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Integral equation methods for scattering from an impedance crack. (English) Zbl 1041.65094
The authors investigate the uniqueness and existence for the scattering problem for time-harmonic waves from an impedance crack in two dimensions. They combine a single and double layer potential approach in a Hölder space setting leading to a system of integral equations that contains a hypersingular operator. Its numerical solution via a fully discrete collocation method based on trigonometric and interpolatory quadrature rules is investigated.

MSC:
65N38 Boundary element methods for boundary value problems involving PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
78A45 Diffraction, scattering
78M15 Boundary element methods applied to problems in optics and electromagnetic theory
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