{"id":738,"date":"2021-06-28T12:27:28","date_gmt":"2021-06-28T10:27:28","guid":{"rendered":"https:\/\/www.hsu-hh.de\/tet\/?page_id=738"},"modified":"2021-06-28T12:32:13","modified_gmt":"2021-06-28T10:32:13","slug":"extreme-point-method-for-electrostatic-problems","status":"publish","type":"page","link":"https:\/\/www.hsu-hh.de\/tet\/en\/extreme-point-method-for-electrostatic-problems","title":{"rendered":""},"content":{"rendered":"\n<p><strong>Extreme point method for electrostatic problems<\/strong><\/p>\n\n\n\n<p>The external field of an electrically charged body can be calculated approximately by superposing a finite number of electrical charges that are in an equilibrium on its surface. This equilibrium is characterized by a minimum of the electrostatic energy of the system. Due to the slow convergence of the superimposed point potentials against the electrostatic potential in the outer space of the charged body (~ 1 \/ \u221an, n: number of charge carriers), this method in its original form is not competitive with other methods for numerical field calculation, such as edge integral methods.<\/p>\n\n\n\n<p>The underlying idea is to subdivide the approximating point cloud into two classes and only consider interactions between &#8222;charges&#8220; of the different classes. The geometric duality of the two classes ensures that the points in each class have a good distribution. A two-dimensional analogue of this method was already investigated by K. Menke in the last century. In the latter case, a rapid asymptotic decay of the error on smooth curves in the order of magnitude could also be demonstrated. At this speed of convergence, a few points are sufficient to represent the outer field precisely, so that this procedure can be used efficiently as a formal method for numerical field calculation.<\/p>\n\n\n\n<p>An analysis shows that the largest proportion of errors arises from the fact that when calculating the potential of a finite charge distribution the energy of the charge carriers in their own field would be infinite and cannot be taken into account.<\/p>\n\n\n\n<p>The use of extreme point methods is by no means limited to static problems: By expanding the minimization task for determining the extreme points by an additional time-dependent external field, it is possible to take into account a coupling of transient effects within the enclosed volume with the external field. In particular, the coupling of a transient finite element simulation within the volume with the extreme point method is promising.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"711\" height=\"729\" src=\"https:\/\/www.hsu-hh.de\/tet\/wp-content\/uploads\/sites\/673\/2017\/11\/Extremalpunkte.jpg\" data-credit=\"HSU\/TET\" alt=\"Extremalpunkte\" class=\"wp-image-271\" srcset=\"https:\/\/www.hsu-hh.de\/tet\/wp-content\/uploads\/sites\/673\/2017\/11\/Extremalpunkte.jpg 711w, https:\/\/www.hsu-hh.de\/tet\/wp-content\/uploads\/sites\/673\/2017\/11\/Extremalpunkte-293x300.jpg 293w\" sizes=\"auto, (max-width: 711px) 100vw, 711px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Extreme point method for electrostatic problems The external field of an electrically charged body can be calculated approximately by superposing a finite number of electrical charges that are in an [&hellip;]<\/p>\n","protected":false},"author":794,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-738","page","type-page","status-publish","hentry","category-research"],"_links":{"self":[{"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/pages\/738","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/users\/794"}],"replies":[{"embeddable":true,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/comments?post=738"}],"version-history":[{"count":6,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/pages\/738\/revisions"}],"predecessor-version":[{"id":748,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/pages\/738\/revisions\/748"}],"wp:attachment":[{"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/media?parent=738"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/categories?post=738"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.hsu-hh.de\/tet\/wp-json\/wp\/v2\/tags?post=738"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}