Advanced numerical methods for wave propagation problems: The Arlequin method & Potential formulation for elastodynamics

Abstract

The thesis is divided in two parts that, in addition to the intellectual curiosity, share a common aim, the development of efficient techniques for wave propagation problems. First, we develop an ovelapping domain decomposition technique (the Arlequin method) that is well adapted for the treatment of local phenomena. We present the method for Helmholtz and wave equation, but in principle, it can be used in other fields. Second, we tackle the numerical resolution of linear elastodynamics equation for isotropic homogeneous media and we present a potential formulation that allows to discretize separately the pressure and the shear waves. The result is a method that is more efficient when both waves travel with different velocities.