DSpace Repository :: Browsing by Author "Artaza Covarrubias, Fernando Antonio"

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Acoustic scattering and elastic waves: a hybridizable discontinuous Galerkin approach and an incursion in the method of fundamental solutions.
(Universidad de Concepción, 2025) Artaza Covarrubias, Fernando Antonio; Solano Palma, Manuel; Sánchez-Vizuet, Tonatiuh
We are interested in the computational simulation of the interaction between a transient acous tic wave and a bounded elastic solid in an unbounded fluid medium. We start by placing an artificial boundary surrounding the solid, where we impose boundary conditions that do not necessarily represent the physics of the problem. After applying the Laplace transform to the original problem, we propose and analyze a coupled Hybridizable Discontinuous Galerkin (HDG) scheme, in which two mixed variables are included (the stress tensor and the velocity of the acoustic wave) and the symmetry of the stress tensor is imposed weakly by adding the antisymmetric part of the strain tensor (the rotation) as an additional unknown. The optimal convergence of the method is demonstrated theoretically and some preliminary numerical re sults are presented. In the last chapter, we introduce the Method of Fundamental Solutions and use it to solve some boundary value problems in order to familiarize ourselves with this tool and set the basis to couple the Method of Fundamental Solutions with an HDG scheme in a future work.