A complete time-harmonic radiation boundary for discrete elastodynamic models

A complete radiation boundary has been designed for time-harmonic wave propagation problems in an elastic medium. The algorithm was designed without computational efficiency in mind; the purpose is to obtain a totally transparent boundary for two- or three-dimensional discrete models such as finite elements and finite differences. The displacement values at a grid of nodes external to the artificial boundary is calculated using an integral representation obtained by the reciprocity properties of a viscoelastic medium. The required values are the displacements and tractions at the artificial boundary and the Green's functions appropriate for the model. This algorithm results in a full complex matrix for nodes associated with the artificial boundary and the results are complex because of the presence of radiative damping from outgoing waves escaping the interior model. At first glance, the proposed method appears to be inefficient and restrictive, but it allows the model size to be reduced significantly because this method can eliminate all outgoing waves without specific geometrical restrictions. With this method, a class of difficult linear problems in soil-structure interaction and wave propagation can now be solved.; Keywords. radiation boundary, wave propoagation, soil-structure interaction, finite element analysis, finite difference analysis...