PhysicalDot-DistributedSimulation

Solving a system of ordinary differential equations

Setting the task

Given $N$ material points with masses $m_k$, whose positions at the initial moment of time are given by radius vectors $r_k$, and velocities by vectors $v_k$, $k = \overline{1, N}$. It is required to determine the trajectories of all particles at all time points from $0$ to $t_{end}$.

Input format

The program is given a file with the masses, initial coordinates and velocities of all material points. The first line of the file consists of a single number n — the number of dots.

Output format

A csv file, each line of which has the following format:

The equation that needs to be solved

Iterative formulas for solving each equation

Computer configuration

• CPU: Intel(R) Core(TM) i5-10400F CPU @ 2.90GHz 2.90 GHz. | Cores: 6 | Hyper Threading
• RAM: 32.0 GB
• OS: Ubuntu 22.04.3 LTS

Received solutions

Several solutions have been obtained iterative , parallel with threads reassignment , parallel without threads reassignment Visualization was also created, studies of the speed of execution of various solutions were conducted and numerical characteristics were measured, such as acceleration and efficiency.

Visualization

vis_output20.mp4

Metrics investigation

Computation time

Speed Up

Efficiency

Conclusions on working with multithreading

• The minimum execution time is achieved with the largest number of program threads;
• Threads, the number of which is many times higher than the number of processor cores, make a minimal contribution to the acceleration of calculations;
• For a large number of threads, there is an obvious overhead in time;
• Hyper Threading technology allows you to increase computing performance by 33% (with 12 active system threads instead of 6);
• After a certain threshold, the efficiency remains unchanged as the amount of data increases.