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Inverse Problems and Imaging (IPI)
 

Convex source support in half-plane

Pages: 429 - 448, Volume 4, Issue 3, August 2010      doi:10.3934/ipi.2010.4.429

 
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Lauri Harhanen - Aalto University, Department of Mathematics and Systems Analysis, P.O. Box 11100, FI-00076 Aalto, Finland (email)
Nuutti Hyvönen - Aalto University, Department of Mathematics and Systems Analysis, P.O. Box 11100, FI-00076 Aalto, Finland (email)

Abstract: This work extends the concept of convex source support to the framework of inverse source problems for the Poisson equation in an insulated upper half-plane. The convex source support is, in essence, the smallest (nonempty) convex set that supports a source that produces the measured (nontrivial) data on the horizontal axis. In particular, it belongs to the convex hull of the support of any source that is compatible with the measurements. We modify a previously introduced method for reconstructing the convex source support in bounded domains to our unbounded setting. The performance of the resulting numerical algorithm is analyzed both for the inverse source problem and for electrical impedance tomography with single pair of boundary current and potential as the measurement data.

Keywords:  Convex source support, convex scattering support, inverse source problems, inverse boundary value problems, inclusions.
Mathematics Subject Classification:  Primary: 35R30; Secondary: 65N21.

Received: September 2009;      Revised: March 2010;      Available Online: July 2010.