Associating a limit perturbation model in 3D with reduced meshes for simulations of the localization of certain electromagnetic inhomogeneities
S.M. Mefire 11 LAMFA, CNRS, Universite de Picardie, 33, rue Saint-Leu, 80039 Amiens, France.
Received by the editors October 20, 2008 and, in revised form, July 27, 2009.
Simulations of the localization of certain small electromagnetic inhomogeneities, in a three-dimensional bounded domain, are performed by making use of a framework recently introduced by the author and of a nonstandard discretization process of this domain. This framework is based on a limit model in electric field and on the combination of a limit perturbation model in the tangential boundary trace of the curl of the electric field, with a Current Projection method or an Inverse Fourier method. As opposed to our recent paper relating to this framework and to experiments requiring the usual discretization process of the domain, inhomogeneities that are one order of magnitude smaller are numerically localized here.AMS subject classifications: 65N21, 65N30, 78A25
Key words: Inverse problems, Maxwell equations, electric fields, inhomogeneities, Electrical Impedance Tomography, Current Projection method, FFT, numerical boundary measurements, edge elements, least square systems, Incomplete Modified Gram-Schmidt preconditioning, composite numerical integrations.