oru.sePublications
Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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
A dynamical regularization algorithm for solving inverse source problems of elliptic partial differential equations
Örebro University, School of Science and Technology. Faculty of Mathematics, Chemnitz University of Technology, Chemnitz, Germany. (Mathematics)ORCID iD: 0000-0003-4023-6352
Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing, People's Republic of China.
Department of Mathematics, Zhejiang University, Hangzhou, People's Republic of China.
Örebro University, School of Science and Technology.ORCID iD: 0000-0003-0332-2315
2018 (English)In: Inverse Problems, ISSN 0266-5611, E-ISSN 1361-6420, Vol. 34, no 6, article id 065001Article in journal (Refereed) Published
Abstract [en]

This study considers the inverse source problem for elliptic partial differential equations with both Dirichlet and Neumann boundary data. The unknown source term is to be determined by additional boundary conditions. Unlike the existing methods found in the literature, which usually employ the first-order in time gradient-like system (such as the steepest descent methods) for numerically solving the regularized optimization problem with a fixed regularization parameter, we propose a novel method with a second-order in time dissipative gradient-like system and a dynamical selected regularization parameter. A damped symplectic scheme is proposed for the numerical solution. Theoretical analysis is given for both the continuous model and the numerical algorithm. Several numerical examples are provided to show the robustness of the proposed algorithm.

Place, publisher, year, edition, pages
Institute of Physics (IOP), 2018. Vol. 34, no 6, article id 065001
Keywords [en]
inverse source problems, dynamical system, regularization, convergence, symplectic method
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:oru:diva-66813DOI: 10.1088/1361-6420/aaba85ISI: 000431055900001OAI: oai:DiVA.org:oru-66813DiVA, id: diva2:1202572
Funder
Knowledge Foundation, 20170059
Note

Funding Agencies:

Alexander von Humboldt foundation  

Natural Science Foundation of China  11401304  11571311

Available from: 2018-04-27 Created: 2018-04-27 Last updated: 2018-05-14Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full text

Authority records BETA

Zhang, YeGulliksson, Mårten

Search in DiVA

By author/editor
Zhang, YeGulliksson, Mårten
By organisation
School of Science and Technology
In the same journal
Inverse Problems
Computational Mathematics

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 2358 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • 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