Solution of elliptic inverse problems using the Poincaré-Steklov operator

Issue title: Special Volume: Proceedings of the eleventh International Symposium on Applied Electromagnetics and Mechanics ISEM-Versailles ISEM 03

Article type: Research Article

Authors: Kharytonov, A.A.^a

Affiliations: [a] Institute of Experimental and Applied Physics, Kiel University, Olshausenstrasse 40, D-24098 Kiel, Germany. Tel.: +49 431 880 3928; Fax: +49 431 880 1685; E-mail: exp503@physik.uni-kiel.de

Abstract: We consider some inverse boundary problems which are to determine the coefficients or functions of elliptic differential equations inside the domain Ω from a knowledge of boundary conditions (the Cauchy data) on ∂Ω. An algorithm for the numerical solution of such problems is presented. The iterative methods and the theory of the Poincaré-Steklov operator are the basis of our consideration. This algorithm can be used for the solution of the inverse conductivity problem and for the determination of the potential in the Schrödinger equation.

Keywords: inverse problem, parameter identification, Poincaré-Steklov operator, Oseen linearization, Schrödinger equation

DOI: 10.3233/JAE-2004-537

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 19, no. 1-4, pp. 63-67, 2004