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Summary: INTERNATIONAL JOURNAL OF c 2009 Institute for Scientific
NUMERICAL ANALYSIS AND MODELING Computing and Information
Volume 6, Number 1, Pages 5088
USING REDUCED MESHES FOR SIMULATIONS OF THE
LOCALIZATION OF SMALL ELECTROMAGNETIC
INHOMOGENEITIES IN A 3D BOUNDED DOMAIN
M. ASCH AND S.M. MEFIRE
(Communicated by Gang Bao)
Abstract. We are concerned in this work with simulations of the localization of a finite number
of small electromagnetic inhomogeneities contained in a three-dimensional bounded domain. Typ-
ically, the underlying inverse problem considers the time-harmonic Maxwell equations formulated
in electric field in this domain and attempts, from a finite number of boundary measurements,
to localize these inhomogeneities. Our simulations are based on an approach that combines an
asymptotic formula for perturbations in the electromagnetic fields, a suited inversion process, and
finite element meshes derived from a non-standard discretization process of the domain. As op-
posed to a recent work, where the usual discretization process of the domain was employed in the
computations, here we localize inhomogeneities that are one order of magnitude smaller.
Key words. inverse problems, Maxwell equations, electric fields, inhomogeneities, Current Pro-
jection method, MUSIC method, FFT, edge elements, numerical measurements, composite nu-
merical integrations.
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