[aspect-devel] aspect: error related to changing number of processors

[Wolfgang Bangerth]

On 08/31/2012 08:06 AM, Markus Bürg wrote:
> Hello Magali,
>> - When I change this back to 1e-12, the model runs fine on 4
>> processors. Its interesting that
>> using this smaller accuracy is only a problem on 4 processors, does
>> that make any sense to you?
> This is one of the challenging tasks in using multiple processors. The
> results are becoming a little bit different depending on the number of
> processors on uses, because - briefly speaking - first the computations
> start on every processor independently and then the results are put
> together to form the global solution you obtain. Usually the
> differences, which happen by these different distributions of data among
> the processors, is neglectable small. But, since you have set the
> tolerance to a really small value of 1e-15, these differences became
> visible for you.

Magali, I'm sure you've already figured this out, but as a corollary, if 
you set the tolerance to a very very small value, the iterative solver 
may not converge any more because at one point the roundoff you 
accumulate in each iteration is as large as the accuracy you gain in 
each iteration. That this is triggered on a particular number of 
processors but not another is, I believe, just an accident that has to 
do with the order in which processors add up their results in reduction 
operations such as dot products.

Best
  W.


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