Extended-domain-eigenfunction method (EDEM): a study of ill posedness and regularization
2013 (English)In: Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, Vol. 46, no 8Article in journal (Refereed) Published
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
Medical and Health Sciences
IdentifiersURN: urn:nbn:se:liu:diva-89796DOI: 10.1088/1751-8113/46/8/085207ISI: 000314821900010OAI: oai:DiVA.org:liu-89796DiVA: diva2:609797
Funding Agencies|Swedish Research Council||Australian Postgraduate Award||2013-03-072013-03-072013-03-07