Source supports in electrostatics
type: Item
instance of: scholarly article
title: Source supports in electrostatics
zbMATH Open document ID: 1152.35111
author: Martin Hanke
author: Nuutti Hyvönen
author: Manfred Lehn
author: Stefanie Reusswig
published in: BIT
publication date: 2008-09-12T00:00:00Z
review text: The paper deals with the inverse source problem of electrostatic in a bounded and convex domain in \({\mathbb R}^2\) with compactly supported source, i.e., the problem of reconstructing the source term in the Poisson equation supplemented by the homogeneous Neumann boundary conditions, from the given Dirichlet boundary values. By comparing the dimensions, it is obvious that the knowledge of the Dirichlet data does not suffice to reconstruct uniquely the source function. Moreover, not even the support of the source can be determined. In the paper, the authors try to determine the smallest set that carries the source which is compatible with the given data. For this, the concept of the convex scattering support developed in the series of works by Kusiak and Sylvester is adopted for the case of electrostatics in a bounded domain. Namely, the authors introduce the notion of discoidal source support, i.e., the smallest set made up by the intersection of discs within the domain, which carries a source compatible with the given data. Numerical examples are provided in the case of the unit disk.
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N21
zbMATH DE Number: 5343404
zbMATH Keywords: inverse source problem
zbMATH Keywords: scattering support
zbMATH Keywords: source support
reviewed by: Dmitry Shepelsky
MaRDI profile type: Publication
full work available at URL: s10543-008-0172-1
OpenAlex ID: W2093848116
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DOI: 10.1007/S10543-008-0172-1
description: scientific article; zbMATH DE number 5343404