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    <p>Hello everyone,</p>
    <p><br>
    </p>
    <p>Sorry for the delay, I was exploring all the possibilities that
      you have provided to me! I believe that the problem was solved.<br>
    </p>
    <p>Here is what I have done : <br>
    </p>
    <p><br>
    </p>
    <p>I have increased lx1, I have computed the components of the
      vorticity field using wgradm1. Then when I compute gradient of
      vorticity for every iteration, I diffuse it  over 5 time steps
      (with low values of dt) and this removes the problem at the
      interface of the elements!</p>
    <p><br>
    </p>
    <p>Thank you for your help,</p>
    <p><br>
    </p>
    <p>Best wishes,</p>
    <p><br>
    </p>
    <p>Arnold<br>
    </p>
    <p><br>
    </p>
    <br>
    <div class="moz-cite-prefix">Le 06/03/2017 à 07:38, Arnold Wakim a
      écrit :<br>
    </div>
    <blockquote cite="mid:cc5f1ae0-7219-77fb-f81d-26279406cada@onera.fr"
      type="cite">
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      <p>Good Morning,</p>
      <p><br>
      </p>
      <p>Sorry for taking so long to answer. First I wanted to say that
        I really appreciate all of your help! <br>
      </p>
      <p>I am currently trying all these methods : <br>
      </p>
      <p>- as suggested by Paul Fischer, increasing LX1 and low pass
        filtering.<br>
      </p>
      <p>- and smoothing the derivatives. I will keep you posted on the
        results.<br>
      </p>
      <p><br>
      </p>
      <p>What I am trying to do is studying optimal perturbations using
        a DIRECT-ADJOINT approach so as to optimize quantities. <br>
        However, when I am writing the equations, I have no choice but
        taking the spatial derivatives of vorticity. <br>
      </p>
      <p>Computing the derivatives is made for every DIRECT Numerical
        Simulation of the perturbations. Then I call the ADJOINT solver
        of Nek5000</p>
      <p>In order to converge towards optimum this may take several
        iterations let's say N ( roughly N=10 however since the
        gradients are not well resolved then I cannot tell whether I'm
        converged or not). The point is that I am computing vorticity,
        then computing the gradients of the same initial field, and
        this, N times. This leads to the problem I am facing. <br>
      </p>
      <p>Hope that helps understanding the issue. If you have more
        questions, please do not hesitate to ask.</p>
      <p><br>
      </p>
      <p>Best wishes,</p>
      <p><br>
      </p>
      <p>Arnold<br>
      </p>
      <p><br>
      </p>
      <p><br>
      </p>
      <p><br>
      </p>
      <p><br>
      </p>
      <div class="moz-cite-prefix">Le 03/03/2017 à 21:33, <a
          moz-do-not-send="true" class="moz-txt-link-abbreviated"
          href="mailto:nek5000-users@lists.mcs.anl.gov">nek5000-users@lists.mcs.anl.gov</a>
        a écrit :<br>
      </div>
      <blockquote
        cite="mid:mailman.1580.1488574096.2967.nek5000-users@lists.mcs.anl.gov"
        type="cite">call col2(dTdx,bm1,n)                    ! collocate
        with the mass matrix<br>
        call dssum(dTdx,nx1,ny1,nz1)       ! smooth<br>
        call col2(dTdx,bintm1,n)                ! collocate with the
        inverse mass matrix</blockquote>
      <br>
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                  style="font-size: 9pt" size="2">Arnold Wakim</font></font></font></strong><font
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                Doctorant,<br>
                Département d´</font></font></font><font color="#0668b3"><font
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              Doctorant,<br>
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            </font></font></font><font color="#0668b3"><font
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                  <br>
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