Ilario Mazzieri

Paola F. Antonietti, Francesco Bonaldi, Ilario Mazzieri

We address the spatial discretization of an evolution problem arising from the coupling of viscoelastic and acoustic wave propagation phenomena by employing a discontinuous Galerkin scheme on polygonal and polyhedral meshes. The coupled nature of the problem is ascribed to suitable transmission conditions imposed at the interface between the solid (elastic) and fluid (acoustic) domains. We state and prove a well-posedness result for the strong formulation of the problem, present a stability analysis for the semi-discrete formulation, and finally prove an a priori $hp$-version error estimate for the resulting formulation in a suitable (mesh-dependent) energy norm. We also discuss the time integration scheme employed to obtain the fully discrete system. The convergence results are validated by numerical experiments carried out in a two-dimensional setting.

Sofi Esterhazy, Felix Schneider, Ilario Mazzieri et al.

Motivated by the need to detect an underground cavity within the procedure of an On-Site-Inspection (OSI), of the Comprehensive Nuclear Test Ban Treaty Organization, the aim of this paper is to present results on the comparison of our numerical simulations with an analytic solution. The accurate numerical modeling can facilitate the development of proper analysis techniques to detect the remnants of an underground nuclear test. The larger goal is to help set a rigorous scientific base of OSI and to contribute to bringing the Treaty into force. For our 3D numerical simulations, we use the discontinuous Galerkin Spectral Element Code SPEED jointly developed at MOX (The Laboratory for Modeling and Scientific Computing, Department of Mathematics) and at DICA (Department of Civil and Environmental Engineering) of the Politecnico di Milano.