Hypersingular integral equations in diffraction problems on a cube (Q2730500)

Direct method of numerical analysis of diffraction problems on a perfectly conducting and acoustically hard cube by use of hypersingular integral equations are considered. A presentation of boundary equations with symmetries in the form of an operational convolution on the group of symmetries and regularization of hypersingular integral boundary operators are used in the methods considered. It is shown that on the base of the canonical presentation of hypersingular integral equations with symmetries, one can construct, by regularization of integral operators apposition, one can construct effective numerical schemes of solving the diffraction problems on the perfectly conducting and the acoustically hard cubes with wave dimensions \(ka=12\) (\(k\) is the wave number) for a plane initial wave with arbitrary directions of incidence. Several numerical examples and results of investigations are presented.