Abstract
The research of analytical solutions for the diffraction by generic singularities is a difficult task [1], and our presentation concerns some of our recent results in the case of singular objects with non perfectly reflective surface. In this case, the field cannot be generally written as a sum of discrete modes where each one satisfies the boundary conditions, and delicate analytical spectral methods in complex plane are necessary. The methods, that we present here concisely, concern, in 2D and 2D 1/2 cases, a new spectral method for the diffraction by a three-part impedance plane, the causal time expression of the field scattered by a frequency dispersive wedge-shaped region, a new class of canonical cases for the diffraction by an anisotropic impedance wedge, and in 3D case, the scattering by impedance cones in acoustics and electromagnetics.
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