this paper we consider the case where the goal is to find a number of small objects (inhomogeneities) inside an otherwise known conductor. Taking advantage of the smallness of the inhomogeneities, we can use asymptotic analysis to design a direct (i.e., noniterative) reconstruction algorithm for the determination of their locations. The viability of this direct approach is documented by numerical examples. Mathematics Subject Classification (2000): 65N21, 35R30, 35C20 1 Introduction Techniques for recovering the conductivity distribution inside a body from measurements of current flows and voltages on the body's surface go under the heading of electrical impedance tomography (EIT). The vast and growing literature reflects the many possible applications of this method, e.g. for medical diagnosis or nondestructive evaluation of materials. For further details we refer to the recent survey paper [8]. Since the underlying inverse problem is nonlinear and severely ill-posed it is generally advisable to incorporate all available a-priori knowledge ? Supported by the Deutsche Forschungsgemeinschaft (DFG) under grant HA 2121/2-3 ?? Supported by the National Science Foundation under grant DMS-0072556 2 Martin Br uhl, Martin Hanke, Michael S. Vogelius about the unknown conductivity. One such type of knowledge could be that the body consists of a smooth background (of known conductivity) containing a number of unknown, small inclusions with a significantly higher or lower conductivity. This situation arises for example in mine detection, where one tries to locate the position of buried anti-personnel mines from electromagnetic data. The mines have a higher (metal) or lower (plastic) conductivity than the surrounding soil and they are small relative to the area being imaged....

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We derive asymptotic formuli for two dimensional steady state voltage potentials associated with thin, "curve-like" conductivity imperfections. Our derivation is formal, and based on asymptotic matching of terms in an appropriate set of integral equations. In combination with the formuli (rigorously) derived in [3] for imperfections of small diameter, these new formuli cover the generic imperfections of small area in two dimensions. 1 Introduction The aim of this paper is to advance the development of asymptotic formuli for steady state voltage potentials associated with a finite number of small imperfections inside an otherwise uniform conductor. Our interest in such formuli owes to the fact, that they provide extremely powerful tools to solve the inverse problem of identifying the conductivity imperfections, given electric boundary measurements (cf. [3], [7]). We have already in [3] derived formuli of this kind for conductivity imperfections of the form # # = # N i=1 (x i + #B i ...

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Report no. OxPDE-08/10 Thin cylindrical conductivity inclusions in a 3-dimensional domain: polarization tensor and

the perturbation of the electromagnetic energy due to the

Recovery of small electromagnetic inhomogeneities from boundary measurements in time-dependent Maxwell’s equations