Solving 2D exterior soft scattering elastodynamic problems by BEM and by FEM-BEM coupling using potentials

We consider the decomposition into scalar potentials for the simulation of transient 2D soft scattering elastic wave propagation problems in unbounded isotropic homogeneous media. The vector elastodynamic equation is reformulated in terms of two scalar wave equations, that are coupled by the Dirichlet boundary conditions. These are successively solved by using their associated space-time Boundary Integral Equation (BIE) representations. The corresponding Boundary Element Method (BEM) is obtained by combining a time convolution quadrature formula with a classical space collocation method. Then, the same boundary integral representation and its discretization are used to define a non-reflecting condition to be imposed on an artificial boundary delimiting the exterior computational domain of interest. In this latter a Finite Element Method (FEM) is applied