ESAIM: Mathematical Modelling and Numerical Analysis

Research Article

Asymptotic formulas for perturbations in the electromagnetic fields due to the presence of inhomogeneities of small diameter

Vogelius, Michael S.a1 and Volkov, Darkoa2

a1 Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. (vogelius@hilbert.rutgers.edu)

a2 Department of Mathematics, Rutgers University, New Brunswick, NJ 08903, USA. (dvolkov@math.rutgers.edu)

Abstract

We consider solutions to the time-harmonic Maxwell's Equations of a TE (transverse electric) nature. For such solutions we provide a rigorous derivation of the leading order boundary perturbations resulting from the presence of a finite number of interior inhomogeneities of small diameter. We expect that these formulas will form the basis for very effective computational identification algorithms, aimed at determining information about the inhomogeneities from electromagnetic boundary measurements.

(Received October 19 1999)

(Revised February 11 2000)

(Online publication April 15 2002)

Key Words:

  • Maxwell equations;
  • inverse problems.

Mathematics Subject Classification:

  • 35J25;
  • 35R30;
  • 78A30
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