Projects

There will be three projects. Each of the projects count for 10% of your final grade. The projects will be made available and shall be handed in using Blackboard.

The first project is due September 22nd. Please see Blackboard for the problem statement.

There are some issues with the incomplete LU-factorization. If you want to calculate M.dot(x) where M is the sparse incomplete LU-decomposition of A, you need to do something like:

M=spilu(A)
z=np.zeros_like(x)
z[M.perm_c]=x
z=M.L.dot(M.U.dot(z))
z=z[M.perm_r]

The second project is due October 20th. The problem statement is available on Blackboard.

The third project is due November 17th. The problem statement is available on Blackboard.

There is a potential pitfall in the Multigrid task: The formulas in Saad appear to be using the convention that the gridsize is on the left-hand side of the equation, i.e. \[ \frac{1}{h^2}\mathrm{A}\mathbf{u}=\mathbf{f}\] while we have been applying the gridsize to the right-hand side of the equation, i.e. \[ \mathrm{A}\mathbf{u}=h^2\mathbf{f}.\] If you use the second convention, the restriction operator on page 422 in Saad has to be multiplied with 4.