# Evaluation of Parallel Computing on MPI Version PHITS Code
## 3 Results  
### Computational Simulation Evaluation  
In order to compare with the measured values, \(10^{9}\) calculations were performed at depths of 15 mm, 50 mm, 100 mm, and 200 mm of 1 m\({}^{3}\) water implemented based on PNNL data (relative error \(\leq\) 0.05). In the case of the beam profile at field size 4 cm \(\times\) 4 cm, the results showed values within the presented reference range except for \(\delta_{2}\). In particular, if we look at each part of the profile, and the result of \(\delta_{3}\) showed a result of minimum 0.2% (200 mm, cross-plane) and of maximum 1.2% (50 mm, in-plane and cross-plane). Other cases were also within the reference range of 2%, but for \(\delta_{2}\), which is value for the build-up section or the relatively high-dose and high-gradient part, it showed a maximum of 34.8% (50 mm, in-plane) and minimum value of 6.1% (200 mm, in-plane). Those values are significantly exceeding the threshold of 3%. The data for relatively low-dose, low-slope area of the beam profile showed a maximum of 22.5% (15 mm, cross-plane) and a minimum of 4.7% (200 mm, in-plane). Evaluated data from the low-dose, low-slope region seem excessive but are still acceptable because this region's criterion is 30%. Compared to the previous two results, the evaluation value for beam fringe, \(\delta_{50-90}\), was within the reference range in a stable manner (Table 2). For the other case, of 10 cm \(\times\) 10 cm field size, the results showed the same tendency, but the details are slightly different. For example, the result of \(\delta_{3}\) showed a result of minimum 0.5% (15 mm, in-plane and 200 mm, cross-plane) and of maximum 0.9% (50 mm, in-plane and cross-plane). Other cases were also within 1%. Those values are much smaller than the reference range of 2%, but \(\delta_{2}\) value showed a maximum of 22.3% (15 mm, in-plane) and a minimum value of 5.3% (200 mm, cross-plane). Those are also exceeding the reference value of 3%. Evaluated values for \(\delta_{4}\) showed a maximum of 30.1% (15 mm, cross-plane) and a minimum of 4.6% (100 mm, cross-plane). In contrast to the in-plane data, the reference value has slightly been exceeded while showing a large value in all depth measurements. Regarding data for the beam fringe, \(\delta_{50-90}\) also showed stable results, from 1 mm to 2 mm of being included in the criterion (Table 3). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{3}{c}{**In-Plane**} & \multicolumn{3}{c}{**Cross-Plane**} & \multirow{2}{*}{**Reference Value**} \\ \cline{2-2} \cline{4-9}  & **15 mm** & **50 mm** & **100 mm** & **200 mm** & **15 mm** & **50 mm** & **100 mm** & **200 mm** \\ \hline \(\delta_{2}\) & 22.3\% & 34.8\% & 7.3\% & 6.1\% & 10.4\% & 17.4\% & 28.9\% & 26.5\% & 3\% \\ \(\delta_{3}\) & 0.5\% & 1.2\% & 0.3\% & 0.5\% & 0.4\% & 1.2\% & 0.7\% & 0.2\% & 2\% \\ \(\delta_{50-90}\) & 2 mm & 2 mm & 1 mm & 1 mm & 2 mm & 1 mm & 1 mm & 1 mm & 2 mm \\ \(\delta_{4}\) & 15.1\% & 23.3\% & 7.3\% & 4.7\% & 22.5\% & 13.1\% & 10.3\% & 11.2\% & 30\% \\ \hline \end{tabular}
\end{table} 
Table 2: Beam profile analysis of measured and simulated values for Varian Clinac 6 MV: Data of 4 cm \(\times\) 4 cm field size were analyzed at 15 mm, 50 mm, 100 mm, and 200 mm depths. Each part of beam profile was analyzed in order of \(\delta_{2}\), \(\delta_{3}\), \(\delta_{50-90}\), \(\delta_{4}\). All values were within criterion, except for \(\delta_{2}\), which represents high dose and high gradient. Figure 4 shows the beam profile comparison between measured data and simulated data by PHITS. The in-plane profile of both field sizes have been sorted in the order of 15 mm, 50 mm, 100 mm, and 200 mm. A constant magnification was implied for convenience to facilitate checking a lot of data at once. Magnification constant: 1, 0.8, 0.6, 0.4 for 15 mm, 50 mm, 100 mm, and 200 mm, respectively. Figure 5 shows the cross-plane profile of both calculated and measured data has also been sorted in order of 15 mm, 50 mm, 100 mm, and 200 mm.