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On Detecting the Shape of an Unknown Object in an Electric Field

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Details

Original languageEnglish
Title of host publicationProgress in Industrial Mathematics at ECMI 2014
EditorsG. Russo, V. Capasso, G. Nicosia, V. Romano
PublisherSpringer International Publishing
ISBN (Electronic)978-3-319-23413-7
ISBN (Print)978-3-319-23412-0
DOIs
Publication statusPublished - 2016
Publication typeA4 Article in a conference publication
EventEUROPEAN CONFERENCE ON MATHEMATICS FOR INDUSTRY -
Duration: 1 Jan 2000 → …

Publication series

NameMathematics in Industry
PublisherSpringer-Verlag
Volume22
ISSN (Electronic)1612-3956

Conference

ConferenceEUROPEAN CONFERENCE ON MATHEMATICS FOR INDUSTRY
Abbreviated titleECMI
Period1/01/00 → …

Abstract

The problem discussed in this paper is detecting the shape of an unknown object in a 2-dimensional static electric field. For simplicity, the problem is defined in a partially rectangular domain, where on a part of the boundary the potential and/or its normal derivative are known. On the other part of the boundary the boundary curve is unknown, and this curve is to be determined. The unknown part of the boundary curve describes the shape of the unknown object.
The problem is defined in the complex plane by an analytic function w=f(z) = u(x,y)+iv(x,y) with the potential u as its real part. Then the inverse function is given as f^{-1}(w) = x(u,v)+iy(u,v), where the functions x and y are harmonic in a rectangle with an unknown boundary condition on one boundary. The alternating-field technique is used to solve the unknown boundary condition.

Keywords

  • free boundary problem, industrial mathematics

Publication forum classification

Field of science, Statistics Finland