[petsc-users] Efficient Use of GAMG for Poisson Equation with Full Neumann Boundary Conditions

[Hong]

Fabian,
Too much time was spent on the matrix operations during setup phase, which
has plenty room for optimization.
Can you provide us a stand-alone code used in your experiment so we can
investigate how to make our gamg more efficient?

Hong

On Wed, Feb 18, 2015 at 12:20 PM, Barry Smith <bsmith at mcs.anl.gov> wrote:

>
>   Fabian,
>
>    CG requires that the preconditioner be symmetric positive definite. ICC
> even if given a symmetric positive definite matrix can generate an
> indefinite preconditioner.
>
>   Similarly if an algebraic multigrid application is not "strong enough"
> it can also result in a preconditioner that is indefinite.
>
>   You never want to use ICC for pressure type problems it cannot compete
> with multigrid for large problems so let's forget about ICC and focus on
> the GAMG.
>
> > -pressure_mg_coarse_sub_pc_type svd
> > -pressure_mg_levels_ksp_rtol 1e-4
> > -pressure_mg_levels_ksp_type richardson
> > -pressure_mg_levels_pc_type sor
> > -pressure_pc_gamg_agg_nsmooths 1
> > -pressure_pc_type gamg
>
>   There are many many tuning parameters for MG.
>
>    First, is your pressure problem changing dramatically at each new
> solver? That is, for example, is the mesh moving or are there very
> different numerical values in the matrix?  Is the nonzero structure of the
> pressure matrix changing? Currently the entire GAMG process is done for
> each new solve, if you use the flag
>
> -pressure_pc_gamg_reuse_interpolation true
>
> it will create the interpolation needed for GAMG once and reuse it for all
> the solves. Please try that and see what happens.
>
>  Then I will have many more suggestions.
>
>
>   Barry
>
>
>
> > On Feb 17, 2015, at 9:14 AM, Fabian Gabel <gabel.fabian at gmail.com>
> wrote:
> >
> > Dear PETSc team,
> >
> > I am trying to optimize the solver parameters for the linear system I
> > get, when I discretize the pressure correction equation Poisson equation
> > with Neumann boundary conditions) in a SIMPLE-type algorithm using a
> > finite volume method.
> >
> > The resulting system is symmetric and positive semi-definite. A basis to
> > the associated nullspace has been provided to the KSP object.
> >
> > Using a CG solver with ICC preconditioning the solver needs a lot of
> > inner iterations to converge (-ksp_monitor -ksp_view output attached for
> > a case with approx. 2e6 unknowns; the lines beginning with 000XXXX show
> > the relative residual regarding the initial residual in the outer
> > iteration no. 1 for the variables u,v,w,p). Furthermore I don't quite
> > understand, why the solver reports
> >
> > Linear solve did not converge due to DIVERGED_INDEFINITE_PC
> >
> > at the later stages of my Picard iteration process (iteration 0001519).
> >
> > I then tried out CG+GAMG preconditioning with success regarding the
> > number of inner iterations, but without advantages regarding wall time
> > (output attached). Also the DIVERGED_INDEFINITE_PC reason shows up
> > repeatedly after iteration 0001487. I used the following options
> >
> > -pressure_mg_coarse_sub_pc_type svd
> > -pressure_mg_levels_ksp_rtol 1e-4
> > -pressure_mg_levels_ksp_type richardson
> > -pressure_mg_levels_pc_type sor
> > -pressure_pc_gamg_agg_nsmooths 1
> > -pressure_pc_type gamg
> >
> > I would like to get an opinion on how the solver performance could be
> > increased further. -log_summary shows that my code spends 80% of the
> > time solving the linear systems for the pressure correction (STAGE 2:
> > PRESSCORR). Furthermore, do you know what could be causing the
> > DIVERGED_INDEFINITE_PC converged reason?
> >
> > Regards,
> > Fabian Gabel
> > <gamg.128.out.531314><icc.128.out.429762>
>
>
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