[aspect-devel] Solver for compostion equation and preconditioner for Stokes

[Wolfgang Bangerth]

Ying,

> I am currently interested in developing the solver using Discontinuous
> Galerkin method for problems involving single compositional field, which has
> discontinuity but no Temperature dependency. The viscosity and density for the
> Stokes equation will be dependent only on the compositional field.  I am a new
> person to “Aspect”.  All my work done right now is based on the modification
> of step-31 in deal.ii examples. However, when I use the same Data parameters
> (density, viscosity, initial condition etc.) and apply the FEM method to run
> both in Step-31 I modified and Aspect, the two results are very different.
>
> Below are my questions:
>
> 1, I didn’t find anything mentioned in the Aspect manual regarding the
> numerical scheme used for the compositional field.  I thought it might be the
> same as the temperature equation with default viscosity stabilization, however
> the results from aspect show large overshoot (around 15%) for the
> compositional field.

Are you saying that if you set up a problem in such a way that the temperature 
and the compositional fields have the same initial conditions, that you get 
different results?

I would not be surprised to hear that that is so, but it would probably be 
good to investigate why that is so. Can you share an input file that 
demonstrates this?


> So I guess either I didn’t set up correct parameters for
> the compositional field, or the solver for compositional filed is indeed
> without any stabilization treatment.

No, the idea is that the compositional and temperature solvers should use the 
same numerical method.


> 2, in the aspect paper of M. Kronbichler, T. Heister, W. Bangerth in 2012, it
> gives a very detail explanation of the “poor but cheap” preconditioner used in
> Aspect. A better but expensive preconditoner will be applied if the cheap one
> failed for more than 30 iterations.  I am just wondering what kind of good but
> expensive precondioner used in Aspect, as for large variation viscosity
> problems, the cheap one is always not good enough.

I think that's also explained in the paper, but the upshot is that the poor 
and cheap preconditioner uses

   [X  B  ]
   [0 M^-1]

as a preconditioner where X corresponds to one cycle of an algebraic multigrid 
on the velocity-velocity block A. The expensive but better preconditioner uses 
the same block structure as above, but X corresponds to A^{-1} (solved with CG 
and using the algebraic multigrid as a preconditioners).

Best
  W.

-- 
------------------------------------------------------------------------
Wolfgang Bangerth               email:            bangerth at math.tamu.edu
                                 www: http://www.math.tamu.edu/~bangerth/