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https://github.com/ghonimo/heat-diffusion-grid-simulation-using-mpi-ece588

This repository contains the code and documentation for a parallelized heat diffusion simulator implemented using the Message Passing Interface (MPI). It simulates the diffusion of heat across a 2D grid, using a finite difference method to calculate temperature changes over time. This program was designed for Portland State University ECE 588 Class
https://github.com/ghonimo/heat-diffusion-grid-simulation-using-mpi-ece588

c heatmap mpi mpi-applications mpich parallel-computing parallel-programming perl portland-state-university

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This repository contains the code and documentation for a parallelized heat diffusion simulator implemented using the Message Passing Interface (MPI). It simulates the diffusion of heat across a 2D grid, using a finite difference method to calculate temperature changes over time. This program was designed for Portland State University ECE 588 Class

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README 

        
# 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:



```bash

mpicc -o HW4_1 HW4_1.c

```



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



```bash

mpirun -np  ./HW4_1

```

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



```bash

./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.