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The 2D problem of excitation of a circular metamaterial cylinder by a filament source is numeri cally investigated. It is found that, when the relative permittivity and permeability are close to minus unity, high Q resonances occur in cylinders of an electrically small diameter. Near and far field patterns are cal culated. It is discovered that, under resonance conditions, a multilobe scattering pattern typical of superdi rective antennas is formed. The influence of loss on the resonance characteristics is investigated.

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Ahstract: -Wavelets technique is applied for solving of 2D and 3D Dirichlet, Neumann and mix boundary problems. The developed method utilizes Haar or linear Battle-Lemarie wavelets functions and Fredholni integral equations (-or a system of the Fredholm integral equations) of fist kind with smooth or singular kernels and developed new method of "prolonged" boundary conditions. The results of the wavelet technique's using are illustrated by calculations of the scattering pattern by dielectric (-or perfect conducting) cylinder with complicated cross sections, ellipsoid of revolution, perfect conducting screens, single and dual-reflector antennas (both kD E 1 and kD >> 1 regions). The problems of accuracy, choosing auxiliary surfaces are discussed.

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