Project 1

import numpy as np
from scipy.sparse import lil_matrix
from scipy.sparse.linalg import spsolve

# Sample class for mesh node
class Node:
    def __init__(self, x, y):
        self.x = x
        self.y = y

# Sample class for mesh element
class Element:
    def __init__(self, nodes):
        self.nodes = nodes

# Sample implementation of FVM solver
def solve_heat_conduction(mesh_file):
    # Read mesh data from file and create nodes and elements
    nodes = []  # List of Node objects
    elements = []  # List of Element objects

    # Parse the mesh file and populate nodes and elements lists

    # Create connectivity matrix
    num_nodes = len(nodes)
    A = lil_matrix((num_nodes, num_nodes))
    b = np.zeros(num_nodes)

    # Loop through elements to assemble FVM equations
    for element in elements:
        # Compute element properties, gradients, and fluxes
        # Update the global matrix A and vector b based on the FVM equations

    # Solve the system of equations
    temperature = spsolve(A.tocsr(), b)

    return temperature

if __name__ == "__main__":
    mesh_file = "path/to/your/mesh/file.txt"
    temperature_distribution = solve_heat_conduction(mesh_file)

    # Plot temperature distribution or perform other visualizations