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Extended-domain-eigenfunction method (EDEM): a study of ill posedness and regularization
University of S Australia, Australia .
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
University of S Australia, Australia .
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 46, no 8Article in journal (Refereed) Published
Abstract [en]

The extended-domain-eigenfunction method (EDEM) proposed for solving elliptic boundary value problems on annular-like domains requires an inversion process. The procedure thus represents an ill-posed problem, whose numerical solution involves an ill-conditioned system of equations. In this paper, the ill-posed nature of EDEM is studied and numerical solutions based on regularization schemes are considered. It is shown that the EDEM solution methodology lends itself naturally to a formulation in terms of the well-known iterative Landweber method and the more general and faster converging semi-iterative regularization schemes. Theoretical details and numerical results of the regularization schemes are presented for the case of the two-dimensional Laplace operator on annular domains.

Place, publisher, year, edition, pages
Institute of Physics , 2013. Vol. 46, no 8
National Category
Medical and Health Sciences
Identifiers
URN: urn:nbn:se:liu:diva-89796DOI: 10.1088/1751-8113/46/8/085207ISI: 000314821900010OAI: oai:DiVA.org:liu-89796DiVA: diva2:609797
Note

Funding Agencies|Swedish Research Council||Australian Postgraduate Award||

Available from: 2013-03-07 Created: 2013-03-07 Last updated: 2013-03-07

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