Double absorbing boundary formulations for acoustics and elastodynamics

Wave problems in unbounded domains are often treated numerically by truncating the domain to produce a finite computational domain. The double absorbing boundary (DAB) method, which was invented recently as an alternative to methods of high-order absorbing boundary conditions and to the perfectly matched layer, is investigated here for problems in acoustics and elastodynamics. The paper offers two main contributions. The first one pertains to the well-osedness of the DAB scheme for the acoustics problem written in second-order form. The energy method is employed to obtain uniform-in-time estimates of the norm of the solution and the auxiliary functions, thus establishing the well-osedness and asymptotic stability of the DAB formulation. The second part pertains to the extension of the DAB to isotropic elastodynamics, written in first-order conservation form. Numerical experiments for an elastic wave guide demonstrate the performance of the scheme.