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

Houde Han, Leevan LING*, Tomoya Takeuchi

*Corresponding author for this work

Research output: Contribution to journalJournal articlepeer-review

20 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)878-896
Number of pages19
JournalCommunications in Computational Physics
Issue number4
Publication statusPublished - Apr 2011

Scopus Subject Areas

  • Physics and Astronomy (miscellaneous)

User-Defined Keywords

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


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