north-east neighbour on fine grid corresponding to coarse grid point
ef[2*i-1+1, 2*j-1+1] = 0.25*(unc[i,j] + unc[i,j+1] +
unc[i+1,j] + unc[i+1,j+1])
end end
end
```
The relaxation of the solution is done using the Gauss-Seidel method for each grid level as formulated in Section 6.2.1 for a fixed number of iterations. The Julia implementation of relaxation operation is provided in Listing 25. The pseudocode for V-cycle multigrid framework for three levels if provided in Algorithm 5. The implementation of a complete multigrid framework in Julia for two levels is given in Listing 26.

✝ ✆

**Listing 25.** Implementation of relaxation operation (using Gauss-Seidel iterative method) in multigrid framework. ✞ ☎

✝ ✆

```