def interpolation(self, u: VectorHeat1D) -> VectorHeat1D:
"""
Interpolate input vector u using linear interpolation.
Note: In the 1d heat equation example, we consider homogeneous Dirichlet BCs in space.
The Heat1D vector class only stores interior points.
:param u: approximate solution vector
:return: input solution vector u interpolated to a fine grid
"""
# Get values at interior points
sol = u.get_values()
# Create array for interpolated values
ret_array = np.zeros(int(len(sol) * 2 + 1))
# Linear interpolation
for i in range(len(sol)):
ret_array[i * 2] += 1 / 2 * sol[i]
ret_array[i * 2 + 1] += sol[i]
ret_array[i * 2 + 2] += 1 / 2 * sol[i]
# Create and return a VectorHeat1D object with interpolated values
ret = VectorHeat1D(len(ret_array))
ret.set_values(ret_array)
return ret
def restriction(self, u: VectorHeat1D) -> VectorHeat1D:
"""
Restrict input vector u using standard full weighting restriction.
Note: In the 1d heat equation example, we consider homogeneous Dirichlet BCs in space.
The Heat1D vector class only stores interior points.
:param u: approximate solution vector
:return: input solution vector u restricted to a coarse grid
"""
# Get values at interior points
sol = u.get_values()
# Create array for restricted values
ret_array = np.zeros(int((len(sol) - 1) / 2))
# Full weighting restriction
for i in range(len(ret_array)):
ret_array[i] = sol[2 * i] * 1 / 4 + sol[2 * i + 1] * 1 / 2 + sol[
2 * i + 2] * 1 / 4
# Create and return a VectorHeat1D object with the restricted values
ret = VectorHeat1D(len(ret_array))
ret.set_values(ret_array)
return ret