# N-body simulation

Project of Parallel and Concurrent Programming on the Cloud course. Professor: Vittorio Scarano

### Problem statement

In an n-body problem, we need to find the positions and velocities of a collection of interacting particles over a period of time. For example, an astrophysicist might want to know the positions and velocities of a collection of stars, while a chemist might want to know the positions and velocities of a collection of molecules or atoms. An n-body solver is a program that finds the solution to an n-body problem by simulating the behavior of the particles. The input to the problem is the mass, position, and velocity of each particle at the start of the simulation, and the output is typically the position and velocity of each particle at a sequence of user-specified times, or simply the position and velocity of each particle at the end of a user-specified time period.

The problem is described here.

### N^2 Solution

Consider only the solution that is quadratic in the number of particles.

nbody.c

### Benchmarking

1) Provide a solution to the problem exploiting parallel computation and develop a C program using MPI. The provided implementation can use either Point-to-Point communication or Collective communication routines. 2) Benchmark the solution on Amazon AWS (EC2) on General Purpose instances (e.g. M3.medium family) or on Compute optimize instances (e.g. C3.large family). Testing the solution using 1, 2, 3, 4, 5, 6, 7, 8 instances. 3) Both weak and strong scalability have to be analyzed:

• Strong Scaling: Keeping the problem size fixed and pushing in more workers or processors. Goal: Minimize time to solution for a given problem.
• Weak Scaling: Keeping the work per worker fixed and adding more workers/processors (the overall problem size increases). Goal: solve the larger problems.
###### HINT

1) The results should be presented as two different scatter x-y charts, where the x-axis denotes the number of MPI processors used and the y-axis value represents the time in milliseconds.
2) The number of MPI processors should be equal to the number of cores.

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