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<p><tt>Matthias,</tt></p>
<p><tt>In the off-chance that the various mesh components (node
sets, line-sets, surface facet sets, ...) have been written to
the simulation results output as distinct displayable graphics
objects, you might be able to use the PV Extract Block filter to
get the 3-D volume "separated" from the other mesh objects, and,
then use PV's Gradient filter?</tt></p>
<p><tt>(I routinely do this via EnSight's PART-construct for my simulation
results output.)</tt></p>
<p><tt>Sam Key</tt><br>
</p>
<br>
<div class="moz-cite-prefix">On 9/27/2016 9:43 AM, Zenker, Dr.
Matthias wrote:<br>
</div>
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<p class="MsoNormal"><span style="color:#1F497D">Hi again,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US">I
have examined my mesh (which you can find in the attachment)
with Salome and gmsh – there are no flat faces at the
boundaries. But there are line elements! So I am relieved as
far as my worried questions in the last mail are concerned –
mesher and the FEM solver are doing their work as they
should.
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US">But
IMO it makes no sense to compute the derivatives over the
line elements and average it with the derivatives over the
face elements. Is it possible that this is exactly what
happens in the gradient filter (and in the computederivative
+ celldatatopointdata filters)? If so, why? And can that be
switched off, as IMO it should?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US">Or,
to put it differently: Apparently ParaView does not make a
difference between a line and a face. Why is this so?
Shouldn’t it do that?<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US">Thanks
for a clarification,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US">Matthias<o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D" lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US">Von:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US"> Zenker, Dr. Matthias
<br>
<b>Gesendet:</b> Dienstag, 27. September 2016 17:00<br>
<b>An:</b> 'Moreland, Kenneth'<br>
<b>Cc:</b> <a class="moz-txt-link-abbreviated" href="mailto:paraview@paraview.org">paraview@paraview.org</a><br>
<b>B</b></span><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">etreff:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">
AW: [Paraview] Gradient filter: boundary effects<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal">Hi Ken,<o:p></o:p></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">thank you for pointing
this out! I was not aware that boundary lines are also
inifinitely flat cells. This seems true for all
boundaries, also the internal boundaries between the two
faces.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The question for me is
now: Is this normal, or does that mean that the whole FEM
simulation is corrupt? Should I have a mesh that does not
have those line cells? The mesh has been calculated by the
Salome mesher, which uses netgen. The boundaries were
declared as groups. The mesh has then been exported as
unv, imported by Elmer which has done the FEM
calculations, and saved the results as vtu. If those line
cells represent a problem, where in this chain do I have
to look for the mistake?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Matthias<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
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<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US">Von:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US"> Moreland, Kenneth [<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">mailto:kmorel@sandia.gov</a>]
<br>
<b>Gesendet:</b> Dienstag, 27. September 2016 16:41<br>
<b>An:</b> Zenker</span><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif"">,
Dr. Matthias<br>
<b>Cc:</b> <a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a><br>
<b>Betreff:</b> Re: [Paraview] Gradient filter:
boundary effects<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US">Matthias,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">As I suspected, your
data has some boundary elements that are throwing off
the gradient calculation. The data you sent me has line
cells around the boarder of the data. The easiest way to
see these line cells is to go to the Properties panel
and change the “Line Width” parameter to something
large. (Attached is an image that shows the boundary
cells by setting the line width to 20.)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">So in the example
you gave, the gradient is computed correctly in the
triangles, but the finite differences computation for
the line cells can only compute the gradient in the
direction of the line. Thus, there is no y component for
the gradient in these line cells. Because the line cells
share the points of the triangles along the bottom, the
gradient average becomes incorrect.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-Ken<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"><o:p> </o:p></span></p>
<blockquote style="border:none;border-left:solid #B5C4DF
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<p class="MsoNormal"><b><span style="color:black"
lang="EN-US">From: </span></b><span
style="color:black" lang="EN-US">"Zenker, Dr.
Matthias" <<a moz-do-not-send="true"
href="mailto:Matthias.Zenker@erbe-med.com">Matthias.Zenker@erbe-med.com</a>><br>
<b>Date: </b>Tuesday, September 27, 2016 at 9:51 AM<br>
<b>To: </b>"Moreland, Kenneth" <<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">kmorel@sandia.gov</a>><br>
<b>Cc: </b>"<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>"
<<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>><br>
<b>Subject: </b>[EXTERNAL] AW: [Paraview] Gradient
filter: boundary effects</span><span
style="font-size:12.0pt;color:black" lang="EN-US"><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Times New
Roman","serif"" lang="EN-US"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Hi Ken,</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">if you want to have a look – here is a
simple test file. At the bottom side, there are 4
adjacent cells having grad(y)~7900 from
computederivatives, but all 3 nodes on the bottom side
have grad(y) ~ 5300 from celldatatopointdata.</span><span
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Thanks,</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Matthias</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
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<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US">Von:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US"> Moreland, Kenneth [<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">mailto:kmorel@sandia.gov</a>]
<br>
<b>Gesendet:</b> Dienstag, 27. September 2016
15:40<br>
<b>An:</b> Zenker, Dr. Matthias<br>
<b>Cc:</b> <a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a><br>
<b>Betreff:</b> Re: [Paraview] Gradient filter:
boundary effects</span><span lang="EN-US"><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Matthias,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">If values are
being pulled from 7900 units down to 5300 units,
there must be some neighbor with lower values. Why
that is happening for you I cannot say without
looking at your data. Perhaps on the boundary there
are some malformed or 2D cells with invalid
gradients.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-Ken<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span style="color:black"
lang="EN-US">From: </span></b><span
style="color:black" lang="EN-US">"Zenker, Dr.
Matthias" <<a moz-do-not-send="true"
href="mailto:Matthias.Zenker@erbe-med.com">Matthias.Zenker@erbe-med.com</a>><br>
<b>Date: </b>Tuesday, September 27, 2016 at
9:06 AM<br>
<b>To: </b>"Moreland, Kenneth" <<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">kmorel@sandia.gov</a>><br>
<b>Cc: </b>"<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>"
<<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>><br>
<b>Subject: </b>[EXTERNAL] AW: [Paraview]
Gradient filter: boundary effects</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Times New
Roman","serif"" lang="EN-US"> </span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Hi Ken,</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">what I don’t understand is that the
cell gradients are correct, but their average at
the border is not. (Example: All cell gradients
adjacent to one node at the border have approx.
7900 units in y direction, the node has approx.
5300)</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">So it seems I cannot determine the
gradient in the postprocessing step, but have to
calculate it in the FEM solver (where I do get
correct results now – I didn’t initially, which
was the reason why I tried it with ParaView).</span><span
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Thank you anyway, I have learned new
bits of ParaView again (which is great software
BTW)!</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Have a nice holiday (if I interpret
your autoreply correctly)!</span><span
lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:#1F497D"
lang="EN-US">Matthias</span><span lang="EN-US"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US">Von:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US"> Moreland, Kenneth [<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">mailto:kmorel@sandia.gov</a>]
<br>
<b>Gesendet:</b> Dienstag, 27. September
2016 14:36<br>
<b>An:</b> Zenker, Dr. Matthias; <a
moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a><br>
<b>Betreff:</b> Re: [Paraview] Gradient
filter: boundary effects</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">You could
run the results through the point to cell
filter, but that would give you the same answer
as the gradient of unstructured dataset filter
with the faster approximation option on.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-Ken<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span
style="color:black" lang="EN-US">From: </span></b><span
style="color:black" lang="EN-US">"Zenker,
Dr. Matthias" <<a moz-do-not-send="true"
href="mailto:Matthias.Zenker@erbe-med.com">Matthias.Zenker@erbe-med.com</a>><br>
<b>Date: </b>Tuesday, September 27, 2016 at
8:28 AM<br>
<b>To: </b>"Moreland, Kenneth" <<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">kmorel@sandia.gov</a>>,
"<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>"
<<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>><br>
<b>Subject: </b>[EXTERNAL] AW: [Paraview]
Gradient filter: boundary effects</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Times New
Roman","serif"" lang="EN-US"> </span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US">Hi
Kenneth,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">thank you
for the quick answer!<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">So it
seems not that trivial to calculate an
electrical field between a rod and a plane
given the potential…<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The
compute derivatives filter does not give me
the problem at the boundary indeed. Instead it
gives a value per cell, not per node, which
does not look nice.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Is there a
friendly filter or switch which would give me
the smoothed surface representation back?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thanks,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Matthias<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<div style="border:none;border-left:solid blue
1.5pt;padding:0cm 0cm 0cm 4.0pt">
<div>
<div style="border:none;border-top:solid
#B5C4DF 1.0pt;padding:3.0pt 0cm 0cm 0cm">
<p class="MsoNormal"><b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US">Von:</span></b><span
style="font-size:10.0pt;font-family:"Tahoma","sans-serif""
lang="EN-US"> Moreland, Kenneth [<a
moz-do-not-send="true"
href="mailto:kmorel@sandia.gov">mailto:kmorel@sandia.gov</a>]
<br>
<b>Gesendet:</b> Dienstag, 27. September
2016 14:14<br>
<b>An:</b> Zenker, Dr. Matthias; <a
moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a><br>
<b>Betreff:</b> Re: [Paraview] Gradient
filter: boundary effects</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Matthias,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The
gradient is estimated with finite
differences. Thus, it is not wholly
unexpected that there could be differences
at the boundaries. However, the algorithm
does
<i>not</i> assume zero for adjacent cells at
the boundaries.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">The way
the unstructured gradient filter works is
that it computes the local gradient in each
cell at each of the cell’s points. Then for
every point it averages the gradient from
all incident cells at that point. (If you
have the Faster Approximation option on,
then the filter only computes one gradient
per cell in the center and averages those.
Faster, but more artifacts, particularly at
the edges.)<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">If this
averaging is causing you an issue, you might
try the Compute Derivatives filter. This
does a wholly local operation within each
cell, so you should not see any artifacts
(unless the field itself has artifacts at
the boundaries).<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">-Ken<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<blockquote style="border:none;border-left:solid
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<p class="MsoNormal"><b><span
style="color:black" lang="EN-US">From:
</span></b><span style="color:black"
lang="EN-US">ParaView <<a
moz-do-not-send="true"
href="mailto:paraview-bounces@paraview.org">paraview-bounces@paraview.org</a>>
on behalf of "Zenker, Dr. Matthias" <<a
moz-do-not-send="true"
href="mailto:Matthias.Zenker@erbe-med.com">Matthias.Zenker@erbe-med.com</a>><br>
<b>Date: </b>Tuesday, September 27,
2016 at 5:45 AM<br>
<b>To: </b>"<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>"
<<a moz-do-not-send="true"
href="mailto:paraview@paraview.org">paraview@paraview.org</a>><br>
<b>Subject: </b>[EXTERNAL] [Paraview]
Gradient filter: boundary effects</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span
style="font-family:"Times New
Roman","serif""
lang="EN-US"> </span><span lang="EN-US"><o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span lang="EN-US">Hi,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">when I
use the gradient filter (unstructured
dataset), I observe edge effects which are
IMO unphysical. For the nodes on the outer
boundary of my domain, the gradient
magnitude is smaller than I would expect.
The behavior is like the filter tries to
use the adjacent nodes to calculate the
gradient, and since there are none
outside the domain, it assumes zero and
finds a lower result.<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">If so,
I would consider this a bug – is there a
fix or workaround?<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Thanks,<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">Matthias<o:p></o:p></span></p>
<div class="MsoNormal"
style="text-align:center" align="center"><span
style="font-size:12.0pt;font-family:"Times New
Roman","serif""
lang="EN-US">
<hr align="center" size="2" width="100%">
</span></div>
<div>
<p class="MsoNormal"
style="margin-bottom:12.0pt"><span
style="font-size:8.0pt" lang="EN-US"><br>
Erbe Elektromedizin GmbH Firmensitz:
72072 Tuebingen Geschaeftsfuehrer:
Christian O. Erbe, Reiner Thede
Registergericht: Stuttgart HRB 380137</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
</blockquote>
</div>
<div class="MsoNormal" style="text-align:center"
align="center"><span
style="font-size:12.0pt;font-family:"Times
New Roman","serif""
lang="EN-US">
<hr align="center" size="2" width="100%">
</span></div>
<div>
<p class="MsoNormal"
style="margin-bottom:12.0pt"><span
style="font-size:8.0pt" lang="EN-US"><br>
Erbe Elektromedizin GmbH Firmensitz: 72072
Tuebingen Geschaeftsfuehrer: Christian O.
Erbe, Reiner Thede Registergericht:
Stuttgart HRB 380137</span><span
lang="EN-US"><o:p></o:p></span></p>
</div>
</blockquote>
</div>
<div class="MsoNormal" style="text-align:center"
align="center"><span
style="font-size:12.0pt;font-family:"Times
New Roman","serif"" lang="EN-US">
<hr align="center" size="2" width="100%">
</span></div>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span
style="font-size:8.0pt" lang="EN-US"><br>
Erbe Elektromedizin GmbH Firmensitz: 72072
Tuebingen Geschaeftsfuehrer: Christian O. Erbe,
Reiner Thede Registergericht: Stuttgart HRB
380137</span><span lang="EN-US"><o:p></o:p></span></p>
</div>
</blockquote>
</div>
<div class="MsoNormal" style="text-align:center"
align="center"><span
style="font-size:12.0pt;font-family:"Times New
Roman","serif"" lang="EN-US">
<hr align="center" size="2" width="100%">
</span></div>
<div>
<p class="MsoNormal" style="margin-bottom:12.0pt"><span
style="font-size:8.0pt" lang="EN-US"><br>
Erbe Elektromedizin GmbH Firmensitz: 72072 Tuebingen
Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
Registergericht: Stuttgart HRB 380137<o:p></o:p></span></p>
</div>
</blockquote>
</div>
</div>
</div>
<hr>
<div style="font-size:8pt; font-family: 'Calibri',sans-serif;"><br>
Erbe Elektromedizin GmbH Firmensitz: 72072 Tuebingen
Geschaeftsfuehrer: Christian O. Erbe, Reiner Thede
Registergericht: Stuttgart HRB 380137<br>
<br>
</div>
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