[dune-pdelab] some problems in dune

[Dr. Olaf Ippisch]

Dear Robert,

in my opinion the advantage of AMG to GMG is that it still works if you
have heterogeneity on the fine grid, whereas GMG only works well if the
heterogeneity is resolved on the coarse grid. It has nothing to do with
the number of coarse grid elements.

The idea of AMG is to coarsen the system long enough to make an exact
solution on the coarse grid feasible. Therefore a coarsentarget of 1 is
usually not a good idea. However, there are situations where this still
can make sense. I used a coarsen target of 1 when solving linear
equation systems originating from the discretisation of a parabolic
problem on a system with more than a hundred thousand processors. In the
case of a parabolic problem the equation is strictly diagonally dominant
and the iteration number should stay constant independend of the number
of unknowns anyhow. The AMG is then used to cope with heterogeneity and
smoothing on the coarse grid is sufficient. If you deal with elliptic
problems it is essential to solve the problem on the coarse grid with an
exact solver, else the convergence will be very poor. However, this
involves repartitioning the system to fewer nodes, which can be rather
costly. Thus it pays off to avoid it in the parabolic case on very large
machines.

Best regards,
Olaf Ippisch


Am 03.11.14 um 10:18 schrieb Robert Jendrny:
> Moin moin,
> 
> I know that I changed the coarsentarget to 1 because this should be the
> advantage of AMG compared to GMG
> Also with other coarsentarget values I got iteration numbers which were
> exploding ... the '1' was just an example output for you
> 
> If I change usesuperlu=false to usesuperlu=true I get the message: You
> are using AMG without superlu, please install it or set it to false
> So where can I find superlu to install it on my pc
> 
> I think that AMG together with Q2 is not valid ;-)
> The AMG algorithm should know that you are using Q2 in two dimensions
> ... but the matrix structure is equal or nearly the same if you use Q1
> in three dimensions ...
> 
> I think I have to wait for Markus' answer :-)
> 
> Yours
> Robert
> 
> 
> On 10/31/2014 02:08 PM, Rebecca de Cuveland wrote:
>> Hey,
>>
>> why did you change the coarsentarget parameter? The default is
>> somewhere at 1000 nodes, and it seems you have 1? That is certainly
>> not a reasonable choice. (You have only one unknown on your coarsest
>> level).
>>
>> I also see in your code that you do not use Superlu as solver on the
>> coarsest level (usesuperlu = false). As the warning that you
>> explicitly supress with this flag states: Use superlu, sometimes this
>> has a drastic impact on the solution.
>>
>> Does something change, when you use superlu and a coarsentarget of at
>> least 100 (or even more)?
>>
>> One last thing, we spoke about AMG in combination with Q2 today in our
>> group meeting:
>> Nobody has really used this in pdelab, and we are not sure if the
>> implementation in istl is also valid for Q2. Perhaps Markus can say
>> something about that?
>>
>> Bye,
>> Rebecca
>>
> 
> 

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