![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.](https://image.slidesharecdn.com/pythonproject-160601064347/85/Python-project-5-320.jpg)
![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];
}](https://image.slidesharecdn.com/pythonproject-160601064347/85/Python-project-6-320.jpg)
Python project
- 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