[petsc-users] -ksp_diagonal_scale

[Jed Brown]

On Thu, Dec 22, 2011 at 20:50, Mohamad M. Nasr-Azadani <mmnasr at gmail.com>wrote:

> 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?
>

yes


>
> 2) Also, as mentioned on the web for -ksp_diagonal_scale
> "Tells KSP<http://www.mcs.anl.gov/petsc/petsc-3.1/docs/manualpages/KSP/KSP.html#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?
>

It's perhaps slightly surprising that it's that much worse, but there is
nothing saying that the diagonal scaled matrix will be better. Most
preconditioners correct the diagonal scaling.


>
> 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.
>

You probably don't have a reason to use diagonal scaling.
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