A choice of interpolation schemes for the boundary‐element method in elastodynamics

It is known that the boundary‐element coefficient matrices in steady‐state elastodynamics are frequency‐dependent. For a multifrequency run, the coefficient matrices have to be reformed at each different frequency. This procedure usually involves heavy numerical integration, and hence is very time consuming. In this paper, two interpolation schemes are initially introduced to accelerate the process of matrix reformation without sacrificing the solution accuracy. In the first scheme, the coefficient matrices are first slightly transformed and then interpolated in the frequency domain. In the second scheme, the Green function is interpolated in the spatial domain. Comparison between these two schemes both in terms of accuracy and efficiency is presented. Finally, a hybrid scheme that takes advantage of the best of both interpolation schemes is proposed. Numerical examples are given to demonstrate the three different interpolation schemes.