This document describes a Python project to simulate heat transfer in a room with four walls and a fireplace using the Jacobi iteration method. The members are Young Song, Hung Lay, and Caleb Jang. It outlines approaching the problem by modeling the room as a grid, initializing air temperatures to 0°C, walls to 20°C and the fireplace to 100°C. It then discusses using sequential and parallel Jacobi iteration to calculate air temperatures over iterations and plotting the results as temperature contours at 10°C intervals. Sample output shows the temperature grid converging towards the boundary conditions over iterations.

1. Python Project
Members: Young Song, Hung Lay, Caleb Jang

2. Problem
• A room has four walls and a fireplace. Temperature of wall is 20°C, and
temperature of fireplace is 100°C. Write a parallel program using Jacobi
iteration to compute the temperature inside the room and plot (preferably in
color) temperature contours at 10°C intervals using Xlib calls or similar
graphics calls as available on your system.

3. Approach

4. Approach
• Known: Fire: 100 C, Wall: 20 C
• Unknown: Air: ?
• Initial Air: 0 C

5. Initial Matrix
[20 20 100 20 20]
[20 0 0 0 20]
[20 0 0 0 20]
[20 0 0 0 20]
[20 20 20 20 20]
The temperature of air which is initially set 0
increases during iterations.

6. Sequential Code
• Using a fixed number of iterations
for (iteration = 0; iteration < limit; iteration++)
{ for (i = 1; i < n; i++)
for (j = 1; j < n; j++) g[i][j] = 0.25*(h[i-1][j]+h[i+1][j]+h[i][j-1]+h[i][j+1]);
for (i = 1; i < n; i++) /* update points */
for (j = 1; j < n; j++) h[i][j] = g[i][j];
}

7. Parallel Methods
Split the fixed amount of iterations into process using Partitioning.
Start =0
RNG = iterations/num of process
Process 1: Start to Start+RNG, then Start = Start+RNG
Process 2: Start to Start+RNG, then Start = Start+RNG
Process 3: Start to Start+RNG, then Start = Start+RNG
.
.
.

8. Code Result

9. Graphical Result for Ideal Result

10. Graph from real tables
20 20 20 20 100 100 20 20 20 20
20 22.3 26.05 34.63 58.90 58.90 34.63 26.05 22.3 20
20 23.14 27.27 33.56 42.08 42.08 33.56 27.27 23.14 20
20 22.98 26.35 30.25 33.78 33.78 30.25 26.35 22.98 20
20 22.42 24.90 27.30 29.02 29.02 27.30 24.90 22.42 20
20 21.8 23.53 25.04 25.98 25.98 25.04 23.53 21.8 20
20 21.24 22.40 23.34 23.88 23.88 23.34 22.40 21.24 20
20 20.77 21.47 22.02 22.34 22.34 22.02 21.47 20.77 20
20 20.37 20.70 20.95 21.20 21.20 20.95 20.70 20.37 20
20 20 20 20 20 20 20 20 20 20