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<p class="MsoNormal"><span lang="EN-US">Dear GetDP community,<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">I am facing a problem with the implementation of constraints in a magnetodynamical model : I basically have two constraints to enforce and they interact badly in a way that is almost unpredictable, causing erroneous results.
First, I enclose with this mail a schematics to explain the problem. To simplify, I am considering one fourth of the cross-section (the top-right part) of a dipole in 2D. I have a conducting domain that is carrying a known current I in the Z-direction (note
that the current density itself is not set). There is a symmetry with the X-axis, the lower-right corner should also have a conductor carrying I, and with the Y-axis, the top-left and bottom-left corner having each a conductor with a –I current.<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">To achieve this, I am using the H-Phi formulation and I use two separate constraints :<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US">One on the current flowing through the upper-right conductor. This is done by generating à cut in the air with the Cohomology module, then I create a DoF on it and constraining it to be my total current.<o:p></o:p></span></p>
<p class="MsoListParagraph" style="text-indent:-18.0pt;mso-list:l0 level1 lfo2"><![if !supportLists]><span lang="EN-US" style="font-family:Symbol"><span style="mso-list:Ignore">·<span style="font:7.0pt "Times New Roman"">
</span></span></span><![endif]><span lang="EN-US">Second is a Phi = cst condition on the X-axis to generate the mirror symmetry.
<o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US">However, Cohomology generates its edge chain randomly and when it hits the X-axis, then the two constraints interact badly and mess the solution up. If I understand well, in this case, Phi should be equal to a constant
on the elements of the X-axis on one side of the cohomology cut and another constant on the other side, with the difference between the constants being the Jump in Phi over the cut. Am I correct with this ?
<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">I know that an option to circumvent the problem would be to model half of the windings instead of one fourth like I am doing now. By modeling the complete right side for example, I would get rid of the boundary condition
on the X-axis and thus of the problem. However, this also mean doubling the size of my model and I would like to avoid it if possible. Thus, I would like to know if someone knows how I could change the implementation of my constraints to get the correct effect.
Your help would be greatly appreciated.<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">Sincerely yours,<o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span style="font-family:"Tahoma",sans-serif;color:#000099;mso-fareast-language:FR">Guillaume DILASSER</span><span style="font-size:10.0pt;font-family:"Tahoma",sans-serif;color:#000099;mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial",sans-serif;color:#000099;mso-fareast-language:FR">Doctorant SACM / LEAS<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial",sans-serif;color:#000099;mso-fareast-language:FR">CEA - Centre de Saclay - Bât.123 - PC 319c</span><span style="color:#000099;mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial",sans-serif;color:#000099;mso-fareast-language:FR">91191 Gif sur Yvette Cedex - France -</span><span style="color:#000099;mso-fareast-language:FR"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial",sans-serif;color:#000099;mso-fareast-language:FR"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:7.5pt;font-family:"Arial",sans-serif;color:#000099;mso-fareast-language:FR"><a href="mailto:guillaume.dilasser@cea.fr"><span style="color:blue">guillaume.dilasser@cea.fr</span></a><o:p></o:p></span></p>
<p class="MsoNormal"><o:p> </o:p></p>
<p class="MsoNormal"><span lang="EN-US"><o:p></o:p></span></p>
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