liu.seSearch for publications in DiVA
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
Linköping University, Department of Mathematics, Applied Mathematics. Linköping University, The Institute of Technology.
2012 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Let  be a bounded domain in Rn with a Lipschitz boundary Г divided into two parts Г0 and Г1 which do not intersect one another and have a common Lipschitz boundary. We consider the following Cauchy problem for the Helmholtz equation:

where k, the wave number, is a positive real constant, аv denotes the outward normal derivative, and f and g are specified Cauchy data on Г0. This problem is ill–posed in the sense that small errors in the Cauchy data f and g may blow up and cause a large error in the solution.

Alternating iterative algorithms for solving this problem are developed and studied. These algorithms are based on the alternating iterative schemes suggested by V.A. Kozlov and V. Maz’ya for solving ill–posed problems. Since these original alternating iterative algorithms diverge for large values of the constant k2 in the Helmholtz equation, we develop a modification of the alterating iterative algorithms that converges for all k2. We also perform numerical experiments that confirm that the proposed modification works.

Place, publisher, year, edition, pages
Linköping: Linköping University Electronic Press, 2012. , 6 p.
Series
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1530
National Category
Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-77300Local ID: LIU-TEK-LIC-2012:15ISBN: 978-91-7519-890-3 (print)OAI: oai:DiVA.org:liu-77300DiVA: diva2:526247
Presentation
2012-05-02, Nobel (BL32), B-huset, ing°ang 23, Campus Valla, Linköpings universitet, Linköping, 15:15 (English)
Opponent
Supervisors
Available from: 2012-05-11 Created: 2012-05-11 Last updated: 2012-06-04Bibliographically approved
List of papers
1. An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
Open this publication in new window or tab >>An alternating iterative procedure for the Cauchy problem for the Helmholtz equation
2014 (English)In: Inverse Problems in Science and Engineering, ISSN 1741-5977, E-ISSN 1741-5985, Vol. 22, no 1, 45-62 p.Article in journal (Refereed) Published
Abstract [en]

We present a modification of the alternating iterative method, which was introduced by V.A. Kozlov and V. Maz’ya in for solving the Cauchy problem for the Helmholtz equation in a Lipschitz domain. The method is implemented numerically using the finite difference method.

Place, publisher, year, edition, pages
Taylor & Francis, 2014
National Category
Mathematics
Identifiers
urn:nbn:se:liu:diva-77298 (URN)10.1080/17415977.2013.827181 (DOI)000328245900005 ()
Conference
6th International Conference "Inverse Problems: Modeling and Simulation", 21-26 May 2012, Antalya, Turkey
Available from: 2012-05-11 Created: 2012-05-11 Last updated: 2017-12-07Bibliographically approved

Open Access in DiVA

An alternating iterative procedure for the Cauchy problem for the Helmholtz equation(117 kB)648 downloads
File information
File name FULLTEXT01.pdfFile size 117 kBChecksum SHA-512
1d6431c42d5a87453d7e4c4f0daa7cf8c79fa367d81f41e8097bf3947edb0f2b60c0d2c3221185d5720e268fdf90c259739e8ae43be5a9cdfee484bdc2af3b94
Type fulltextMimetype application/pdf
omslag(48 kB)46 downloads
File information
File name COVER01.pdfFile size 48 kBChecksum SHA-512
5c7458f218840af341ff3197c8a6394633f30ff8afa310191212d2715531d6bf1af3659821e7d4e3a0d9f00eba4d35e721ec3d03da77d0271da880d25fa565b7
Type coverMimetype application/pdf

Authority records BETA

Mpinganzima, Lydie

Search in DiVA

By author/editor
Mpinganzima, Lydie
By organisation
Applied MathematicsThe Institute of Technology
Mathematics

Search outside of DiVA

GoogleGoogle Scholar
Total: 648 downloads
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

isbn
urn-nbn

Altmetric score

isbn
urn-nbn
Total: 929 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • oxford
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf