[Nek5000-users] Spectral method with Nek

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

The number of MPI ranks, P,  is <= E, the number elements.

In the E=1 case you can use only one mpi rank.

Also, no guarantees that, as a spectral code, E=1 would be faster than an equivalent
number of spectral element points given that the code is optimized for the multi element case.

The bottom line, however, is that E=1 corresponds to a spectral method.

Paul

________________________________________
From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
Sent: Tuesday, August 02, 2016 11:53 AM
To: nek5000-users at lists.mcs.anl.gov
Subject: Re: [Nek5000-users] Spectral method with Nek

Thanks Paul for the reply.
In fact, in one case I increased the order of polynomial significantly
and I was able to resolve the small scales and, thereby, the route to
chaos. But my experience was using one element with larger order of
polynomial as compared to various elements but lower order of
polynomials was slower (less computationally efficient, specially when I
performed parallel using openmpi). Is there any explanation for this?
Thanks again.

On 8/2/2016 12:11 PM, nek5000-users at lists.mcs.anl.gov wrote:
> This is absolutely true - one element corresponds to a spectral calculation.
>
> You do need, however, enough points to resolve the scales of motion, as is always
> the case, which means you need large values of N.   (The first spectral results were
> 32^3, and then the breakthrough 100^3 by Orszag in the early 70s - the famed centicubed
> simulations.)
>
> Paul
>
> ________________________________________
> From: nek5000-users-bounces at lists.mcs.anl.gov [nek5000-users-bounces at lists.mcs.anl.gov] on behalf of nek5000-users at lists.mcs.anl.gov [nek5000-users at lists.mcs.anl.gov]
> Sent: Tuesday, August 02, 2016 10:53 AM
> To: nek5000-users at lists.mcs.anl.gov
> Subject: [Nek5000-users] Spectral method with Nek
>
> All,
>
> I was wondering if the following statement is true or false:
>
> "If a single element is used for the whole domain then one can claim the
> Nek simulation is spectral instead of spectral element".
>
> Based on this, I carried out DNS on cavity for relatively large Reynolds
> numbers and I was not able to capture the instability mechanisms with
> one element (even when I increased the power of polynomial to 12 or 18).
> While I'm not surprised, I just wanted to see if anyone else has a
> similar experience.
>
> As a side question, why Nek utilizes Legendre polynomials instead of
> Chebyshev for each element? Is this because we're also interested in
> modeling non-uniformly spaced nodes?
>
> Best,
> Saleh
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