Heat Distribution Simulation using MPI

This repository contains a C program designed to simulate heat distribution across a 2D grid. The simulation is parallelized using the Message Passing Interface (MPI) to enhance performance and demonstrate the application of distributed computing in computational physics problems.

Problem Description

The program models the temporal evolution of heat distribution on a 2D grid, representing a simplified scenario of heat conduction in a square plate. The simulation uses a finite difference method to approximate the heat equation, with specific initial and boundary conditions.

Initial and Boundary Conditions

• Grid Size: The computational domain is a 2D grid of size 1000 x 1000 points.
• Initial Temperature Distribution:
  • All points within the central region defined by coordinates (200, 200) to (800, 800) are initialized to 500 degrees.
  • The temperature of all other points is set to zero.
• Boundary Conditions: Points on the boundary of the grid maintain a constant temperature of zero throughout the simulation.

Simulation Parameters

T(x,y)(t) = T(x,y)(t-1) + Cx * (T(x+1,y)(t-1) + T(x-1,y)(t-1) – 2 * T(x,y)(t-1)) + Cy * (T(x,y+1)(t-1) + T(x,y-1)(t-1) – 2 * T(x,y)(t-1))

Where Cx and Cy are constants that govern the rate of heat transfer along the x and y axes, respectively.

• Time Steps: The simulation progresses through 4000 time steps.
• Reporting: After every 200 time steps, the program prints the temperatures at specific grid points: (1, 1), (150,150), (400, 400), (500, 500), (750, 750), and (900,900).

Implementation Details

The program is implemented in C and utilizes MPI to distribute the computation across multiple processors within a distributed memory system, aiming for a high degree of parallel speedup. The domain is divided among the MPI processes, each responsible for a portion of the grid. MPI collectives and point-to-point communication are used to synchronize boundary conditions and gather results.

Building and Running

To compile the program with MPI, use:

mpicc -o HW4_1 HW4_1.c

To run the compiled binary across a specific number of processes:

mpirun -np <num_processes> ./HW4_1

To run in batch more, comparing the performance of with different cores, you can execute the perl script below:

./automate/batch_run.pl

Output

The program outputs the temperatures of specified grid points after every 200 timesteps and displays the total runtime in nanoseconds and seconds.

License

This project is open-sourced under the MIT License.