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<p>Hi Michael,</p>
<p> </p>
<p>Thanks for your prompt reply. I am actually interpolating B for each calculated value of H with my own measured data and I am building my Jacobian matrix using the JacNL function. The derivatives have been carried the way you've mentioned, as an external
calculation in the Function field by applying the dAkimaInterpolation scheme. The first formulation (using permeability) gives me reasonable results. The formulation with B doesn't work though still. The fact that Dt has not been implemented might be the reason.
How can the time derivative calculated in the Function block? </p>
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<p>Best Regards,</p>
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<p>Jonathan</p>
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<div style="DIRECTION: ltr" id="divRpF176225"><font color="#000000" size="2" face="Tahoma"><b>From:</b> michael.asam@infineon.com [michael.asam@infineon.com]<br>
<b>Sent:</b> Monday, October 15, 2012 9:57 AM<br>
<b>To:</b> Velasco Alvarado Jonathan; getdp@geuz.org<br>
<b>Subject:</b> RE: Time-dependent non-linear problem and time derivatives<br>
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<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">Hi John,</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">regarding the first formulation:</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">The term-op-type Dt is actually not implemented. GetDP uses DtDof instead, which is</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">in many cases wrong. The newest version (nightly build) gives here now a warning.</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">You can overcome this problem when you calculate the time derivative of the complete</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">(nonlinear) expression in a separate function (located in the Function{ ... } block).
</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">Regarding the 2<sup>nd</sup> formulation with B:</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">The Galerkin equation has to be linear with respect to the Dof, which is not the case</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">here. You have to linearize it, either with functional iterations (Picard iteration)</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">or with Newton’s method.</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">Please have a look in the reference manual at page 22, chapter 4.10 Fields -> Dof.</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">Best regards,</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US">Michael</span></p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
<p class="MsoNormal"><span style="FONT-FAMILY: 'Calibri','sans-serif'; COLOR: #1f497d; FONT-SIZE: 11pt" lang="EN-US"></span> </p>
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<p class="MsoNormal"><b><span style="FONT-FAMILY: 'Tahoma','sans-serif'; FONT-SIZE: 10pt">From:</span></b><span style="FONT-FAMILY: 'Tahoma','sans-serif'; FONT-SIZE: 10pt"> getdp-bounces@ace20.montefiore.ulg.ac.be [mailto:getdp-bounces@ace20.montefiore.ulg.ac.be]
<b>On Behalf Of </b>Velasco Alvarado Jonathan<br>
<b>Sent:</b> Friday, October 12, 2012 3:29 PM<br>
<b>To:</b> getdp@geuz.org<br>
<b>Subject:</b> [Getdp] Time-dependent non-linear problem and time derivatives</span></p>
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<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">Hello everyone,</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">I am currently working on a time-dependent non-linear magnetodynamic case. The permeability is my non-linear term but I don't want it to be included in my calculations for simplicity.
For this reason, I am using the flux density instead of permeability times field strength (B = mu*H). I am currently using this formulation (T-ohm) and it seems to work:</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">Galerkin { Dt[ mu_non[{H}]*Dof{H} , {H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }<br>
Galerkin { [ 1/sig[]* Dof{Curl H} , {Curl H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">However, if I substitute B into my equation:
</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">Galerkin { Dt[ B[Dof{H}] , {H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }<br>
Galerkin { [ 1/sig[* Dof{Curl H} , {Curl H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">It doesn't seem to do anything. I was wondering if there is a way to take the time derivative of my non-linear term in terms of a magnetic flux density as shown above.
</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">BR,
</span></p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt"></span> </p>
<p><span style="FONT-FAMILY: 'Tahoma','sans-serif'; COLOR: black; FONT-SIZE: 10pt">John</span></p>
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