Time-dependent absorbing boundary conditions for elastic wave propagation

This paper develops a finite element scheme to generate the spatial- and time-dependent absorbing boundary conditions for unbounded elastic-wave problems. This scheme first calculates the spatial- and time-dependent wave speed over the cosine of the direction angle using the Higdon's one-way first-order boundary operator, and then this operator is used again along the absorbing boundary in order to simulate the behaviour of unbounded problems. Different from other methods, the estimation of the wave speed and directions is not necessary in this method, since the wave speed over the cosine of the direction angle is calculated automatically. Two- and three-dimensional numerical simulations indicate that the accuracy of this scheme is acceptable if the finite element analysis is appropriately arranged. Moreover, only the displacements along absorbing boundary nodes need to be set in this method, so the standard finite element method can still be used.