[petsc-users] -ksp_diagonal_scale

[Dominik Szczerba]

I am scaling my systems when dealing with small (microscopic) scales
in SI dimensions. This is because otherwise I have very small (near
epsilon) entries in the matrix and the solution fails or takes
significantly longer to converge. I used to do it by hand so far, if
there is a way to do it in Petsc - especially automatically detecting
the optimal scale - I am all ears.

Dominik

On Fri, Dec 23, 2011 at 11:11 AM, Alexander Grayver
<agrayver at gfz-potsdam.de> wrote:
> Hi,
>
> Sorry for small offtopic.
> I would also be interested more to know how it scales system? I mean what is
> idea behind this scaling.
>
> Regards,
> Alexander
>
>
> On 23.12.2011 03:50, Mohamad M. Nasr-Azadani wrote:
>
> Hi guys,
>
> Three questions:
> 1) As mentioned on the web when we use
> -ksp_diagonal_scale_fix: scale the matrix back AFTER the solve
>
> with -ksp_diagonal_scale does it also scale back the RHS vector associated
> with the KSP solver?
>
> 2) Also, as mentioned on the web for -ksp_diagonal_scale
> "Tells KSP to symmetrically diagonally scale the system before solving. "
>
> When I used this option to solve for the Pressure (Poisson equation with
> Neumann B.C., descritized via structured fisytenite-difference method), the
> number of iterations for convergence was trippled, e.g. without this option,
> it converges in 18 iteration, but with this option it goes up to 50-60
> iterations.
> (GMRES + BoomerAMG as the preconditioner).
> Is this something you would expect?
>
> 3) How could the linear system resulting from the Poisson equation for
> pressure (incompressible flow) can be more diagonally scaled? To elaborate
> more, for the uniform grid case and let's say a second order central scheme
> finite difference discretization, the sum of the off-diagonal coefficients
> are equal to the diagonal coefficient.
>
> Thanks,
> Best,
> Mohamad
>
>