<html xmlns:v="urn:schemas-microsoft-com:vml" xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=us-ascii">
<meta name="Generator" content="Microsoft Word 12 (filtered medium)">
<style id="owaParaStyle"><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
@font-face
{font-family:Tahoma;
panose-1:2 11 6 4 3 5 4 4 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
a:link, span.MsoHyperlink
{mso-style-priority:99;
color:blue;
text-decoration:underline;}
a:visited, span.MsoHyperlinkFollowed
{mso-style-priority:99;
color:purple;
text-decoration:underline;}
p
{mso-style-priority:99;
margin:0cm;
margin-bottom:.0001pt;
font-size:12.0pt;
font-family:"Times New Roman","serif";}
span.E-MailFormatvorlage18
{mso-style-type:personal-reply;
font-family:"Calibri","sans-serif";
color:#1F497D;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:612.0pt 792.0pt;
margin:70.85pt 70.85pt 2.0cm 70.85pt;}
div.WordSection1
{page:WordSection1;}
--></style><!--[if gte mso 9]><xml>
<o:shapedefaults v:ext="edit" spidmax="1026" />
</xml><![endif]--><!--[if gte mso 9]><xml>
<o:shapelayout v:ext="edit">
<o:idmap v:ext="edit" data="1" />
</o:shapelayout></xml><![endif]-->
</head>
<body lang="DE" link="blue" vlink="purple">
<div class="WordSection1">
<p class="MsoNormal"><span lang="EN-US" style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Hi John,<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"><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:<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<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.<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"><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<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).
<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"><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 2<sup>nd</sup> formulation with B:<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<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)<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.<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.<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"><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,<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<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"><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"><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"><o:p> </o:p></span></p>
<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"">From:</span></b><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif""> 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<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<div>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">Hello everyone,<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span 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:<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span 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 ; }<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">However, if I substitute B into my equation:
<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span 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 ; }<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span 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.
<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">BR,
<o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black"> <o:p></o:p></span></p>
<p><span style="font-size:10.0pt;font-family:"Tahoma","sans-serif";color:black">John<o:p></o:p></span></p>
</div>
</div>
</body>
</html>