[Nek5000-users] Element connectivity information

[nek5000-users at lists.mcs.anl.gov]

Hi Paul,

Thank you for a quick response.
My current understanding is that the error occurs since Arnoldi treats  
the velocities in the duplicated points as separate degrees of freedom  
(which they are not in Nek5000, since they come out always equal).
So, therefore I am not so sure that a weighting operation would remove  
the problem.
Anyway, I will test what you suggest in a few cases and tell you how  
it comes out.

But if it turns out that counting the points once is the only option  
(asymmetrically, as you point out), is it possible to do this?
(Another option is always that I make changes inside the Arnoldi  
algorithm, but this might be a bit more elaborate.)

Thanks a lot,

Outi

14 Mar 2012 kl. 13:40 skrev nek5000-users at lists.mcs.anl.gov:

>
>
> Hi Outi,
>
> We encounter this problem all the time in conjugate gradient
> and gmres iteration.
>
> For reasons of symmetry (and, hence, commutativity and associativity,
> which are two essential ingredients for parallel execution), I would
> suggest that you not try to store the data only once, but rather
> scale by the inverse counting-matrix (aka, multiplicity), so that  
> interface points are not counted twice when computing your inner
> products.
>
> The inverse counting-matrix is stored in vmult() and tmult().  A
> typical application is:
>
>      alpha = glsc3(vx,vmult,vx,n)   (n=nx1*ny1*nz1*nelv)
>
> which gives the l2 inner product:  alpha := sum_i (vx_i)^2 for a  
> vector VX.
>
> Note that if you instead want the L2 inner product
>
>      alpha = \int_Omega (vx)^2 dV
>
> you would compute this as:
>
>      alpha = glsc3(vx,bm1,vx,n)
>
>            = vx^T B vx
>
> which is the inner product of vx with the (diagonal) mass matrix B.
>
> If you want the average of the physical rms (say), it would be:
>
>
>      alpha = glsc3(vx,bm1,vx,n)
>      if (alpha.gt.0) alpha = sqrt(alpha/volvm1)
>
>
> etc.
>
> In summary, for linear algebra, use vmult(). For physics, use bm1()
> (B, on Mesh 1).
>
>
> Please let me know if this help to resolve your problem.
>
> Best regards,
>
> Paul
>
>
>
> On Wed, 14 Mar 2012, nek5000-users at lists.mcs.anl.gov wrote:
>
>> Hi Neks,
>>
>> I am using Nek5000 coupled to an Arnoldi algorithm for hydrodynamic  
>> stability computations. In these, I form a vector of the  
>> velocities, which I regularly pass to the Arnoldi solver. Then, a  
>> new velocity vector is formed which is passed back to Nek5000.
>>
>> Now, the code works as it is, but in addition to the physical modes  
>> it produces some spurious modes, which I think originate from the  
>> fact that the velocities at the element-common boundaries are  
>> accounted for twice. To fix this, I need to access the element  
>> connectivity information. Can you please guide me to in which  
>> variable this is stored?
>>
>> In particular, this is what I would like to do:
>> -  add the element-common points to the local vector only for one  
>> of two adjacent elements (and for a corner point, only one of the  
>> four elements adjacent to it).
>> - for the vector that Arnoldi returns, make sure that the new  
>> values of the velocity are inserted also for the other adjacent  
>> element(s).
>>
>> Thanks a lot in advance!
>> Outi
>>
>>
>>
>>
>>
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