Recovery of an interface from boundary measurement in an elliptic differential equation
type: Item
instance of: scholarly article
title: Recovery of an interface from boundary measurement in an elliptic differential equation
zbMATH Open document ID: 1259.65164
author: W. Fang
author: Suxing Zeng
published in: Advances in Computational Mathematics
publication date: 2012-05-23T00:00:00Z
review text: Let \(\Omega\) be a smooth bounded domain in \(\mathbb R^{2}\) and \(S\subset \Omega\) a subdomain. This paper considers the elliptic boundary value problem \(\Delta u(x)=p(x)u(x)\) in \(\Omega\), \(\partial u(x )/\partial \nu=g(x)\) on \(\partial \Omega\), where \(\nu\) denotes the unit outward normal to \(\partial \Omega\) and \(p(x)=p_{0}\chi_{S}(x)\), which arises from a semiconductor transistor model. This paper studies the inverse problem of recovering an interior interface from a boundary measurement in this boundary value problem. The authors set up a nonlinear least-squares formulation for solving the inverse problem, and establish the necessary derivatives with respect to the interface. Then they propose both the Gauss-Newton iterative method and the conjugate gradient method for the least-squares problem and present implementation of these methods using integral equations.
reviewed by: Riikka Korte
Mathematics Subject Classification ID: 65N21
Mathematics Subject Classification ID: 35J25
Mathematics Subject Classification ID: 35R30
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 82D37
zbMATH DE Number: 6038156
zbMATH Keywords: elliptic boundary value problem
zbMATH Keywords: semiconductor transistor model
zbMATH Keywords: inverse problem
zbMATH Keywords: nonlinear least-squares
zbMATH Keywords: Gauss-Newton iterative method
zbMATH Keywords: conjugate gradient method
Wikidata QID: Q115384789
MaRDI profile type: Publication
full work available at URL: s10444-011-9204-5
OpenAlex ID: W2034708348
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DOI: 10.1007/S10444-011-9204-5
description: scientific article; zbMATH DE number 6038156