N Body distributed simulation

This project consists of two main parts: a simulation program (calcul.cpp) and a visualization program (visualisation.cpp). The simulation program calculates the positions of bodies in a gravitational field and writes the results to a CSV file. The visualization program reads the CSV file and displays the positions of the bodies.

Speedup

The following table shows the speedup achieved by parallelizing the simulation program using MPI. The simulation was run on a cluster of 18 nodes, each with Intel I9-10900k 10 cores @3.70GHz processors for a total of 180 cores.

Number of bodies	Number of steps	Number of cores	Time
10000	300	1	834,45s
10000	300	10	86,61s
10000	300	20	54,96s
10000	300	180	24,1s

Prerequisites

• C++ compiler (supporting C++11)
• MPI (Message Passing Interface) for parallel computing
• OpenGL, GLUT libraries for visualization
• CMake (version 3.26 or higher)

Compilation and Execution

Simulation Program

The simulation program is parallelized using MPI and can be compiled and run using the mpicxx compiler and mpiexec command.

To compile the program, navigate to the directory containing calcul.cpp and run the following command:

mpicxx -std=c++11 -o nbody_simulation calcul.cpp

This will create an executable named nbody_simulation.

To run the program, use the mpiexec command. The -hostfile option specifies the file containing the host list. The program takes two arguments: the total number of bodies and the number of steps to simulate. For example, to simulate 5000 bodies for 500 steps, run:

mpiexec -hostfile <file path> ./nbody_simulation 5000 500

This will create a CSV file named nbody_simulation.csv in the data directory.

Visualization Program

The visualization program uses OpenGL and GLUT for graphics. It can be compiled using CMake.

First, navigate to the project root directory and create a new directory for the build:

mkdir build
cd build

Then, run CMake to generate the Makefile:

cmake ..

Next, compile the program using the generated Makefile:

make

This will create an executable named Projet_Systemes_Distribues_visualisation.

To run the visualization program for 5000 bodies and 500 steps, simply execute the following command:

./Projet_Systemes_Distribues_visualisation 5000 500

This will open a window displaying the positions of the bodies as calculated by the simulation program.