| 1. |
- Aarao, J, et al.
(author)
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Extended-domain-eigenfunction method (EDEM): a study of ill posedness and regularization
- 2013
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In: Journal of Physics A. - : Institute of Physics. - 1751-8113 .- 1751-8121. ; 46:8
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Journal article (peer-reviewed)abstract
- 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.
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| 2. |
- Aarao, J, et al.
(author)
-
Numerical implementation of the EDEM for modified Helmholtz BVPs on annular domains
- 2011
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In: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. - : Elsevier Science B.V., Amsterdam.. - 0377-0427. ; 235:5, s. 1342-1353
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Journal article (peer-reviewed)abstract
- In a recent paper by the current authors a new methodology called the Extended-Domain-Eigenfunction-Method (EDEM) was proposed for solving elliptic boundary value problems on annular-like domains. In this paper we present and investigate one possible numerical algorithm to implement the EDEM. This algorithm is used to solve modified Helmholtz BVPs on annular-like domains. Two examples of annular-like domains are studied. The results and performance are compared with those of the well-known boundary element method (BEM). The high accuracy of the EDEM solutions and the superior efficiency of the EDEM over the BEM, make EDEM an excellent alternate candidate to use in the animation industry, where speed is a predominant requirement, and by the scientific community where accuracy is the paramount objective.
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| 3. |
- Aarao, J, et al.
(author)
-
The extended-domain-eigenfunction method for solving elliptic boundary value problems with annular domains
- 2010
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In: JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL. - : Iop. - 1751-8113 .- 1751-8121. ; 43:18, s. 185202-
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Journal article (peer-reviewed)abstract
- Standard analytical solutions to elliptic boundary value problems on asymmetric domains are rarely, if ever, obtainable. In this paper, we propose a solution technique wherein we embed the original domain into one with simple boundaries where the classical eigenfunction solution approach can be used. The solution in the larger domain, when restricted to the original domain, is then the solution of the original boundary value problem. We call this the extended-domain-eigenfunction method. To illustrate the methods strength and scope, we apply it to Laplaces equation on an annular-like domain.
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