Klaus Erhard and Roland Potthast 2003 Inverse Problems 19 1139 doi:10.1088/0266-5611/19/5/308
The point source method for reconstructing an inclusion from boundary measurements in electrical impedance tomography and acoustic scattering
Klaus Erhard and Roland Potthast
Show affiliationsWe employ the point source method (PSM) for the reconstruction of some field u on parts of a domain Ω from the Cauchy data for the field on the boundary ∂Ω of the domain. Then, the boundary condition for a perfectly conducting inclusion or a sound-soft object in Ω can be used to find the location and shape of the inhomogeneity. The results show that we can detect perfectly conducting inclusions in impedance tomography from the voltages for one injected current. For acoustic scattering a sound-soft object is found from the knowledge of one (total) field and its normal derivative on ∂Ω. The work redesigns the PSM, which was first proposed in the framework of inverse scattering, to solve inverse boundary value problems. Numerical examples are provided for impedance tomography and the sound-soft acoustic boundary value problem.
- PACS
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43.20.Fn Scattering of acoustic waves
02.60.Lj Ordinary and partial differential equations; boundary value problems
- MSC
- Subjects
- Dates
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Issue 5 (October 2003)
Received 2 May 2003, in final form 11 August 2003
Published 5 September 2003
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The point source method for reconstructing an inclusion from boundary measurements in electrical impedance tomography and acoustic scattering
Klaus Erhard and Roland Potthast 2003 Inverse Problems 19 1139
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