Linear sampling methods for inverse boundary value problems in potential theory
type: Item
instance of: scholarly article
title: Linear sampling methods for inverse boundary value problems in potential theory
zbMATH Open document ID: 1020.65080
DOI: 10.1016/S0168-9274(02)00123-X
author: Rainer Kress
author: L. Kühn
published in: Applied Numerical Mathematics
publication date: 2003-03-10T00:00:00Z
review text: Let \(D\) be a bounded domain in \(\mathbb{R}^2\) with connected \(C^2\) boundary \(\partial D\) and outward unit normal \(\nu\) and \(y\) a point in \(\mathbb{R}^2\setminus \overline{D}\). Let \(\Phi(x,y) = 1/(2\pi)\ln(1/|x-y|)\) be the fundamental solution of Laplace's equation in \(\mathbb{R}^2\). Further, assume that \(B\) is a bounded domain with connected \(C^2\) boundary \(\partial B\) that contains \(\overline{D}\). The authors consider the inverse problem of determining the shape of \(D\), i.e., the boundary \(\partial D\) from the knowledge of \(w(x,y)\) for all \(x,y\) in \(\partial B\) with \(w(x,y)\) being a harmonic function in \(\mathbb{R}^2\setminus \overline{D}\) satisfying \(\partial w/\partial \nu = - \partial \Phi(\cdot,y)/\partial \nu\) on \(\partial D\). They develop linear sampling methods suggested by \textit{D. Colton} and \textit{A. Kirsch} [Inverse Probl. 12, 383-393 (1996; Zbl 0859.35133)] for the problem and describe both the mathematical foundation and the numerical implementation of the method.
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 35J05
Mathematics Subject Classification ID: 35R30
zbMATH DE Number: 1879057
zbMATH Keywords: Laplace's equation
zbMATH Keywords: inverse problem
zbMATH Keywords: linear sampling methods
reviewed by: Dinh Nho Hào
MaRDI profile type: Publication
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full work available at URL: s0168-9274(02)00123-x
OpenAlex ID: W2151980377
description: scientific article; zbMATH DE number 1879057