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Dear all,<br>
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In the context of my Master Thesis, I would like to create a 3D model of wires used at high frequencies which means that the conductors will be affected by the skin effect. In order to restrict the number of elements despite this effect, I wanted to refine
the mesh exclusively in the skin around the inner conductors’ edges. There will be a rough mesh beyond the skin inside the wires and a rougher mesh in the air outside the wires.<br>
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I used an <em>Attractor</em> and a <em>Threshold </em>fields to achieve this goal. Their effects lead to the proper modeling of the skin in the wires. I restricted those effects inside the conductors using a <em>Restrict </em>field. Nevertheless, the characteristic
length in the air isn’t respected anymore and the air’s mesh seems to be affected by the fields despite the <em>Restrict, </em>particularly on the external boundary.<br>
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I wrote a code as a simple example (a wire in an air box) :<br>
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<font color="#006FC9">//Data and parameters</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> Xair = 0.005;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> Yair = 0.005;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> Zair = 0.01;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> lcAir = 0.001;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> lenght = 0.0075;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> rWire = 0.0005;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> Freq = DefineNumber [1e5, Name "Parameters/Frequence (Hz)" ];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> sigma_Cu = 6e7;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> skinDepth = Sqrt[1/(sigma_Cu*Pi*Freq*4e-7*Pi)];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> lcwire = skinDepth/2;</font><br>
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<font color="#006FC9">//Circle definition</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> center = newp ; Point(newp) = {0,0,- lenght/2,lcwire};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circlePoints[] += newp; Point(newp) = {rWire,0,- lenght/2,lcwire};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circlePoints[] += newp; Point(newp) = {0,-rWire,- lenght/2,lcwire};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circlePoints[] += newp; Point(newp) = {- rWire,0,- lenght/2,lcwire};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circlePoints[] += newp; Point(newp) = {0,rWire,- lenght/2,lcwire};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> edgeconds[] += newl; Circle(newl) = {circlePoints[0],center,circlePoints[1]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> edgeconds[] += newl; Circle(newl) = {circlePoints[1],center,circlePoints[2]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> edgeconds[] += newl; Circle(newl) = {circlePoints[2],center,circlePoints[3]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> edgeconds[] += newl; Circle(newl) = {circlePoints[3],center,circlePoints[0]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circlePoints[] = {};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> toSurf = newll; Line Loop (newll) = {edgeconds[]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += news; circleSurfaces_TX = news; Plane Surface(news) = {toSurf};</font><br>
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<font color="#006FC9">//Circle extrude</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> out[] = Extrude {0,0,lenght} {Surface{circleSurfaces_TX}; Layers{4};};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += out[0];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> circleVolume[] += out[1];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += out[2];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += out[3];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += out[4];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] += out[5];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holes[] += newsl; Surface Loop (newsl) = {holesSurf[]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> surfEdge[] += holesSurf[];</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> holesSurf[] = {}; out[] = {};</font><br>
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<font color="#006FC9">//Air box definition</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] = {};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {Xair,-Yair,-Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {Xair,Yair,-Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {Xair,Yair,Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {Xair,-Yair,Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {-Xair,-Yair,-Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {-Xair,Yair,-Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {-Xair,Yair,Zair,lcAir};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airPoints[] += newp; Point(newp) = {-Xair,-Yair,Zair,lcAir};</font><br>
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<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airLines[] += newl; Line(newl) = {airPoints[0],airPoints[1]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> {…}</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airLines[] += newl; Line(newl) = {airPoints[3],airPoints[7]};</font><br>
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<font color="#006FC9"> //Face 1</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> toSurf = newll; Line Loop (newll) = {airLines[0],airLines[1],airLines[2],airLines[3]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airSurface[] += news; Plane Surface(news) = {toSurf};</font><br>
</div>
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<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> {…}</font><br>
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<font color="#006FC9"> //Face 6</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> toSurf = newll; Line Loop (newll) = {-airLines[2],-airLines[11],-airLines[9],-airLines[6]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airSurface[] += news; Plane Surface(news) = {toSurf};</font><br>
</div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
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<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airSurfLoop = newsl; Surface Loop(newsl) = {airSurface[]};</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> airVolume = newv;</font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"> Volume(newv) = {airSurfLoop,holes[]};</font><br>
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<font color="#006FC9"> </font><font color="#006FC9"><strong>Field[1] = Attractor;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[1].NNodesByEdge = 50;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[1].EdgesList = {edgeconds[]};</strong></font></div>
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<font color="#006FC9"><strong><br>
</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2] = Threshold;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].IField = 1;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].LcMin = skinDepth/3;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].LcMax = 1.2*rWire;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].DistMin = lcwire/2;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].DistMax = rWire;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].Sigmoid = 0;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[2].StopAtDistMax = 1;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong><br>
</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[3] = Restrict;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[3].IField = 2;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Field[3].FacesList = {circleSurfaces_TX[]};</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Background Field = 3;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong><br>
</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Mesh.CharacteristicLengthFromPoints=1;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Mesh.CharacteristicLengthExtendFromBoundary=0;</strong></font></div>
<div style="font-family:Calibri,Arial,Helvetica,sans-serif; font-size:16px; margin-top:0px; margin-bottom:0px">
<font color="#006FC9"><strong> </strong></font><font color="#006FC9"><strong>Mesh.CharacteristicLengthFromCurvature=0;</strong></font></div>
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<strong><br>
</strong></div>
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The result looks as following :<br>
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<img size="567742" contenttype="image/png" contextid="img611124" tabindex="0" aria-haspopup="true" style="" aria-owns="_ariaId_425" aria-flowto="_ariaId_425" height="180" sizeoption="small" src="cid:536fbebb-f462-43c2-bd46-f25e223e2264"><img size="198714" contenttype="image/png" contextid="img914580" tabindex="0" aria-haspopup="true" style="" aria-owns="_ariaId_426" aria-flowto="_ariaId_426" height="180" sizeoption="small" src="cid:ae9a6672-99dd-4800-bc50-8d10d169fd15"><img size="191764" contenttype="image/png" contextid="img873700" tabindex="0" aria-haspopup="true" style="" aria-owns="_ariaId_427" aria-flowto="_ariaId_427" height="180" sizeoption="small" src="cid:05a6a46d-0a81-4e41-9e8c-276632a9a23b">
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Can someone help me to understand how can I solve this problem ?<br>
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Thank you in advance for your answer.<br>
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Regards,<br>
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Alexis Desmoort<br>
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University of Mons<br>
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