 
Summary: Correction of order three for the expansion of two
dimensional electromagnetic elds perturbed by the
presence of inhomogeneities of small diameter
Habib Ammari Darko Volkov y
April 2, 2003
Abstract
The derivation of the correction of order 3 for the expansion of 2 dimensional
electromagnetic elds perturbed by the presence of dielectric inhomogeneities of small
diameter was completed in [3]. However previous numerical work such as that in [6] and
in [14] do not corroborate the existence of these correcting terms. The inhomogeneities
used in all those numerical simulations were collections of ellipses. In this paper we
propose to elucidate this discrepancy. We prove that the correction of order 3 is zero for
any inhomogeneity that has a center of symmetry. We present numerical experiments
for asymmetric inhomogeneities. They illustrate the importance of the correction of
order 3. Finally we prove that numerical schemes based on the usual quadrature for
solving mixed linear integral equations on a smooth contour with smooth integration
kernels and kernels involving logarithmic singularities preserve at the discrete level the
fact that correcting terms of order 3 are zero for inhomogeneities that are symmetric
about their center.
Key words: time harmonic TE Maxwell's equations, boundary integral equations,
