[petsc-users] Multigrid preconditioning of entire linear systems for discretized coupled multiphysics problems

[Mark Adams]

It sounds like AMG is used on the whole system. I've done this for a
different saddle point system but it required enough algorithm extension
that I wrote a paper on it.  These methods are not in GAMG.

I would at least not use smoothed aggregation, use plane aggregation
(-pc_gamg_agg_nsmooths 0).  It might work if it has a stable MG smoother.

Mark

@Article{,
  author =   {Adams, M.~F.},
  title =   {Algebraic multrigrid methods for constrained linear systems
with applications to contact problems in solid mechanics},
  journal =   {Numerical Linear Algebra with Applications},
  year =   {2004},
  volume =   {11},
  number =   {2-3},
  pages =   {141-153}
}

On Thu, Mar 5, 2015 at 5:33 PM, Jed Brown <jed at jedbrown.org> wrote:

> Fabian Gabel <gabel.fabian at gmail.com> writes:
>
> > AMG has apparently been used (successfully?) for fully-coupled
> > finite-volume discretizations of Navier-Stokes:
> >
> > http://dx.doi.org/10.1080/10407790.2014.894448
> > http://dx.doi.org/10.1016/j.jcp.2008.08.027
>
> These papers effectively bring a pressure projection or SIMPLE-type
> algorithm into a coupled system.  It's not a saddle-point formulation
> and is not uniformly valid across parameters (I think; methods of this
> sort normally aren't, but I haven't analyzed it).  The multigrid
> algorithm is not described and might not be purely algebraic.
>
> Note that the 2014 paper copies liberally from the 2009 paper.
>
> You can try formulating Navier-Stokes this way and test existing solvers
> if you like, but I predict it doesn't come without tradeoffs.
>
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