High order local absorbing boundary conditions for acoustic and elastic scattering

Abstract

The formulation of high order local absorbing boundary conditions in terms of farfield expansions (FE-ABC) for time-harmonic waves is considered. Our previously constructed FE-ABC for single and multiple acoustic scattering are improved. Furthermore, we extend the FE-ABC to elastic scattering. By decomposing the vector elastic displacement in terms of scalar potentials, the Navier's equation of elasticity is reduced to a boundary value problem consisting of two Helmholtz equations coupled through their boundary conditions. As a result, the formulation of the elastic FE-ABC from the acoustic case becomes natural. In this work, we present some numerical results by coupling the FE-ABC with finite difference methods and a general curvilinear finite element method based on isogeometric analysis. We present our results for two and three dimensional acoustic and elastic scattering problems from obstacles of arbitrary shape.