Seminar in Numerical Analysis: Martin Hanke-Bourgeois (Universität Mainz)

Small volume asymptotics for elliptic equations and their use in impedance tomography

We reconsider the impact of small volume perturbations of the conductivity coefficient of second order elliptic equations in divergence form. The asymptotic expansion of the associated Neumann-Dirichlet operators on bounded domains allows the development and analysis of sophisticated algorithms to solve corresponding inverse boundary value problems of impedance tomography. Examples of such algorithms are the MUSIC scheme and the topological derivative. Novel applications include the incorporation of discrete electrode models and the exploitation of multiple driving frequencies.

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