Assumption:

you have the necessary mathematical equations and problem setup specific to your application.

```python

import numpy as np

from scipy.sparse import dia_matrix

from scipy.sparse.linalg import spsolve

def compute_modified_weak_galerkin():

# Define problem parameters and variables

# Modify these according to your problem

# Define the domain

a = 0.0 # Start of the domain

b = 1.0 # End of the domain

# Define the number of elements and nodes

num_elements = 100 # Number of elements

num_nodes = num_elements + 1 # Number of nodes

# Define the weak form parameters

alpha = 1.0 # Coefficient alpha

beta = 1.0 # Coefficient beta

# Define the boundary conditions

u_a = 0.0 # Dirichlet condition at the left boundary

u_b = 1.0 # Dirichlet condition at the right boundary

# Compute element size

h = (b - a) / num_elements

# Construct the stiffness matrix A

A = dia_matrix((num_nodes, num_nodes))

# Construct the load vector b

b = np.zeros(num_nodes)

# Iterate over each element

for i in range(num_elements):

# Compute the element bounds

x_left = a + i * h

x_right = a + (i + 1) * h

# Compute the element midpoint

x_mid = 0.5 * (x_left + x_right)

# Compute the element size

h_e = x_right - x_left

# Compute the element contributions to the stiffness matrix A

A[i, i] += alpha / h_e

A[i, i + 1] -= alpha / h_e

A[i + 1, i] -= alpha / h_e

A[i + 1, i + 1] += alpha / h_e

# Compute the element contributions to the load vector b

b[i] += beta * h_e / 2

b[i + 1] += beta * h_e / 2

# Apply the Dirichlet boundary conditions

A[0, 0] = 1.0

A[0, 1] = 0.0

b[0] = u_a

A[-1, -1] = 1.0

A[-1, -2] = 0.0

b[-1] = u_b

# Solve the linear system

u = spsolve(A, b)

# Return the solution

return u

# Call the function to compute the Modified Weak Galerkin Method

solution = compute_modified_weak_galerkin()

# Print the solution

print("Solution:", solution)

```

The program defines the problem parameters such as the domain, number of elements, weak form coefficients, and boundary conditions. It then constructs the stiffness matrix and load vector using the Modified Weak Galerkin Method formulation. Finally, it applies the Dirichlet boundary conditions and solves the resulting linear system using the sparse solver from SciPy. The computed solution is printed at the end.

Good luck!! AI tools used

Dear Abdulhameed Qahtan Abbood Al-Tai ,

The modified weak Galerkin method does not require the penalty parameter by comparing with traditional DG methods.

Article A modified weak Galerkin method for H(curl)-elliptic problem

Regards,

Shafagat

Thanks for the reply, please, is there a FreeFEM++ code to solve this problem? It will be much easier than other software.