Debye sources and the numerical solution of the time harmonic Maxwell equations. (English) Zbl 1190.35215
The paper puts forward a new representation for solutions to the problem of scattering of a monochromatic electromagnetic wave on a body made of an ideal conductor. The representation amounts to solving an effective Fredholm integral equation for fictitious densities of electric and magnetic charges on the surface of the body, which generalizes the classical Lorenz-Debye-Mie solutions for scattering on a conducting sphere, that represents the electric and magnetic fields in terms of two Debye’s scalar potentials. The approach elaborated in this paper avoids well-known problems encountered in the scattering theory, such as spurious resonances and the low-frequency breakdown. The method makes it possible to develop a new proof of the existence of the solution to the scattering problem with vanishing normal components at the conducing boundary, in the case when the boundary is not simply connected.
Reviewer: Boris A. Malomed (Tel Aviv)
Keywords:
electromagnetic scattering; Fredholm integral equation; spherical harmonic; spurious resonance; low-frequency breakdownReferences:
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