http://dx.doi.org/10.4208/cicp.200110.060910a">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

An energy regularization for Cauchy problems of Laplace equation in annulus domain

Language

English

Abstract

Detecting corrosion by electrical field can be modeled by a Cauchy problem of Laplace equation in annulus domain under the assumption that the thickness of the pipe is relatively small compared with the radius of the pipe. The interior surface of the pipe is inaccessible and the nondestructive detection is solely based on measurements from the outer layer. The Cauchy problem for an elliptic equation is a typical ill-posed problem whose solution does not depend continuously on the boundary data. In this work, we assume that themeasurements are available on the whole outer boundary on an annulus domain. By imposing reasonable assumptions, the theoretical goal here is to derive the stabilities of the Cauchy solutions and an energy regularization method. Relationship between the proposed energy regularization method and the Tikhonov regularization with Morozov principle is also given. A novel numerical algorithm is proposed and numerical examples are given. © 2011 Global-Science Press.

Keywords

Error bounds, Inverse problem, Method of fundamental solution, Stability, Tikhonov regularization

Publication Date

2010

Source Publication Title

Communications in Computational Physics

Volume

9

Issue

4

Start Page

878

End Page

896

Publisher

Global Science Press

ISSN (print)

18152406

ISSN (electronic)

19917120

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