IJPAM: Volume 90, No. 3 (2014)

APPLICATION OF CORE IDENTIFICATION TO
STAR-SHAPE CONSTANT CONDUCTIVITY INCLUSION

Agah D. Garnadi
Department of Mathematics
Faculty of Mathematics and Natural Sciences
Bogor Agricultural University
Jl. Meranti, Kampus IPB Darmaga, Bogor, 16680, INDONESIA


Abstract. The problem of determining the interface separating a constant conductivity inclusion with star-shaped support from boundary measurement data of a solution of the corresponding PDEs is considered. An equivalent statement as a nonlinear integral equation is obtained. The problem is analyzed and implemented numerically using truncated Fourier series expansion.

It is also verified that the Fréchet derivative at fixed circular support is a compact operator, this demonstrate the problem is ill-posed. Furthermore, its singular systems is explicitely obtained which indicating the degree of ill-posedness of the problem is severely ill-posed.

Numerical experiments based on simplified iteratively regularized Gauss-Newton method (sIRGNM) are presented.

Received: May 30, 2011

AMS Subject Classification: 31A25, 35R30, 65N21

Key Words and Phrases: impedance tomography, inverse source problem, nonlinear integral equation, Fourier series expansion, simplified regularized Gauss-Newton

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DOI: 10.12732/ijpam.v90i3.1 How to cite this paper?
Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2014
Volume: 90
Issue: 3