[aspect-devel] Solver for compostion equation and preconditioner for Stokes (Ying He)

Ying He yinghe at math.ucdavis.edu
Mon Oct 26 21:14:14 PDT 2015

Dear Wolfgang,

Thanks for your reply.

On 2015-10-26 12:00, aspect-devel-request at geodynamics.org wrote:
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>    1. Re: Solver for compostion equation and preconditioner for
>       Stokes (Wolfgang Bangerth)
> ----------------------------------------------------------------------
> Message: 1
> Date: Mon, 26 Oct 2015 09:20:32 -0500
> From: Wolfgang Bangerth <bangerth at tamu.edu>
> To: aspect-devel at geodynamics.org
> Subject: Re: [aspect-devel] Solver for compostion equation and
> 	preconditioner for Stokes
> Message-ID: <562E36B0.9050802 at tamu.edu>
> Content-Type: text/plain; charset=utf-8; format=flowed
> 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 only used Aspect to run compositional fields problem (temperature 
independent), and used step-31 in deal.ii to run temperature problem 
with advection term only. Those two runs are applied with the same 
initial conditions and computational domain. I believe that the results 
should be essential the same, although I gave them two different names, 
as they are the solutions solved from the same system equations (stokes 
+ time-dependent homogeneous advection).

> 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?

Sure. Two input files can be download at the following links.
The first input is for the case with a ratio 1 of jump viscosity
The second input is for the case with a ratio 10 of jump viscosity

>> 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).
Thanks for your clarification, although I thought that the word 'cheap' 
or 'expensive' also corresponds to the lower right schur complement 
matrix: 1/eta M^-1 --> cheap, and 'B A^{-1}B^T'--> expensive. So for 
aspect, is the lower right matrix always the matrix M^{-1} even for the 
jump viscosity case?

> Best
>   W.
> --
> ------------------------------------------------------------------------
> Wolfgang Bangerth               email:            
> bangerth at math.tamu.edu
>                                  www: 
> http://www.math.tamu.edu/~bangerth/
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Ying He

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