# Evaluation of Parallel Computing on MPI Version PHITS Code
## 1 Introduction  
The Monte Carlo method has been utilized to evaluate the dose distribution of complex structures by simulating radiation behavior, and numerous codes have been developed for a variety of applications [1; 2; 3; 4]. The Particle and Heavy Ion Transport Code System (PHITS), recently developed in Japan, offers a variety of functions such as Digital Imaging and Communications in Medicine (DICOM) format file and International Atomic Energy Agency (IAEA) phase space (phsp) data file to PHITS input file convert system as well as a research- or practice-friendly environments, such as radiation therapy research and shielding design [5].  
Indeed, there are several efforts for the modeling of linear accelerator (Linac) to assess in-and-out-of-field dose distribution or radiation behavior. Other searches present it as feasible, with exact blueprints provided from those machines' manufacturers and complicated sequences to derive Linac head. To overcome these problems, IAEA provide a phsp data base which is defined as a collection of representative pseudo-particles emerging from a radiotherapy source, including radioisotope and the enormous type of Linac beam data, along with those particles' properties such as energy, particle type, position, direction, statistical weight, etc. Unfortunately, this data base is not able to use some MCNP codes. In PHITS, the user is able to utilize it through the tools of PSFC4 PHITS, as mentioned before [6; 7; 8].  
However, this also requires a large number of iterative calculations to obtain reliable results, and it is difficult for users with insufficient computing infrastructure to quickly evaluate and provide feedback [9]. While various methods have been proposed andused to solve this problem [10; 11; 12], there is a burden in some cases, such as writing a parallel processing algorithm in Python [13; 14]. On the other hand, the parallel computing method utilizing the Message Passing Interface (hereafter referred to as MPI) is the most fundamental method and was introduced at the outset of performance enhancement efforts for the MCNP. This method is a fundamental technique for achieving an increase in computing power proportional to the number of processors utilized for computations [15].  
In a study by [PERSON] et al. (1996), the results of parallel computing of MCNP code using MPI depended on the number of processors and [PERSON]'s law, which converged to a constant value due to the limitation that parallel processing could not be performed, was applied to these results [15]. [PERSON] (1998) evaluated the performance improvement of parallel computing using MPI, a parallel virtual machine (PVM) based on MCNP, reporting that the method using MPI was more efficient and confirming that the degree of performance improvement in the method using MPI increased linearly with an error of up to 5% for up to 32 processors and an error of 13% when using 64 processors [16]. [PERSON] et al. evaluated the results of MCNP parallel computing with MPI based on the number of processors and provided recommendations for the number of efficient processors required based on the amount of work [17].  
As shown in the previous research, studies on the efficiency of the Monte Carlo method using MPI have mainly been conducted with a focus on the MCNP code, with a scarcity of research results on the relatively recently developed PHITS code. For the abovementioned reasons, this study was conducted to verify IAEA phase space data converted to source input file through the PSFC4 PHITS tool in the PHITS code package and evaluate the efficiency of the cluster system based on [PERSON]'s law.