Variational approach in weighted Sobolev spaces to scattering by unbounded rough surfaces. (English) Zbl 1241.35044

Chandler-Wilde, Simon N.; Elschner, Johannes

SIAM J. Math. Anal. 42, No. 6, 2554-2580 (2010).

In the last years, several papers in the domain of acoustics have paid attention to the problem of the scattering of sound waves (including also the case of airborne transmission) in rough surfaces in connection with multiple scattering in ordered and quasi-ordered arrays of scatterers. This topic is important, among other reasons, for the use of some structures as acoustic screens, where the presence of the ground can modify the scattering problem. The paper here commented belongs to the mathematical development of the scattering theory by unbound rough surfaces. This is a very interesting paper where the authors squeeze “the juice” of the mathematical setting of the problem. Particularly interesting is Section 5 of the paper, devoted to the applications and FEM analysis of the variational formulation.

Reviewer: Lluís Miquel García Raffi (València)

MSC:

35J05	Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35J20	Variational methods for second-order elliptic equations
35P25	Scattering theory for PDEs
78A45	Diffraction, scattering

Keywords:

nonsmooth boundary; radiation condition; variational formulation; weighted Sobolev spaces; Helmholtz equation; FEM analysis