A high performance scaled boundary finite element method

Abstract

Dynamic soil-structure interaction in the time domain may be described by the scaled boundary finite element method (SBFEM). Unfortunately the non locality in time and space implies significant numerical effort. Two essential improvements are demonstrated, boosting the performance of this method. The original discretisation scheme assuming a constant change of the acceleration unit-impulse response matrix within each time step is only conditionally stable, requiring a rather small minimum step size. Here a new scheme assuming the acceleration unit-impulse response matrix to vary linearly within each time step and an extrapolation parameter provide more stability to the solution. For large problems the linearization of the acceleration unit-impulse response matrix for late times is employed. Then, based on integration by parts, a new and very efficient recursive integration scheme for the evaluation of the soil-structure interaction vector described by convolution integral is developed, regaining a strong locality in time. The combination of the two enhancements leads to a very significant reduction of computational effort and linear dependency with respect to the number of time steps, and allows also the use of larger time steps. Examples analyzed by authors did not show instability of the solution for a wide range of parameters.