Simulations, Data Analysis and Algorithms

# Table 2 Runtime diagnostics for the parallelization ofphewwhen 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

$$\boldsymbol {N}_{\mathbf{tasks}}$$ 32 64 128 256 512 1,024 2,048
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