# Evaluation of Parallel Computing on MPI Version PHITS Code
## 4 Discussion  
The phsp data provided by the IAEA showed results that matched well with actual measured values. However, in the high-dose, high-gradient part, the results were significantly higher than the reference value. Considering that there is no notable difference in the comparison graph of the measured and simulated values according to the location of the ionization chamber, this may be due to the relatively short corresponding part with little comparison data, and minute differences in factors cause rapid changes. This presented result in this study is similar to those by [PERSON] et al. [7]. Referring to their research, large differences in out-of-field region (\(\delta_{2}\), \(\delta_{4}\) in our study) are unavoidable because of lower radiation dose and larger uncertainties in the calculated data. Other results presented by [PERSON] et al. showed similar results compared to ours. In their study, there is almost a 60% difference at the out-of-field regions but differences of 2% and 2 mm at the plateau region [6]. In consideration that the abovementioned study was conducted for the modeling of a linear accelerator, our results are acceptable as well. Nevertheless, in order to obtain a reliable dose distribution through phsp data in the future, we suggest that a careful consideration or work to supplement this discrepancy is necessary (Figures 4-6). It was confirmed that there is a difference in simulation performance even if the performance of the node, which could be checked primarily, such as GHz and RAM size, was nearly same [13]. This was one of the factors that delayed the overall required time, as it was necessary to wait for the calculation results of nodes with poor performance in the process of collecting the results after distributing them by bch. So, for more effective cluster operations, it may be necessary to configure it by evaluating the performance of each node in advance. Figure 8: Speedup factor increase trend according to bch change: the average value of five average CPU times required to perform \(3\times 10^{8}\) iterations of the computational simulation for the PDD in the 10 cm \(\times\) 10 cm field size was analyzed. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **30 bch** & **300 bch** & **3000 bch** & **30,000 bch** \\ \hline K-Factor & 0.258 & 0.259 & 0.313 & 0.402 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: K-factor. Because it is a part where parallel processing such as data communication and collection is impossible in the configured cluster, it has been calculated using the least squares method. Additionally, there is another trend among bch that might affect the simulation time founded on our study. This tendency was clearly observed in Figure 4. Every bch is reduced by 1/10, which is equal to \"calculation per bch\" increased by ten times, and required average CPU time was also decreased. At the same time, results from the speedup factor indicated similar trend. Increments of the speedup factor value are becoming greater when bch decreases. For more detailed analysis, the comparison between 30 bch and 30,000 bch has been notable. There are similar tendencies with results of Tables 5 and 6. The increments of the speedup factor from 30,000 bch to 30 bch showed the largest increase. (300 bch with 12 processors shows highest result as 2.29, but in consideration of standard deviation, there is some uncertainty). Additionally, this trend has been observed throughout all data. Those trends give an indication that result collection process after each bch is much more influenced by simulation time than was our expectation. Again, from the results of the speedup factor according to bch, it can be inferred that, as the number of calculations per bch increases, the fraction of time used for data processing and transmission/reception through the network decreases among the total required time.