Numerical aspects on coupling between complementary boundary value problems

Abstract

The consequences of nonuniqueness for integral equations used in the numerical resolution of electromagnetic scattering problems are investigated from a practical point of view. The scatterers are closed perfectly conducting cylinders of arbitrary cross section illuminated by a plane wave in both <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">E</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</tex> polarizations. It is shown how to detect the frequencies at which nonuniqueness occurs, and how to avoid the resulting errors by the use of the notion of an equivalent problem. This approach is compared to other ones proposed by different authors. A new interpretation of the computed solution, when uniqueness conditions are not satisfied, is given and it is shown how to use such a solution in the computation of the resonant modes of the interior problem, even for degenerate modes.