## 3 Results and Discussion
### Parallel Solution  
A DO loop of the _User_ method in the previous section (Figure 5) consists of the calls that are independent. Therefore, this loop can be effectively parallelized (Figure 7)--the parallel user finite forward difference (_Parallel_) method. In this case, Open MP is employed in order to parallelize the subroutine coded in the Fortran programming language. The _Parallel_ method was used in the same MBD simulation of the piston-liner interaction with reduced number of flexible piston mode shapes. Table 2 presents the results. As expected, the maximum CPU utilization increased, in this case, from 18.5 to 46.5%. This resulted in an acceleration of the computation time from 25 min and 10.4 s to 17 min and 38.7 s (acceleration 1.43 times). The use of the _Parallel_ method required 5.51% more iterations compared to the _Default_ method, the results of which are presented in Table 1. These results show that the _Parallel_ method significantly accelerated the simulation, even if only a low number of the flexible body mode shapes were used. The larger the number of the mode shapes included, the greater the acceleration of the parallel solution. Until now, the parallel solution to the sensitivity analysis of the subroutine has only been applied to a simplified analysis with a flexible body with 20 mode shapes. To properly include elastic deformation of the bearing surface, all nodes on that surface should be the boundary nodes in the component mode synthesis. If each boundary node has three degrees of freedom in the finite element model, the number of degrees of freedom in the MBD simulation is increased by three times the number of boundary nodes. Fortunately, the dominant load of a journal bearing is radial, meaning that only the radial degree of freedom of each boundary node of the computational grid can be excluded from the modal \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Default** & **User** \\ \hline Maximum CPU usage (\%) & 18.5 & 18.0 \\ Elapsed time (MM:SS) & 25:10.4 & 25:20.2 \\ Simulation time acceleration (-) & 1 & 0.99 \\ Iteration count (-) & 7877 & 8311 \\ Iteration count increase (\%) & 0 & 5.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Computational speed of the simulation using the _Default_ and with the _User_ method for a reduced number of mode shapes. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Parallel** \\ \hline Maximum CPU usage (\%) & 46.5 \\ Elapsed time (MM:SS) & 17:38.7 \\ Simulation time acceleration (-) & 1.43 \\ Iteration count (-) & 8311 \\ Iteration count increase (\%) & 5.51 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Computational speed of the simulation with the _Parallel_ method for a reduced number of mode shapes. Figure 7: Scheme of _Parallel_ user finite forward difference method, illustrating the parallelization of the sensitivity analysis of the subroutine for deformation-related measurements. superposition during the modal neutral file creation. This leads to a significant reduction in the number of degrees of freedom in the MBD model. However, there are still many boundary nodes on the bearing surfaces that significantly increase computational time. In the demonstrative case of this paper, the MBD model of the piston-liner interaction consisted of a box-type flexible piston with two piston skirts, each containing 29 circumferential and 17 axial nodes. This led to an increase in the mode shape count by 986. The subroutine had measurements related to the modal coordinate as per each mode shape as well as the time derivative of the modal coordinates. Therefore, the parallel DO loop for the _Parallel_ method ran 1972 times. In each of these runs, the iterative solution of hydrodynamics is computed. Therefore, the parallel solution should rapidly decrease the computational time. To confirm these assumptions, two MBD simulations were computed, and both used all 992 piston mode shapes enabled. The first simulation utilized the _Default_ method.