Energetic BEM for the numerical solution of 2D hard scattering problems of damped waves by open arcs

The energetic boundary element method (BEM) is a discretization technique for the numerical solution of wave propagation problems, introduced and applied in the last decade to scalar wave propagation inside bounded domains or outside bounded obstacles, in 1D, 2D, and 3D space dimension. The differential initial-boundary value problem at hand is converted into a space–time boundary integral equations (BIEs), then written in a weak form through considerations on energy and discretized by a Galerkin approach. The paper will focus on the extension of 2D wave problems of hard scattering by open arcs to the more involved case of damped waves propagation, taking into account both viscous and material damping. Details will be given on the algebraic reformulation of Energetic BEM, i.e., on the so-called time-marching procedure that gives rise to a linear system whose matrix has a Toeplitz lower triangular block structure. Numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several space dimensions and for the 1D damped case.