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

Ying He yinghe at math.ucdavis.edu
Tue Oct 6 11:57:00 PDT 2015


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. 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.

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.

Thanks in advance if anyone can answer my questions.


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