# Projects

## Information

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.

## Project 1

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]

## Project 2

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

## Project 3

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.