Project Overview

This repository contains all materials related to the study of eigenmodes and Laplacian matrices for various geometric shapes. It includes Python scripts, computational results, visualizations, and animations.

Directory Structure

• README.md - This file, describing the repository structure.
• assignment.pdf - The assignment or research paper detailing the problem statement and methodology.
• final.ipynb - Jupyter Notebook with all the final solutions used in the research paper.

Figures

• figs/ - Contains all visualization outputs, including eigenmodes, Laplacian heatmaps, and spectral plots.
  • Eigenmode solutions for different geometries (circle, square, rectangle) are provided.
  • Comparisons between dense and sparse representations.
  • Example files: circle_eigenmode0.png, spectrum of eigenfrequencies.png.

GIFs

• gifs/ - Contains animations of eigenmodes.
  • Example: circle_eigenmode_animation.gif.

Results

• results/ - Stores computed Laplacian matrices and eigenvectors.
  • Example files: circle_laplacian_matrix.txt, eigenvectors.txt.

Source Code

• src/ - Contains Python scripts used for computation.
  • Eigens.py - Computes eigenvalues and eigenvectors.
  • Laplacians.py - Constructs Laplacian matrices for different domains.
  • utils/ - Contains utility functions for data processing.

Usage

Ensure you have the required dependencies installed and run the Jupyter notebook final.ipynb to reproduce results and visualizations.

pip install -r requirements.txt
jupyter notebook final.ipynb

License

This project is distributed under an open-source license. Refer to LICENSE for details.