On the coupling between finite elements and integral representation for linear elastic waves scattering problems: Analysis and simulation

Abstract

In this paper, we demonstrate the applicability of an exact truncation method for the solution of waves scattering problems in unbounded media, known as the Jami-Lenoir method, to linear elasticity. Our approach avoids the usual splitting of waves as the sum of longitudinal and transversal waves in the analysis and in the numerical modeling of elastodynamic waves scattering problems. The exact absorbing condition imposed on the computational boundary gathers the outgoing behavior of scattered waves given by their Green's integral representation formula with a modified Kupradze radiation condition that ensures uniqueness results and improve the system's conditioning. The truncation boundary can even be closely located from the obstacle with a distance of a few element lengths. Numerical experiments show the accuracy of the Jami-Lenoir approach and the efficiency of the Schwarz preconditioner for the solution of the exterior Neumann problem with a Krylov iterative solver.