiled with the IBM XL 16.1.1 compiler suite, IBM Spectrum MPI 10.3, IBM ESSL 6.1, and CUDA 10.1.

Fig. \[fig:all\_talos\] shows the total time to solution of CPU-ELPA1, CPU-ELPA2, GPU-ELPA1, and GPU-ELPA2 on the Talos cluster. All eigenvalues 