<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=utf-8">
<meta name="Generator" content="Microsoft Word 12 (filtered medium)">
<style><!--
/* 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;
mso-margin-top-alt:auto;
margin-right:0cm;
mso-margin-bottom-alt:auto;
margin-left:0cm;
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 Jochen,<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 could try to use higher order basis functions. Preferably you should use<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">a P adaption instead of using globally the same order.<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 the Wiki for an example:<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"><a href="https://geuz.org/trac/getdp/wiki/DualFormulations">https://geuz.org/trac/getdp/wiki/DualFormulations</a><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 best is to combine H and P adaption.<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">One additional note:<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">Of course there is always an error by the discretisation of the round shape by plane<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">face elements. Unfortunately GetDP is not able to handle geometrical higher order
<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">elements...<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">Have a nice day!<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>
<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""> mail@jchn.de [mailto:mail@jchn.de]
<br>
<b>Sent:</b> Thursday, August 16, 2012 11:15 AM<br>
<b>To:</b> Asam Michael (IFAG ATV BP PD 1 M1); getdp@geuz.org<br>
<b>Subject:</b> Re: Electrokinetic - GetDP vs. Analytical Solution<o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><o:p> </o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"><a href="mailto:michael.asam@infineon.com">michael.asam@infineon.com</a> hat am 6. August 2012 um 11:55 geschrieben:<br>
<br>
> Hi Jochen,<br>
> <br>
> sorry for the late response.<br>
> The deviation is due to an inadequate mesh-size because the characteristic<br>
> length varies linearly between the two electrodes, whereas the E field is<br>
> proportional to r^-2.<br>
> So the best is to use a field in Gmsh to specify the mesh size by<br>
> an equation, or in case of more complex geometries do adaptive meshing.<br>
> <br>
> Please find attached a modification of your example for adaptive meshing.<br>
> As your geometry is axisymmetrical I've reduced it to 2D.<br>
> Just generate a mesh with Gmsh as usual and run GetDP. Do the post-<br>
> processing "GenerateAdaptionFile" and plot it in Gmsh.<br>
> There do a right click in the main window on the according view number<br>
> and choose "Apply As Background Mesh" and then mesh the geometry<br>
> once again.<br>
> With the adapted mesh size the result should be better.<br>
> For 3D the procedure should be similar.<br>
> <br>
> I hope this is of some help.<br>
> <br>
> Kind regards,<br>
> Michael<br>
><o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"> <o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">Dear Michael,<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"> <o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">thanks for your help!<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">Using your adaptive meshing example (2D), deviation from the analytical result can be decreased from 0,05% with linear variation of mesh size to 0,006% with applied adaptive meshing.<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">But when I transferred this procedure to my 3D problem, the deviation stayed at approx. 5%. What I had to do, was decreasing the outer radius from 200 m to 50 m and modeling just one quarter of the hemisphere to get
more elements per volume (see attached files). with approx. 600000 elements, I get a deviation of 1,03%, which can be decreased by adaptive meshing to 0,94%.<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">Now my RAM is on its limit (32 Bit Win7). Are there any other ways to increase the accuracy without increasing the element size?<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"> <o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">Greetings,<o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt"> <o:p></o:p></p>
<p style="margin:0cm;margin-bottom:.0001pt">Jochen<o:p></o:p></p>
</div>
</body>
</html>