Python project
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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.
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1) The Jacobi Project team uses Jacobi iteration to compute the temperature inside a room with four walls at 20°C and a fireplace at 100°C.
2) They implement the Jacobi iteration method in both sequential and parallel (using MPI) versions to solve the heat diffusion equation.
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The document contains examples of evaluating functions for different values of the variable. It provides the functions and steps to solve for:
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- 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.
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- 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.
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- 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