[aspect-devel] "Not converge" problem with variable viscosity.

Wolfgang Bangerth bangerth at tamu.edu
Fri Sep 4 13:15:44 PDT 2015

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> I'm now performing the basic convection tests with the harmonic
> perturbation (degree l, order m are specified) initial condition
> following the paper Zhong et al 2008. They use the non-dimensional
> parameters so I first dimensionalized everything and then input into
> ASPECT. From the preliminary results, I find that to run the same case
> in 4 global refinement degree CitcomS only needs less than 100 seconds
> while ASPECT needs several hours, even though I don't know whether the
> dimensionalize vs non-dimensionalize should cause a big time difference.

The two cases are not readily comparable. CitcomS uses linear elements, 
whereas deal.II uses quadratic elements. Citcom also starts with a mesh 
of only 6 cells, whereas ASPECT I believe starts with 24. So if both do 
4 global refinements, then ASPECT ends up with a factor of 8x4=32 times 
as many unknowns.

The quadratic elements should also lead to significantly better accuracy 
*per degree of freedom*, but the linear systems that need to be solved 
are worse conditioned and require more work.

So just comparing the number of global refinements does not give you an 
adequate picture of the accuracy of results the two codes give you. My 
expectation is that with the same number of global refinements, you 
would get a *far* more accurate solution out of ASPECT than from CitcomS 
-- at the price of much longer computations, of course.

> CitcomS first use the Uzawa algorithm to transform the set of equations
> from velocities and pressures to a Possion equation for pressure, and
> then solve the problem by multigrid. I don't know deal.ii very well and
> am not sure whether GMRES is slower than multigrid in computation?

I think that in reality the two algorithms should not be overly 
different. You'd need to compare the number of Uzawa iterations with the 
number of GMRES iterations. Within each iteration, CitcomS uses a 
geometric multigrid for the velocity-velocity block, whereas ASPECT uses 
an algebraic multigrid.


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

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