[Nek5000-users] Direct/Adjoint perturbation mode

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

Hi Nek's,

I am willing to investigate the weakly non-linear dynamics of a perturbation
and there for I need the adjoint perturbation. Before going any further, I'd
like to be sure I understood how the native perturbation mode works.

*My understanding of the perturbation mode is the following:*

One first builds the rhs F^(n+1), through *call makefp* in perturb.f,
containing at the moment only the eventual forcing term and all explicit
contributions from the extrapolation of the convective term. Then, *call
cresvipp* transforms the rhs into F^(n+1) + D^T p^n - Hu^n, whereas *call
ophinv* solves delta u = H^(-1) (F^(n+1) + D^T p^n - Hu^n). Following is the
non-divergence free velocity field u^* = u^n + delta u (*call opadd2*). Last
but not least, *call incomprp* solves the following pressure equation:

*DQD^T delta p = -Du^**


and then project u^* onto the closest divergence free velocity field.

Am I correct up to now? If so, I still have a question. It may seem
straightforward for spectral elements boys however I'm a new comer to this
world and I do not understood how is the Helmholtz operator built. I mean I
presume it is done through the *call sethlm* but I don't get why I have h1
and h2 as outputs instead of one single matrix H.

*How I would modify the native perturbation mode into the adjoint one.*

This will come next, as soon as I'm sure I understood correctly how the
native mode works.

Regards,

-- 
Jean-Christophe
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