salastro / ETD-LA

Equilibrium Temperature Distributions using Linear Algebra

Equilibrium Temperature Distributions using Linear Algebra in Python

Overview

This Python project focuses on solving equilibrium temperature distributions on a 2D grid using linear algebraic techniques, specifically Jacobi iteration and matrix inversion. The project is structured into several modules to enhance readability, modularity, and ease of understanding.

Project Structure

1. main.py

• The main script orchestrates the execution of the project. It sets up problem parameters, such as grid size and boundary temperatures, and then calls the solve_temperature_equation function. Finally, it visualizes the temperature distribution using the plot_temperature_distribution function.

2. temperature_solver.py

• Contains the core functions for solving linear systems and calculating solutions:
  • jacobi_iteration: Performs Jacobi iteration to solve a linear system.
  • calculate_inverse_solution: Computes the solution vector using matrix inversion.
  • Example usage of these functions is demonstrated with a sample linear system.

3. plotting.py

• Provides a function (plot_temperature_distribution) to visualize the temperature distribution on a 2D grid using matplotlib.

4. matrix_solvers.py

• Includes a function (calculate_inverse_solution) that calculates the solution vector using matrix inversion.

5. temperature_solver.py

• Defines functions to generate the coefficient matrix and right-hand side vector for the temperature problem:
  • generate_coefficient_matrix: Creates the coefficient matrix and right-hand side vector.
  • solve_temperature_equation: Solves the temperature equation using Jacobi iteration (or matrix inversion).

Getting Started

To run the project locally, follow these steps:

1. Clone the repository:

   git clone https://github.com/salastro/ETD-LA.git
   cd ETD-LA

2. Install dependencies:

   poetry install 

3. Run the main.py script:

   poetry run src/etd_la/main.py [-h] grid_size left_boundary_temp up_boundary_temp right_boundary_temp down_boundary_temp {2d,3d,2d-animation,3d-animation}

   This will execute the example problem, solve the temperature equation, and display the resulting temperature distribution.

Dependencies

• NumPy: For numerical operations and linear algebra.
• Matplotlib: For plotting the temperature distribution.

Contribution Guidelines

If you wish to contribute to this project, please follow the guidelines outlined in the CONTRIBUTING.md file.

License

This project is licensed under the MIT License - see the LICENSE file for details.