[Nek5000-users] Linearized Nek: Compute only the right-hand side

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

Yep,

I have been looking at it and have used it already quite extensively. Up to
now, for stability analysis, I have been using snapshots taken from the
Linearized DNS and then used them to form a Krylov subspace for an Arnoldi
algorithm. However, what I would like to do know is to use Nek as blackbox
for matrix-vector product only. In the perturbation mode, eventhough the
Jacobian matrix is not explicitely formed, the equations still read du/dt =
J * u

What I am interested in is, given u(0), to output only:

u(1) = J * u(0)
u(2) = J * u(1)
...
u(N) = J * u(N-1)

Not sure though if that's clear enough?



On 21 October 2011 12:37, <nek5000-users at lists.mcs.anl.gov> wrote:

>
> Jean-Christophe,
>
> Have you already looked at the perturbation code in nek?
> It already does these things.
>
> Also, it's not clear that you want everything in strong
> form, particularly the 2nd-order spatial terms, since
> the solution is only C0?
>
> Paul
>
>
>
> On Fri, 21 Oct 2011, nek5000-users at lists.mcs.anl.**gov<nek5000-users at lists.mcs.anl.gov>wrote:
>
>
>  Hi Nek's,
>>
>> Given a random initial vector u and the Jacobian matrix of the linearized
>> Navier-Stokes, I would like to calculate the matrix-vector product J * u.
>> In
>> Nek, that would consists in calculating only the right hand side of the
>> equations, that is:
>>
>> RHS = ( -U.grad(u) - u.grad(U) - grad(p) + 1/Re Lap(u)    ;    div(u) )
>>
>> I have a few questions on how to compute those different terms in userchk
>> (Nek is used in post-process mode):
>>
>>  - I would tend to use convop() for the convection terms, however I'm not
>>
>>  sure whereas it would output the strong or weak form (and I need the
>> strong
>>  one obviously)?
>>  - Same question regarding grad(p) and div(u) if I use opgradt() and
>>
>>  opdiv() to calculate them?
>>
>> Last but not least, for the Laplacian I've read a previous mail where it
>> is
>> said that it can be computed using a sequence of wgradm1() and vec_dssum()
>> so I guess I kown how to compute at the strong form for it.
>>
>> Sincerely,
>> --
>> Jean-Christophe
>>
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-- 
Jean-Christophe
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