Extended-domain-eigenfunction method (EDEM): a study of ill posedness and regularization

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

Miklavcic, Stan J.Linköpings universitet,Institutionen för teknik och naturvetenskap,Tekniska högskolan(Swepub:liu)stami86 (författare)
Ward, D A.University of S Australia, Australia (författare)
University of S Australia, AustraliaInstitutionen för teknik och naturvetenskap (creator_code:org_t)

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