American Institute of Mathematical Sciences

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August  2010, 4(3): 547-569. doi: 10.3934/ipi.2010.4.547

Reconstructing electromagnetic obstacles by the enclosure method

Ting Zhou 1,

1. 

Department of Mathematics, University of Washington, Seattle, WA 98105, United States

Received  December 2009 Revised  February 2010 Published  July 2010

We show that one can determine Perfectly Magnetic Conductor obstacles, Perfectly Electric Conductor obstacles and obstacles satisfying impedance boundary condition, embedded in a known electromagnetic medium, by making electromagnetic measurements at the boundary of the medium. The boundary measurements are encoded in the impedance map that sends the tangential component of the electric field to the tangential component of the magnetic field. We do this by probing the medium with complex geometrical optics solutions to the corresponding Maxwell's equations and extend the enclosure method to this case.
Keywords: Maxwell's equations, enclosure methods, complex geometrical optics soltuions..
Mathematics Subject Classification: Primary: 35R30, 35Q6.
Citation: Ting Zhou. Reconstructing electromagnetic obstacles by the enclosure method. Inverse Problems & Imaging, 2010, 4 (3) : 547-569. doi: 10.3934/ipi.2010.4.547
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