{"id":113,"date":"2011-07-09T10:01:22","date_gmt":"2011-07-09T10:01:22","guid":{"rendered":"http:\/\/www.timokorthals.de\/?p=113"},"modified":"2011-07-09T10:01:22","modified_gmt":"2011-07-09T10:01:22","slug":"the-kelvin-transformation","status":"publish","type":"post","link":"http:\/\/www.timokorthals.de\/?p=113","title":{"rendered":"The Kelvin transformation"},"content":{"rendered":"

This post is about some former work for a seminar, I did in the third term. It’s about the problem in FEM-simulation, when you want to simulate a charge and you have neither boundary nor boundaryconditions. The solution here, formulated by Kelvin was, to separete the infinite simulationroom in an inner finite circle and an outer infinite circular disk. Once you’ve done this, you can transform the outer infinite circular disk into an finite circle of the same size of the inner one, regarding:
\n R(r) = \\frac{o^{2}}{r}\\quad\\forall~ r > o
\nnow you can discretisice the “infinite” circular disk in an arbitrary way but with the center as infinite and with the boundarycondition zero (with the assumption that everything dissapears in the in the infinty) .<\/p>\n

\"\"<\/a>
Potential field of two charges<\/figcaption><\/figure>\n

The following files may help to understand the Kelvin transformation. I also wrote an article about the FEM-simulation using finite defferences. So Enjoy reading:<\/strong><\/p>\n

Kelvin_Transfomation<\/a><\/p>\n

Kelvin_Transfomation_Handout<\/a><\/p>\n

Kelvin_Transformation_Praesentation<\/a><\/p>\n

This is the MATLAB-code for the examples in the documents and of course for the Kelvin transformation<\/strong><\/p>\n

MATLAB-code<\/a><\/p>\n

LaTeX source of the documents:<\/strong><\/p>\n

Kelvin_Transformation_Praesentation_LaTeX<\/a><\/p>\n

Kelvin_Transfomation_Handout_LaTeX<\/a><\/p>\n

Kelvin_Transfomation_LaTeX<\/a><\/p>\n

 <\/p>\n

 <\/p>\n","protected":false},"excerpt":{"rendered":"

This post is about some former work for a seminar, I did in the third term. It’s about the problem in FEM-simulation, when you want to simulate a charge and you have neither boundary nor boundaryconditions. The solution here, formulated by Kelvin was, to separete the infinite simulationroom in an inner finite circle and an … Continue reading The Kelvin transformation<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[1,6],"tags":[],"_links":{"self":[{"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=\/wp\/v2\/posts\/113"}],"collection":[{"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=113"}],"version-history":[{"count":0,"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=\/wp\/v2\/posts\/113\/revisions"}],"wp:attachment":[{"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=113"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=113"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.timokorthals.de\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=113"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}