AN EFFICIENT HYBRID DISCONTINUOUS GALERKIN METHOD FOR THE WAVE PROPAGATION IN VISCOELASTIC MEDIA: APPLICATION TO LITHOLOGICAL SITE EFFECTS

Abstract eng:
In a few decades, numerical simulations became an essential tool for estimating ground motion under seismic loading. The study of site effects benefits of the development of accurate and efficient methods, allowing to tackle increasingly complex applications. For the study of P-SV waves propagation, we solve the velocity-stress system supposing that the medium is linear and viscoelastic. The medium attenuation is taken into account according to a Generalized Maxwell Body (GMB) method [EK87] considering n relaxation frequencies chosen in the frequency range of interest. This method is now well known and has been applied for various numerical methods (finite difference, spectral element). It results in a modified system containing additional equations for the anelastic functions (also called memory variables, 3n in 2D and 6n in 3D), describing the strain evolution inside the medium. For the solution of these equations, we propose a high order discontinuous Galerkin finite element (DG) method applicable to unstructured simplicial meshes [FP14]. As for standard finite element methods, the unknowns are approximated using a nodal Lagrange interpolation. But, since the method is discontinuous, the interpolants are defined locally in each mesh element, leading to small size local mass matrices, easily invertible even for high order interpolation. The link between the elements is performed by the numerical fluxes. The method has been validated in [FP14] for the study of lithological site effects using a realistic model of a basin in Nice. The major drawback of the GMB approach is the total number of unknowns, especially when a high interpolation degree and a reasonable number of mechanisms are used (generally between 3 and 5 relaxation frequencies).

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