Table 2 Runtime diagnostics for the parallelization of phew when various numbers of MPI tasks are used. \(\pmb{N_{\mathrm{active}}}\) and \(\pmb{N_{\mathrm{ghost}}}\) are the number of active peaks and ghost peaks respectively and \(\pmb{N_{\mathrm{tot}}=N_{\mathrm{active}}+N_{\mathrm{ghost}}}\) denotes the total number of peaks per MPI task. \(\pmb{N_{\mathrm{sparse}}}\) is the number of entries in the sparse saddle matrix and \(\pmb{N_{\mathrm{collisions}}}\) gives the number of hash table collisions. Sums, maxima and averages are taken over the all MPI tasks

Load imbalance \((\frac{\max\{ N_{\mathrm{tot}} \}}{ \mathrm{avg} \{ N_{\mathrm{tot}}\}} )\)

1.4

1.5

1.8

2.4

2.8

3.3

3.9

Surface effect \((\frac{\sum N_{\mathrm{ghost}}}{\sum N_{\mathrm{active}}} )\)

0.0087

0.012

0.016

0.021

0.030

0.040

0.055

Connectivity \((\frac{\sum N_{\mathrm{sparse}}}{\sum N_{\mathrm{tot}}} )\)

9.4

9.4

9.4

9.3

9.3

9.3

9.2

\(\max \{ \frac{N_{\mathrm{ghost}}}{N_{\mathrm{active}}} \}\)

0.012

0.017

0.044

0.064

0.10

0.15

0.24

\(\max\{N_{\mathrm{tot}}\}\)

3.0 × 10⁵

1.6 × 10⁵

9.6 × 10⁴

6.4 × 10⁴

3.8 × 10⁴

2.2 × 10⁴

1.3 × 10⁴

\(\max\{N_{\mathrm{sparse}}\}\)

3.3 × 10⁶

1.8 × 10⁶

1.2 × 10⁶

8.7 × 10⁵

6.3 × 10⁵

4.7 × 10⁵

3.0 × 10⁵

\(\max\{N_{\mathrm{collisions}}\}\)

4

3

2

3

16

17

13