# Evaluation of Parallel Computing on MPI Version PHITS Code
## 3 Results
### MPI Performance Evaluation  
#### 3.2.1 Individual Node and Three Processor Clusters  
Simulation results on 30,000 bch were 6.35 \(\pm\) 0.09, 5.97 \(\pm\) 0.2, 6.14 \(\pm\) 0.13 for Node 1, Node 2, Node 3, respectively. When this bch was set as \"30\", required average CPU times were 6.0 \(\pm\) 0.04, 5.61 \(\pm\) 0.03, 5.79 \(\pm\) 0.02. From this relationship, it seems that as  
\begin{table}
\begin{tabular}{c c c c} \hline  & **4 cm \(\times\) 4 cm** & **10 cm \(\times\) 10 cm** & **Reference Value** \\ \hline \(\delta_{1}\) & 2.0\% & 1.1\% & 2\% \\ \(\delta_{2}\) & 2 mm & 0 mm & 2 mm \\ \hline \end{tabular}
\end{table}
Table 4: PDD evaluation of measured and simulated values for Varian Clinac 6 MV: It was evaluated by dividing by field size (4 cm \(\times\) 4 cm, 10 cm \(\times\) 10 cm). For \(\delta_{1}\), which represents fall-off region after build-up area, both field sizes were within the criterion. Additionally, discrepancy of build-up region, \(\delta_{2}\), was 2 mm and 0 mm, respectively.  
Figure 5: Superimposed beam profiles of measured and simulated values for Varian Clinac 6 MV: the cross-plane was evaluated by dividing by field size at 15 mm, 50 mm, 100 mm, and 200 mm depth (4 cm \(\times\) 4 cm, 10 cm \(\times\) 10 cm).  
bch decreases, those required times tend to decrease. Individual node performance was evaluated in the order of Node 2, Node 3, and Node 1 in all cases of bch and showed the maximum and minimum differences at 6.3% for 300 bch and 2.4% for 30,000 bch (Table 5, Figure 7).  
On the other hand, the result obtained by a cluster consisting of each node and the same number of processors was 3.63 \(\pm\) 0.02, 3.6 \(\pm\) 0.01, 3.68 \(\pm\) 0.02, 3.72 \(\pm\) 0.02 in order of 30 bch, 300 bch, 3000 bch, 30,000 bch, respectively. There is a similar tendency to the case of Table 5, except the result of 30 bch is listed in Table 6 (it showed slightly increased outcome compared with 300 bch). However, those results showed a performance increase of up to 70.6% (30,000 bch, comparison result with Node 1) and at least 54.5% (30 bch, comparison result with Node 2) (Table 6).  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**No. of Processor** & \multicolumn{2}{c}{**30 bch**} & \multicolumn{2}{c}{**300 bch**} & \multicolumn{2}{c}{**3000 bch**} & \multicolumn{2}{c}{**30,000 bch**} \\ \hline \multirow{2}{*}{3} & Avg & S.D & Avg & S.D & Avg & S.D & Avg & S.D \\  & 3.63 & 0.02 & 3.6 & 0.01 & 3.68 & 0.02 & 3.72 & 0.02 \\ \hline \hline \end{tabular}
\end{table}
Table 6: CPU time (h) of a cluster consisting of three processors. In order to exclude the effect due to the difference in node performance, one processor was mobilized from each node. The results obtained by repeating the same simulation five times, as in the individual node evaluation, were averaged. Avg means the average value at this time, and SD means the standard deviation of the measured values.  
Figure 6: Superimposed measured and simulated PDD values for Varian Clinac 6 MV: It was evaluated by dividing by field size (4 cm \(\times\) 4 cm, 10 cm \(\times\) 10 cm).  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \multicolumn{2}{c}{**Node 1**} & \multicolumn{2}{c}{**Node 2**} & \multicolumn{2}{c}{**Node 3**} \\ \cline{2-6}
**No. of bch** & **Avg** & **S.D** & **Avg** & **S.D** & **Avg** & **S.D** \\ \hline
30 bch & 6.0 & 0.04 & 5.61 & 0.03 & 5.79 & 0.02 \\
300 bch & 6.01 & 0.03 & 5.63 & 0.05 & 5.81 & 0.03 \\
3000 bch & 6.17 & 0.18 & 5.93 & 0.04 & 6.08 & 0.02 \\
30,000 bch & 6.35 & 0.09 & 5.97 & 0.2 & 6.14 & 0.13 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Prior to cluster evaluation, calculations were performed with three processors each to compare individual node performance. Node CPU time (h) is the average of the results of repeating the same operation five times. Avg is the average value at this time, and SD is the standard deviation of the measured value.