On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics

Details On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics On direct numerical treatment of hypersingular integral equations arising in mechanics and acoustics

2003-01-26

arxiv.org/abs/math-ph/0301034v1

Physics

Mathematical Physics

accepted by Acta Mechanica, 19 pages, 3 figures

Scientific paper

In this paper we present a treatment of hypersingular integral equations, which have relevant applications in many problems of wave dynamics, elasticity and fluid mechanics with mixed boundary conditions. The main goal of the present work is the development of an efficient direct numerical collocation method. The paper is completed with two examples taken from crack theory and acoustics: the study of a single crack in a linear isotropic elastic medium, and diffraction of a plane acoustic wave by a thin rigid screen.

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