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<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi Jonathan,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">it turned out that this kind of problem (nonlinear and time dependent)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">is more challenging than expected, but finally here comes the solution.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Just some remarks:<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">1) Dt in the Galerkin equation is actually not implemented. The simulator uses<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">DtDof instead. Therefore your original H-based formulation is calculated not<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">correctly. To circumvent this, the time derivative has to be calculated manually.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">2) All my tries to do this with the function AtAnteriorTimeStep did not succeed. It obviously<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">works not as I expected. But I’ve found a workaround: It’s easy to store the past H<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">in a separate quantity (I call it Hpast) and use it to build the time derivative.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">3) The function InterpolateAkima etc. should be called with a scalar value, not<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">a vector value. With a vector value it seems to work (no warning or error) but the result<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">is different. So I’m not sure what’s going on when you call it with a vector value...<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">4) In general it’s important to distinguish between scalar and vector values. E.g. the function B<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">should return a vector.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">5) The word JacNL tells GetDP that Dof{H} corresponds to the change in H in the iteration,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">not the unknown H itself. Unfortunately this is not documented very well in the reference<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">manual.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Please have a look in the pdf file where I’ve calculated the formulations for Picard’s and
<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Newton’s methods.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">6) In the corrected example from you (see attachments) there are now resolutions<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">for the H-based problem with Picard’s and Newton’s method, as well a B-based<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Newton resolution. (No warranty that they are correct. But I’ve made some<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">plausibility checks :-)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I hope this is of some help.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Cheers<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Michael<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><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";color:#1F497D"><o:p> </o:p></span></b></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Velasco Alvarado Jonathan [mailto:jonathan.velasco@aalto.fi]
<br>
<b>Sent:</b> Wednesday, October 31, 2012 10:04 AM<br>
<b>To:</b> Asam Michael (IFAG ATV BP PD 1 M1); getdp@geuz.org<br>
<b>Subject:</b> RE: Time-dependent non-linear problem and time derivatives</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Thank you again for your response.</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">I have tried to take the derivative manually in the function block and it still doesn't seem to work. Here below I show two ways I've used to take the derivative of the
magnetic flux density with respect to time (dBdt[Ir]). As you can see, in the first attempt I used the Dt function provided by GetDp, as that wouldn't work in my second attempt I used the $Dtime function, as advised before. </span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Function{<br>
.</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> .</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> .</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><br>
mu_non[Ir] = InterpolationAkima[$1]{ListAlt[h_mat2, mu_mat2]};<br>
B[Ir] = InterpolationAkima[$1]{ListAlt[h_mat2, b_mat2]};</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><br>
<strong><span style="font-family:"Tahoma","sans-serif""> dBdt[Ir] = Dt[B[$1]]; </span></strong></span><span style="color:black"><o:p></o:p></span></p>
<p><strong><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> dBdt[Ir] = (B[$1] - B[AtAnteriorTimeStep[$1,1]])/$DTime;</span></strong><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><br>
</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> dmudh [Ir] = dInterpolationAkima[$1]{ListAlt[h_mat2, mu_mat2]}; <br>
dbdh [Ir] = mu_non[$1]+Norm[$1]*dmudh[$1];</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> .</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> .</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> . <br>
}</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Formulation {</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> .</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> . </span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> . <br>
}</span><span style="color:black"><o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><br>
Equation {</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Galerkin { [ 1/sig[]* Dof{Curl H} , {Curl H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; } </span><span style="color:black"><o:p></o:p></span></p>
<p><strong><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Galerkin { [ dBdt[{H}] , {H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }</span></strong><b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"><br>
</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Galerkin { JacNL [dbdh[{H}] * Dof{H} , {H}] ; In Stack ; Jacobian JMat ; Integration GaussIntegration ; }<br>
}<br>
} <br>
}</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Any ideas of why this may not be working?
</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Best Regards,</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Jonathan</span><span style="color:black"><o:p></o:p></span></p>
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<div class="MsoNormal" align="center" style="text-align:center"><span lang="DE" style="color:black">
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> michael.asam@infineon.com
[michael.asam@infineon.com]<br>
<b>Sent:</b> Monday, October 15, 2012 12:07 PM<br>
<b>To:</b> Velasco Alvarado Jonathan; getdp@geuz.org<br>
<b>Subject:</b> RE: Time-dependent non-linear problem and time derivatives</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi John,</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I think the missing Dt implementation is not the root cause for the not working B formulation.</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">GetDP uses DtDof instead which will deliver a result (in your case probably the wrong one).</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The calculation of the time derivative in a function could be done by using there the function
</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Dt (see manual page 16) or you can calculate it manually by using the variable $DTime (page 21).</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The main problem is that you give the Dof as an argument to a function: B[Dof{H}].</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">I think, this is not allowed. (Otherwise you could build nonlinear Galerkin equations ...)</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Instead you should give H from the last iteration to the function: B[{H}].</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Dof{H} means the unknown values of H you are looking for in the actual iteration</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">in contrast to {H}, which represents the known values from the last nonlinear iteration.</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">(Have a look in your first formulation where the usage of {H} and Dof{H} is correct.)</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Cheers</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Michael</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
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<p class="MsoNormal"><b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span lang="EN-US" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> Velasco Alvarado Jonathan [mailto:jonathan.velasco@aalto.fi]
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<b>Sent:</b> Monday, October 15, 2012 9:34 AM<br>
<b>To:</b> Asam Michael (IFAG ATV BP PD 1 M1); getdp@geuz.org<br>
<b>Subject:</b> RE: Time-dependent non-linear problem and time derivatives</span><span style="color:black"><o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Hi Michael,</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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?
</span><span style="color:black"><o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Best Regards,</span><span style="color:black"><o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Jonathan</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> 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</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi John,</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">regarding the first formulation:</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The term-op-type Dt is actually not implemented. GetDP uses DtDof instead, which is</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">in many cases wrong. The newest version (nightly build) gives here now a warning.</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">You can overcome this problem when you calculate the time derivative of the complete</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">(nonlinear) expression in a separate function (located in the Function{ ... } block).
</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Regarding the 2<sup>nd</sup> formulation with B:</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">The Galerkin equation has to be linear with respect to the Dof, which is not the case</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">here. You have to linearize it, either with functional iterations (Picard iteration)</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">or with Newton’s method.</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Please have a look in the reference manual at page 22, chapter 4.10 Fields -> Dof.</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="color:black"> <o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Best regards,</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Michael</span><span style="color:black"><o:p></o:p></span></p>
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<p class="MsoNormal"><b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">From:</span></b><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> 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><span style="color:black"><o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Hello everyone,</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">However, if I substitute B into my equation:
</span><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">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><span style="color:black"><o:p></o:p></span></p>
<p><span style="color:black"> <o:p></o:p></span></p>
<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">BR,
</span><span style="color:black"><o:p></o:p></span></p>
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<p><span lang="DE" style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">John</span><span style="color:black"><o:p></o:p></span></p>
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