on Talos. Overall, we therefore observe that the absolute per-node timings of CPU-ELPA2 in Figs. \[fig:all\_talos\] and \[fig:all\_summit\] are already lower on Talos than on Summit. This difference in the CPU-only results, which are the baseline of the reported speedups, probably exaggerates the comparison of GPU-ELPA2 and CPU-ELPA2 on Summit somewhat, relative to Talos. Nevertheless, the three trends summarized from the tests on Talos are still valid on Summit, that is, the GPU speedup is larger for (1) larger matrix size, (2) fewer nodes, and (3) solving a complex problem instead of a real one. On both computers, the strong scaling of the GPU solvers is never as good as that of the CPU solvers. This can be explained by the workload assigned to the individual nodes. When using a large number of nodes or solving a small matrix, the workload on each node becomes so little that the many GPUs cannot be saturated, and the cost of CPU-GPU communications cannot be amortized. In contrast, when solving a large matrix or using a small number of nodes, a large amount of local work is offloaded to the GPUs, resulting in a significant speedup.

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

Note that in Figs. \[fig:all\_talos\] and 