[petsc-users] Null space and preconditioners

[Mark Adams]

The solution for Neumann problems can "float away" if the constant is not
controlled in some way because floating point errors can introduce it even
if your RHS is exactly orthogonal to it.

You should use a special coarse grid solver for GAMG but it seems to be
working for you.

I have lost track of the simply way to have the KSP solver clean the
constant out, which is what you want.

can someone help Marco?

Mark





On Mon, Mar 21, 2022 at 8:18 AM Marco Cisternino <
marco.cisternino at optimad.it> wrote:

> Good morning,
>
> I’m observing an unexpected (to me) behaviour of my code.
>
> I tried to reduce the problem in a toy code here attached.
> The toy code archive contains a small main, a matrix and a rhs.
>
> The toy code solves the linear system and check the norms and the mean of
> the solution.
>
> The problem into the matrix and the rhs is the finite volume
> discretization of the pressure equation of an incompressible NS solver.
>
> It has been cooked as tiny as possible (16 cells!).
>
> It is important to say that it is an elliptic problem with homogeneous
> Neumann boundary conditions only, for this reason the toy code sets a null
> space containing the constant.
>
>
>
> The unexpected (to me) behaviour is evident by launching the code using
> different preconditioners, using -pc-type <pctype>
> I tested using PCNONE (“none”), PCGAMG (“gamg”) and PCILU (“ilu”). The
> default solver is KSPFGMRES.
>
> Using the three PC, I get 3 different solutions. It seems to me that they
> differ in the mean value, but GAMG is impressive.
>
> PCNONE gives me the zero mean solution I expected. What about the others?
>
>
>
> Asking for residuals monitor, the ratio ||r||/||b|| shows convergence for
> PCNONE and PCILU (~10^-16), but it stalls for PCGAMG (~10^-4).
>
> I cannot see why. Am I doing anything wrong or incorrectly thinking about
> the expected behaviour?
>
>
>
> Generalizing to larger mesh the behaviour is similar.
>
>
>
> Thank you for any help.
>
>
>
> Marco Cisternino
>
>
>
>
>
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