High order absorbing boundary conditions for elastodynamics

A high-order Absorbing Boundary Condition (ABC) is devised on an artificial boundary for time-dependent elastic waves in unbounded domains. The configuration considered is that of a two-dimensional elastic waveguide. The proposed ABC is an extension of the Hagstrom-Warburton ABC which was originally designed for acoustic waves, and is applied directly to the displacement field. The order of the ABC determines its accuracy and can be chosen to be arbitrarily high. A special variational formulation is constructed which incorporates the ABC. A standard FE discretization is used in space, and a Newmark-type scheme is used for time-stepping. A long-time instability is observed, but simple means are shown to dramatically postpone its onset so as to make it harmless during the simulation time of interest.